TSTP Solution File: SCT097-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT097-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.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 May 21 02:50:27 EDT 2024
% Result : Unsatisfiable 8.83s 1.72s
% Output : Refutation 8.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1754
% Syntax : Number of formulae : 2973 (1031 unt; 0 def)
% Number of atoms : 7061 ( 986 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 7130 (3042 ~;3163 |; 0 &)
% ( 925 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 985 ( 983 usr; 926 prp; 0-3 aty)
% Number of functors : 107 ( 107 usr; 18 con; 0-7 aty)
% Number of variables : 6072 (6072 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22251,plain,
$false,
inference(avatar_sat_refutation,[],[f1427,f1432,f1437,f1442,f1447,f1452,f1457,f1462,f1467,f1472,f1477,f1482,f1487,f1492,f1497,f1502,f1507,f1512,f1517,f1522,f1527,f1532,f1537,f1542,f1547,f1552,f1557,f1562,f1567,f1572,f1577,f1582,f1587,f1592,f1597,f1602,f1607,f1612,f1617,f1622,f1627,f1632,f1637,f1642,f1647,f1652,f1657,f1662,f1667,f1672,f1677,f1682,f1686,f1690,f1694,f1698,f1702,f1706,f1710,f1714,f1718,f1722,f1726,f1730,f1734,f1738,f1742,f1746,f1750,f1754,f1758,f1762,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1799,f1803,f1807,f1811,f1815,f1819,f1823,f1827,f1831,f1835,f1839,f1843,f1847,f1851,f1855,f1859,f1863,f1867,f1871,f1875,f1879,f1883,f1887,f1891,f1895,f1899,f1903,f1907,f1911,f1915,f1926,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,f2159,f2180,f2184,f2188,f2192,f2196,f2200,f2204,f2208,f2212,f2216,f2220,f2224,f2228,f2232,f2236,f2240,f2244,f2248,f2252,f2256,f2260,f2268,f2288,f2305,f2309,f2314,f2318,f2322,f2326,f2330,f2334,f2338,f2342,f2346,f2350,f2354,f2358,f2362,f2366,f2370,f2374,f2378,f2382,f2386,f2390,f2394,f2398,f2402,f2406,f2410,f2414,f2418,f2422,f2426,f2430,f2434,f2438,f2443,f2447,f2451,f2455,f2459,f2463,f2467,f2471,f2475,f2479,f2483,f2495,f2499,f2503,f2507,f2511,f2515,f2519,f2538,f2685,f2689,f2693,f2697,f2701,f2709,f2713,f2717,f2721,f2725,f2729,f2733,f2737,f2741,f2745,f2750,f2754,f2758,f2762,f2768,f2987,f3016,f3027,f3031,f3035,f3039,f3043,f3047,f3052,f3057,f3061,f3065,f3069,f3073,f3077,f3081,f3085,f3089,f3093,f3097,f3101,f3105,f3109,f3113,f3117,f3121,f3125,f3129,f3133,f3141,f3145,f3149,f3153,f3157,f3161,f3165,f3169,f3173,f3177,f3181,f3185,f3209,f3511,f3589,f3631,f3635,f3639,f3643,f3647,f3651,f3655,f3659,f3663,f3667,f3671,f3675,f3679,f3683,f3687,f3691,f3695,f3699,f3703,f3707,f3711,f3715,f3719,f3723,f3727,f3731,f3735,f3739,f3743,f3747,f3751,f3755,f3759,f3763,f3768,f3772,f3776,f3780,f3784,f3788,f3792,f3796,f3800,f3804,f3808,f3812,f3817,f3821,f3825,f3829,f3833,f3928,f4051,f4458,f4462,f4466,f4470,f4474,f4478,f4482,f4486,f4490,f4494,f4511,f4515,f4519,f4523,f4527,f4531,f4536,f4540,f4544,f4548,f4552,f4556,f4560,f4564,f4568,f4789,f4793,f4865,f4869,f4873,f4877,f4881,f4885,f4889,f4893,f4897,f4902,f4906,f4912,f4916,f4920,f4924,f4928,f4933,f4937,f4941,f4945,f4949,f4954,f4958,f4962,f4966,f4970,f4974,f4978,f4982,f4987,f5092,f5199,f5329,f5413,f5417,f5421,f5425,f5429,f5433,f5437,f5441,f5445,f5449,f5453,f5457,f5461,f5465,f5469,f5473,f5477,f5481,f5485,f5489,f5493,f5498,f5502,f5506,f5510,f5514,f5518,f5522,f5526,f5530,f5534,f5538,f5542,f5546,f5550,f5598,f5849,f6082,f6086,f6090,f6094,f6098,f6102,f6106,f6110,f6114,f6118,f6122,f6126,f6174,f6329,f6333,f6337,f6341,f6345,f6350,f6354,f6358,f6362,f6367,f6371,f6375,f6379,f6383,f6387,f6391,f6395,f6399,f6403,f6407,f6411,f6415,f6419,f6423,f6427,f6573,f6598,f6620,f6922,f6926,f6930,f6934,f6939,f6943,f6947,f6951,f6955,f6959,f6963,f6967,f6971,f6976,f6989,f6993,f6997,f7001,f7005,f7009,f7013,f7017,f7021,f7025,f7029,f7033,f7037,f7041,f7045,f7049,f7053,f7057,f7061,f7065,f7069,f7073,f7077,f7081,f7085,f7089,f7093,f7097,f7149,f7331,f7567,f7707,f7711,f7715,f7721,f7725,f7729,f7733,f7737,f7741,f7745,f7749,f7753,f7757,f7761,f7765,f7770,f7775,f8432,f8436,f8467,f8488,f8492,f8496,f8500,f8504,f8508,f8512,f8516,f8520,f8530,f8534,f8538,f8542,f8546,f8550,f8554,f8558,f8562,f8566,f8570,f8574,f8578,f8582,f8586,f8590,f8594,f8598,f8602,f8606,f9146,f9243,f9247,f9251,f9255,f9259,f9263,f9267,f9271,f9275,f9279,f9283,f9287,f9291,f9295,f9299,f9303,f9307,f9311,f10214,f10220,f10224,f10228,f10232,f10236,f10240,f10244,f10248,f10252,f10256,f10264,f10268,f10272,f10276,f10280,f10284,f10440,f10552,f10624,f10628,f10632,f10636,f10640,f10644,f10648,f10656,f10660,f10664,f10668,f10672,f10676,f10680,f10684,f10688,f10692,f10696,f10700,f10704,f10708,f10712,f10716,f10720,f10724,f10728,f10732,f10736,f10740,f10744,f10748,f10752,f10756,f10766,f11351,f11355,f11361,f11365,f11369,f11379,f11383,f11387,f11391,f11395,f11399,f11403,f11407,f11411,f11415,f11427,f11431,f11435,f11439,f11443,f11447,f11451,f11455,f11459,f11463,f11467,f11471,f11508,f11694,f11861,f12038,f12042,f12046,f12050,f12054,f12058,f12062,f12066,f12070,f12074,f12078,f12082,f12086,f12090,f12094,f12098,f12102,f12106,f12282,f12565,f12569,f12573,f12577,f12581,f12585,f12589,f12593,f12597,f12601,f12605,f12609,f12613,f12617,f12621,f12625,f12629,f12633,f12637,f12641,f12645,f12649,f12653,f12657,f12661,f12665,f12670,f12945,f13680,f14006,f14010,f14014,f14018,f14022,f14026,f14031,f14035,f14039,f14043,f14047,f14051,f14055,f14059,f14063,f14067,f14071,f14352,f14519,f14746,f14867,f14871,f14875,f14879,f14883,f14887,f14891,f14895,f14899,f14903,f14907,f14911,f14915,f14919,f14923,f14927,f14931,f14935,f15267,f15336,f15340,f15344,f15348,f15352,f15356,f15360,f15364,f15368,f15399,f15403,f15407,f15411,f15415,f15419,f15423,f15427,f15431,f15435,f15439,f15607,f15864,f15868,f15872,f15876,f15880,f15885,f15889,f15895,f15899,f15903,f15907,f15911,f15915,f15919,f16106,f16115,f16424,f16428,f16432,f16436,f16440,f16532,f16536,f16540,f16544,f16548,f16552,f16556,f16560,f16564,f16568,f16572,f17062,f17066,f17070,f17074,f17078,f17149,f17153,f17157,f17161,f17406,f17568,f17572,f17577,f17581,f17585,f17589,f17600,f17793,f17797,f17801,f17805,f17842,f17846,f17850,f17854,f18039,f18107,f18111,f18115,f18119,f18123,f18127,f18131,f18135,f18165,f18555,f18559,f18563,f18567,f18716,f18720,f18836,f18840,f18844,f18943,f18984,f18988,f19068,f19072,f19076,f19080,f19084,f19088,f19406,f19410,f19414,f19418,f19422,f19595,f19637,f19685,f19689,f19721,f19725,f19810,f19814,f19978,f19982,f19986,f20077,f20081,f20085,f20089,f20149,f20343,f20355,f20477,f20481,f20485,f20489,f20495,f20944,f21049,f21053,f21175,f21179,f21183,f21365,f21438,f21442,f21446,f21450,f21929,f21944,f22007,f22070,f22079,f22087,f22131,f22149,f22193,f22230,f22241,f22250]) ).
fof(f22250,plain,
( ~ spl0_53
| spl0_925 ),
inference(avatar_contradiction_clause,[],[f22242]) ).
fof(f22242,plain,
( $false
| ~ spl0_53
| spl0_925 ),
inference(resolution,[],[f22240,f1685]) ).
fof(f1685,plain,
( ! [X14] : c_lessequals(X14,X14,tc_nat)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f1684]) ).
fof(f1684,plain,
( spl0_53
<=> ! [X14] : c_lessequals(X14,X14,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f22240,plain,
( ~ c_lessequals(v_n____,v_n____,tc_nat)
| spl0_925 ),
inference(avatar_component_clause,[],[f22238]) ).
fof(f22238,plain,
( spl0_925
<=> c_lessequals(v_n____,v_n____,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f22241,plain,
( ~ spl0_925
| ~ spl0_921
| spl0_924 ),
inference(avatar_split_clause,[],[f22231,f22227,f22147,f22238]) ).
fof(f22147,plain,
( spl0_921
<=> ! [X16] :
( ~ c_lessequals(X16,v_n____,tc_nat)
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),X16),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f22227,plain,
( spl0_924
<=> hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f22231,plain,
( ~ c_lessequals(v_n____,v_n____,tc_nat)
| ~ spl0_921
| spl0_924 ),
inference(resolution,[],[f22229,f22148]) ).
fof(f22148,plain,
( ! [X16] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),X16),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| ~ c_lessequals(X16,v_n____,tc_nat) )
| ~ spl0_921 ),
inference(avatar_component_clause,[],[f22147]) ).
fof(f22229,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| spl0_924 ),
inference(avatar_component_clause,[],[f22227]) ).
fof(f22230,plain,
( spl0_917
| ~ spl0_924 ),
inference(avatar_split_clause,[],[f1273,f22227,f22067]) ).
fof(f22067,plain,
( spl0_917
<=> hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f1273,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
fof(f22193,plain,
( ~ spl0_922
| spl0_923 ),
inference(avatar_split_clause,[],[f1240,f22190,f22186]) ).
fof(f22186,plain,
( spl0_922
<=> hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_c____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f22190,plain,
( spl0_923
<=> hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_c____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(v_P____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f1240,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_c____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(v_P____)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_c____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PW_1) ).
fof(f22149,plain,
spl0_921,
inference(avatar_split_clause,[],[f1272,f22147]) ).
fof(f1272,axiom,
! [X16] :
( ~ c_lessequals(X16,v_n____,tc_nat)
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),X16),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f22131,plain,
spl0_920,
inference(avatar_split_clause,[],[f867,f22129]) ).
fof(f22129,plain,
( spl0_920
<=> ! [X18,X10,X0,X20,X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X7),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X18,X0,X10,tc_fun(X10,X10)),X20,X0,X10,X10)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),c_Lattices_Olower__semilattice__class_Oinf(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f867,axiom,
! [X10,X0,X18,X6,X7,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X7),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X18,X0,X10,tc_fun(X10,X10)),X20,X0,X10,X10)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),c_Lattices_Olower__semilattice__class_Oinf(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__cases_0) ).
fof(f22087,plain,
spl0_919,
inference(avatar_split_clause,[],[f997,f22085]) ).
fof(f22085,plain,
( spl0_919
<=> ! [X4,X0,X3,X8,X23] :
( ~ c_Relation_Osingle__valued(X8,X0,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,X23,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X23,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f997,axiom,
! [X3,X0,X8,X4,X23] :
( ~ c_Relation_Osingle__valued(X8,X0,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,X23,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X23,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).
fof(f22079,plain,
spl0_918,
inference(avatar_split_clause,[],[f1007,f22077]) ).
fof(f22077,plain,
( spl0_918
<=> ! [X18,X10,X0,X6,X25,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),hAPP(c_COMBC(c_COMBB(c_Finite__Set_Osetsum(X25,X0),X18,tc_fun(X25,X0),tc_fun(tc_fun(X25,tc_bool),X0),X10),X10,tc_fun(X25,tc_bool),X0),X7)),X6) = hAPP(hAPP(c_Finite__Set_Osetsum(X25,X0),hAPP(c_COMBC(c_COMBB(c_Finite__Set_Osetsum(X10,X0),c_COMBC(X18,X10,X25,X0),tc_fun(X10,X0),tc_fun(tc_fun(X10,tc_bool),X0),X25),X25,tc_fun(X10,tc_bool),X0),X6)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f1007,axiom,
! [X10,X0,X18,X6,X7,X25] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),hAPP(c_COMBC(c_COMBB(c_Finite__Set_Osetsum(X25,X0),X18,tc_fun(X25,X0),tc_fun(tc_fun(X25,tc_bool),X0),X10),X10,tc_fun(X25,tc_bool),X0),X7)),X6) = hAPP(hAPP(c_Finite__Set_Osetsum(X25,X0),hAPP(c_COMBC(c_COMBB(c_Finite__Set_Osetsum(X10,X0),c_COMBC(X18,X10,X25,X0),tc_fun(X10,X0),tc_fun(tc_fun(X10,tc_bool),X0),X25),X25,tc_fun(X10,tc_bool),X0),X6)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__commute_0) ).
fof(f22070,plain,
~ spl0_917,
inference(avatar_split_clause,[],[f1275,f22067]) ).
fof(f1275,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f22007,plain,
spl0_916,
inference(avatar_split_clause,[],[f1401,f22005]) ).
fof(f22005,plain,
( spl0_916
<=> ! [X0,X8,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f1401,plain,
! [X2,X0,X1,X8,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ),
inference(definition_unfolding,[],[f1197,f1163,f1163,f1163]) ).
fof(f1163,axiom,
! [X0,X8] : c_Transitive__Closure_Otrancl(X8,X0) = c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
fof(f1197,axiom,
! [X2,X0,X1,X8,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).
fof(f21944,plain,
spl0_915,
inference(avatar_split_clause,[],[f1066,f21942]) ).
fof(f21942,plain,
( spl0_915
<=> ! [X5,X10,X0,X12,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X10),X12),X6))
| hBOOL(hAPP(hAPP(c_in(X10),X5),X6))
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7) = c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X7),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X0,X10,tc_fun(X10,X10)),X5),X0,X10,X10),X12),X6,X0,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f1066,axiom,
! [X10,X0,X6,X7,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X10),X12),X6))
| hBOOL(hAPP(hAPP(c_in(X10),X5),X6))
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7) = c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X7),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X0,X10,tc_fun(X10,X10)),X5),X0,X10,X10),X12),X6,X0,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__if_2) ).
fof(f21929,plain,
spl0_914,
inference(avatar_split_clause,[],[f1069,f21927]) ).
fof(f21927,plain,
( spl0_914
<=> ! [X18,X10,X0,X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool))) = hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X7),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X18,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Ozero__class_Ozero(X10))),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f1069,axiom,
! [X10,X0,X18,X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool))) = hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X7),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X18,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Ozero__class_Ozero(X10))),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__restrict__set_0) ).
fof(f21450,plain,
spl0_913,
inference(avatar_split_clause,[],[f1400,f21448]) ).
fof(f21448,plain,
( spl0_913
<=> ! [X23,X0,X3,X8] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X8,X3,X23,X0),X23,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f1400,plain,
! [X3,X0,X8,X23] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X8,X3,X23,X0),X23,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ),
inference(definition_unfolding,[],[f1009,f1163,f1163]) ).
fof(f1009,axiom,
! [X3,X0,X8,X23] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X8,X3,X23,X0),X23,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).
fof(f21446,plain,
spl0_912,
inference(avatar_split_clause,[],[f1399,f21444]) ).
fof(f21444,plain,
( spl0_912
<=> ! [X0,X8,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X2,X1,X8,X0),X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f1399,plain,
! [X2,X0,X1,X8] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X2,X1,X8,X0),X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ),
inference(definition_unfolding,[],[f1014,f1163,f1163]) ).
fof(f1014,axiom,
! [X2,X0,X1,X8] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X2,X1,X8,X0),X0,X0)),c_Transitive__Closure_Otrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_0) ).
fof(f21442,plain,
spl0_911,
inference(avatar_split_clause,[],[f1068,f21440]) ).
fof(f21440,plain,
( spl0_911
<=> ! [X5,X10,X0,X12,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X10),X5),X6))
| hBOOL(hAPP(hAPP(c_in(X10),X12),X6))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X7),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X0,X10,tc_fun(X10,X10)),X5),X0,X10,X10),X12),X6,X0,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f1068,axiom,
! [X10,X0,X6,X7,X5,X12] :
( hBOOL(hAPP(hAPP(c_in(X10),X5),X6))
| hBOOL(hAPP(hAPP(c_in(X10),X12),X6))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X7),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X0,X10,tc_fun(X10,X10)),X5),X0,X10,X10),X12),X6,X0,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__if_3) ).
fof(f21438,plain,
spl0_910,
inference(avatar_split_clause,[],[f1067,f21436]) ).
fof(f21436,plain,
( spl0_910
<=> ! [X5,X10,X0,X12,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X10),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X10),X12),X6))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X7),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X0,X10,tc_fun(X10,X10)),X5),X0,X10,X10),X12),X6,X0,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f1067,axiom,
! [X10,X0,X6,X7,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X10),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X10),X12),X6))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X7),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X0,X10,tc_fun(X10,X10)),X5),X0,X10,X10),X12),X6,X0,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__if_0) ).
fof(f21365,plain,
spl0_909,
inference(avatar_split_clause,[],[f1396,f21363]) ).
fof(f21363,plain,
( spl0_909
<=> ! [X61,X60,X8] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,t_a),t_a,t_a,t_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X60,X61,X8),t_a,t_a)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,t_a),t_a,t_a,t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f1396,plain,
! [X8,X60,X61] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,t_a),t_a,t_a,t_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X60,X61,X8),t_a,t_a)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,t_a),t_a,t_a,t_a))) ),
inference(definition_unfolding,[],[f1011,f1163,f1163]) ).
fof(f1011,axiom,
! [X8,X60,X61] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),c_Transitive__Closure_Otrancl(X8,t_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,v_sko__Transitive__Closure__Xtrancl__Xcases__1(X60,X61,X8),t_a,t_a)),c_Transitive__Closure_Otrancl(X8,t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).
fof(f21183,plain,
spl0_908,
inference(avatar_split_clause,[],[f1403,f21181]) ).
fof(f21181,plain,
( spl0_908
<=> ! [X3,X4,X0,X23,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,X23,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f1403,plain,
! [X3,X0,X8,X4,X23] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,X23,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ),
inference(definition_unfolding,[],[f1093,f1163,f1163]) ).
fof(f1093,axiom,
! [X3,X0,X8,X4,X23] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,X23,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
fof(f21179,plain,
spl0_907,
inference(avatar_split_clause,[],[f1402,f21177]) ).
fof(f21177,plain,
( spl0_907
<=> ! [X0,X8,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f1402,plain,
! [X2,X0,X1,X8,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ),
inference(definition_unfolding,[],[f1092,f1163,f1163]) ).
fof(f1092,axiom,
! [X2,X0,X1,X8,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
fof(f21175,plain,
spl0_906,
inference(avatar_split_clause,[],[f52,f21173]) ).
fof(f21173,plain,
( spl0_906
<=> ! [X10,X0,X20,X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X7,X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),X6)),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f52,axiom,
! [X10,X0,X6,X7,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X7,X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),X6)),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un__Int_0) ).
fof(f21053,plain,
spl0_905,
inference(avatar_split_clause,[],[f1207,f21051]) ).
fof(f21051,plain,
( spl0_905
<=> ! [X5,X10,X0,X12,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X10),X5),X6))
| hBOOL(hAPP(hAPP(c_in(X10),X12),X6))
| c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X7),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X0,X10,tc_fun(X10,X10)),X5),X0,X10,X10),X12),X6,X0,X10) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f1207,axiom,
! [X10,X0,X6,X7,X5,X12] :
( ~ hBOOL(hAPP(hAPP(c_in(X10),X5),X6))
| hBOOL(hAPP(hAPP(c_in(X10),X12),X6))
| c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X7),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X0,X10,tc_fun(X10,X10)),X5),X0,X10,X10),X12),X6,X0,X10) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__if_1) ).
fof(f21049,plain,
spl0_904,
inference(avatar_split_clause,[],[f1204,f21047]) ).
fof(f21047,plain,
( spl0_904
<=> ! [X2,X0,X10,X22,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| hAPP(X1,X2) = hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Ozero__class_Ozero(X10))),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f1204,axiom,
! [X2,X10,X0,X1,X22] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| hAPP(X1,X2) = hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Ozero__class_Ozero(X10))),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__delta_0) ).
fof(f20944,plain,
spl0_903,
inference(avatar_split_clause,[],[f1065,f20942]) ).
fof(f20942,plain,
( spl0_903
<=> ! [X2,X0,X10,X5,X22,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),X5),X22,X0,X10) = c_Power_Opower__class_Opower(X5,c_Finite__Set_Ocard(X22,X0),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f1065,axiom,
! [X2,X10,X0,X1,X22,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),X5),X22,X0,X10) = c_Power_Opower__class_Opower(X5,c_Finite__Set_Ocard(X22,X0),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__gen__delta_1) ).
fof(f20495,plain,
( spl0_902
| ~ spl0_261
| ~ spl0_273
| ~ spl0_707
| ~ spl0_716
| ~ spl0_901 ),
inference(avatar_split_clause,[],[f20491,f20487,f12623,f12587,f3107,f3059,f20493]) ).
fof(f20493,plain,
( spl0_902
<=> ! [X0,X6,X21,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X21,X6,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X21,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X21,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f3059,plain,
( spl0_261
<=> ! [X6,X0,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f3107,plain,
( spl0_273
<=> ! [X6,X0,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f12587,plain,
( spl0_707
<=> ! [X0,X6,X21,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X21,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f12623,plain,
( spl0_716
<=> ! [X0,X6,X21,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f20487,plain,
( spl0_901
<=> ! [X0,X6,X21,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X21,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X21,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f20491,plain,
( ! [X21,X0,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X21,X6,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X21,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X21,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_261
| ~ spl0_273
| ~ spl0_707
| ~ spl0_716
| ~ spl0_901 ),
inference(forward_demodulation,[],[f20490,f12962]) ).
fof(f12962,plain,
( ! [X2,X3,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X0,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_261
| ~ spl0_707 ),
inference(superposition,[],[f12588,f3060]) ).
fof(f3060,plain,
( ! [X0,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X0,tc_bool))
| ~ spl0_261 ),
inference(avatar_component_clause,[],[f3059]) ).
fof(f12588,plain,
( ! [X21,X0,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X21,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_707 ),
inference(avatar_component_clause,[],[f12587]) ).
fof(f20490,plain,
( ! [X21,X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X21,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X21,X6,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_273
| ~ spl0_716
| ~ spl0_901 ),
inference(forward_demodulation,[],[f20488,f13371]) ).
fof(f13371,plain,
( ! [X2,X3,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X0,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool))
| ~ spl0_273
| ~ spl0_716 ),
inference(superposition,[],[f12624,f3108]) ).
fof(f3108,plain,
( ! [X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X0,tc_bool))
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f3107]) ).
fof(f12624,plain,
( ! [X21,X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_716 ),
inference(avatar_component_clause,[],[f12623]) ).
fof(f20488,plain,
( ! [X21,X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X21,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X21,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool))
| ~ spl0_901 ),
inference(avatar_component_clause,[],[f20487]) ).
fof(f20489,plain,
spl0_901,
inference(avatar_split_clause,[],[f1412,f20487]) ).
fof(f1412,plain,
! [X21,X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X21,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X21,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
inference(forward_demodulation,[],[f406,f392]) ).
fof(f392,axiom,
! [X0,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
fof(f406,axiom,
! [X21,X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X21,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X21,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
fof(f20485,plain,
spl0_900,
inference(avatar_split_clause,[],[f1392,f20483]) ).
fof(f20483,plain,
( spl0_900
<=> ! [X0,X8,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f1392,plain,
! [X2,X0,X1,X8,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ),
inference(definition_unfolding,[],[f1175,f1163,f1163]) ).
fof(f1175,axiom,
! [X2,X0,X1,X8,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).
fof(f20481,plain,
spl0_899,
inference(avatar_split_clause,[],[f1391,f20479]) ).
fof(f20479,plain,
( spl0_899
<=> ! [X2,X0,X8,X5,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f1391,plain,
! [X2,X0,X1,X8,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ),
inference(definition_unfolding,[],[f1174,f1163,f1163]) ).
fof(f1174,axiom,
! [X2,X0,X1,X8,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
fof(f20477,plain,
spl0_898,
inference(avatar_split_clause,[],[f1206,f20475]) ).
fof(f20475,plain,
( spl0_898
<=> ! [X2,X0,X10,X22,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| c_HOL_Ozero__class_Ozero(X10) = hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Ozero__class_Ozero(X10))),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f1206,axiom,
! [X2,X10,X0,X1,X22] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| c_HOL_Ozero__class_Ozero(X10) = hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Ozero__class_Ozero(X10))),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__delta_1) ).
fof(f20355,plain,
spl0_897,
inference(avatar_split_clause,[],[f1205,f20353]) ).
fof(f20353,plain,
( spl0_897
<=> ! [X2,X0,X10,X22,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| hAPP(X1,X2) = c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Oone__class_Oone(X10)),X22,X0,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f1205,axiom,
! [X2,X10,X0,X1,X22] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| hAPP(X1,X2) = c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Oone__class_Oone(X10)),X22,X0,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__delta_0) ).
fof(f20343,plain,
spl0_896,
inference(avatar_split_clause,[],[f1203,f20341]) ).
fof(f20341,plain,
( spl0_896
<=> ! [X2,X0,X10,X22,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| c_HOL_Oone__class_Oone(X10) = c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Oone__class_Oone(X10)),X22,X0,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f1203,axiom,
! [X2,X10,X0,X1,X22] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| c_HOL_Oone__class_Oone(X10) = c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Oone__class_Oone(X10)),X22,X0,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__delta_1) ).
fof(f20149,plain,
spl0_895,
inference(avatar_split_clause,[],[f1398,f20147]) ).
fof(f20147,plain,
( spl0_895
<=> ! [X0,X8,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X2,X1,X8,X0),X1,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f1398,plain,
! [X2,X0,X1,X8] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X2,X1,X8,X0),X1,X0,X0)),X8)) ),
inference(definition_unfolding,[],[f1013,f1163]) ).
fof(f1013,axiom,
! [X2,X0,X1,X8] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1(X2,X1,X8,X0),X1,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_1) ).
fof(f20089,plain,
spl0_894,
inference(avatar_split_clause,[],[f1397,f20087]) ).
fof(f20087,plain,
( spl0_894
<=> ! [X23,X0,X3,X8] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X8,X3,X23,X0),X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f1397,plain,
! [X3,X0,X8,X23] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X8,X3,X23,X0),X0,X0)),X8)) ),
inference(definition_unfolding,[],[f1016,f1163]) ).
fof(f1016,axiom,
! [X3,X0,X8,X23] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1(X8,X3,X23,X0),X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).
fof(f20085,plain,
spl0_893,
inference(avatar_split_clause,[],[f1075,f20083]) ).
fof(f20083,plain,
( spl0_893
<=> ! [X2,X0,X10,X22,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_fequal(X0),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Ozero__class_Ozero(X10))),X22) = hAPP(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f1075,axiom,
! [X2,X10,X0,X1,X22] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_fequal(X0),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Ozero__class_Ozero(X10))),X22) = hAPP(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__delta_H_0) ).
fof(f20081,plain,
spl0_892,
inference(avatar_split_clause,[],[f742,f20079]) ).
fof(f20079,plain,
( spl0_892
<=> ! [X2,X0,X8,X6,X1] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ c_lessequals(c_Relation_OImage(X8,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f742,axiom,
! [X2,X0,X1,X8,X6] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ c_lessequals(c_Relation_OImage(X8,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
fof(f20077,plain,
spl0_891,
inference(avatar_split_clause,[],[f121,f20075]) ).
fof(f20075,plain,
( spl0_891
<=> ! [X10,X0,X20,X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X7,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),X6)),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f121,axiom,
! [X10,X0,X6,X7,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X7,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool))
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),X6)),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X20),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un__disjoint_0) ).
fof(f19986,plain,
spl0_890,
inference(avatar_split_clause,[],[f1395,f19984]) ).
fof(f19984,plain,
( spl0_890
<=> ! [X61,X60,X8] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,t_a),t_a,t_a,t_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X60,X61,X8),X61,t_a,t_a)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f1395,plain,
! [X8,X60,X61] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,t_a),t_a,t_a,t_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X60,X61,X8),X61,t_a,t_a)),X8)) ),
inference(definition_unfolding,[],[f1017,f1163]) ).
fof(f1017,axiom,
! [X8,X60,X61] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),c_Transitive__Closure_Otrancl(X8,t_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(v_sko__Transitive__Closure__Xtrancl__Xcases__1(X60,X61,X8),X61,t_a,t_a)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).
fof(f19982,plain,
spl0_889,
inference(avatar_split_clause,[],[f1076,f19980]) ).
fof(f19980,plain,
( spl0_889
<=> ! [X2,X0,X10,X22,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| c_HOL_Ozero__class_Ozero(X10) = hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_fequal(X0),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Ozero__class_Ozero(X10))),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f1076,axiom,
! [X2,X10,X0,X1,X22] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| c_HOL_Ozero__class_Ozero(X10) = hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_fequal(X0),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Ozero__class_Ozero(X10))),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__delta_H_1) ).
fof(f19978,plain,
spl0_888,
inference(avatar_split_clause,[],[f741,f19976]) ).
fof(f19976,plain,
( spl0_888
<=> ! [X2,X3,X0,X8,X6,X1] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),c_Relation_OImage(X8,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f741,axiom,
! [X2,X3,X0,X1,X8,X6] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),c_Relation_OImage(X8,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
fof(f19814,plain,
spl0_887,
inference(avatar_split_clause,[],[f1394,f19812]) ).
fof(f19812,plain,
( spl0_887
<=> ! [X2,X0,X8,X5,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f1394,plain,
! [X2,X0,X1,X8,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ),
inference(definition_unfolding,[],[f1085,f1163]) ).
fof(f1085,axiom,
! [X2,X0,X1,X8,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
fof(f19810,plain,
spl0_886,
inference(avatar_split_clause,[],[f1077,f19808]) ).
fof(f19808,plain,
( spl0_886
<=> ! [X2,X0,X10,X22,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_fequal(X0),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Oone__class_Oone(X10)),X22,X0,X10) = hAPP(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f1077,axiom,
! [X2,X10,X0,X1,X22] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_fequal(X0),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Oone__class_Oone(X10)),X22,X0,X10) = hAPP(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__delta_H_0) ).
fof(f19725,plain,
spl0_885,
inference(avatar_split_clause,[],[f1224,f19723]) ).
fof(f19723,plain,
( spl0_885
<=> ! [X37,X0,X6,X3,X8] :
( X3 = X37
| ~ c_Relation_Ototal__on(X6,X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X37),X6))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X37,X0,X0)),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X37,X3,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f1224,axiom,
! [X3,X0,X37,X6,X8] :
( X3 = X37
| ~ c_Relation_Ototal__on(X6,X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X37),X6))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X37,X0,X0)),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X37,X3,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).
fof(f19721,plain,
spl0_884,
inference(avatar_split_clause,[],[f1074,f19719]) ).
fof(f19719,plain,
( spl0_884
<=> ! [X2,X0,X10,X22,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| c_HOL_Oone__class_Oone(X10) = c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_fequal(X0),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Oone__class_Oone(X10)),X22,X0,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f1074,axiom,
! [X2,X10,X0,X1,X22] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X22,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X2),X22))
| c_HOL_Oone__class_Oone(X10) = c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(X10),hAPP(c_fequal(X0),X2),tc_bool,tc_fun(X10,tc_fun(X10,X10)),X0),X1,X0,X10,tc_fun(X10,X10)),X0,X10,X10),c_HOL_Oone__class_Oone(X10)),X22,X0,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__delta_H_1) ).
fof(f19689,plain,
spl0_883,
inference(avatar_split_clause,[],[f863,f19687]) ).
fof(f19687,plain,
( spl0_883
<=> ! [X2,X0,X8,X6,X1] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) != c_Relation_OImage(X8,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f863,axiom,
! [X2,X0,X1,X8,X6] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),X6))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) != c_Relation_OImage(X8,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
fof(f19685,plain,
spl0_882,
inference(avatar_split_clause,[],[f314,f19683]) ).
fof(f19683,plain,
( spl0_882
<=> ! [X10,X0,X20,X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X7,X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),c_Finite__Set_Osetprod(X20,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X10)),c_Finite__Set_Osetprod(X20,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X0,X10)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),c_Finite__Set_Osetprod(X20,X6,X0,X10)),c_Finite__Set_Osetprod(X20,X7,X0,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f314,axiom,
! [X10,X0,X6,X7,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X7,X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),c_Finite__Set_Osetprod(X20,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X10)),c_Finite__Set_Osetprod(X20,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X0,X10)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),c_Finite__Set_Osetprod(X20,X6,X0,X10)),c_Finite__Set_Osetprod(X20,X7,X0,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__Un__Int_0) ).
fof(f19637,plain,
spl0_881,
inference(avatar_split_clause,[],[f54,f19635]) ).
fof(f19635,plain,
( spl0_881
<=> ! [X0,X12,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f54,axiom,
! [X2,X0,X1,X5,X12] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
fof(f19595,plain,
spl0_880,
inference(avatar_split_clause,[],[f1179,f19593]) ).
fof(f19593,plain,
( spl0_880
<=> ! [X0,X8,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f1179,axiom,
! [X2,X0,X1,X8,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).
fof(f19422,plain,
( spl0_879
| ~ spl0_712
| ~ spl0_847 ),
inference(avatar_split_clause,[],[f19089,f18037,f12607,f19420]) ).
fof(f19420,plain,
( spl0_879
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f12607,plain,
( spl0_712
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f18037,plain,
( spl0_847
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f19089,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_712
| ~ spl0_847 ),
inference(superposition,[],[f12608,f18038]) ).
fof(f18038,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat)
| ~ spl0_847 ),
inference(avatar_component_clause,[],[f18037]) ).
fof(f12608,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_nat)
| ~ spl0_712 ),
inference(avatar_component_clause,[],[f12607]) ).
fof(f19418,plain,
spl0_878,
inference(avatar_split_clause,[],[f1195,f19416]) ).
fof(f19416,plain,
( spl0_878
<=> ! [X2,X5,X9,X0,X8,X10,X25,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X25)),c_Pair(X1,X5,X10,X25)),X9))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X25)),c_Pair(X2,X5,X0,X25)),c_Relation_Orel__comp(X8,X9,X0,X10,X25))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f1195,axiom,
! [X2,X10,X0,X1,X8,X9,X5,X25] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X25)),c_Pair(X1,X5,X10,X25)),X9))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X25)),c_Pair(X2,X5,X0,X25)),c_Relation_Orel__comp(X8,X9,X0,X10,X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).
fof(f19414,plain,
spl0_877,
inference(avatar_split_clause,[],[f739,f19412]) ).
fof(f19412,plain,
( spl0_877
<=> ! [X32,X0,X8,X2,X1] :
( ~ hBOOL(hAPP(X32,X2))
| hBOOL(hAPP(X32,X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X32,X2,X8,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X32,X2,X8,X0),X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f739,axiom,
! [X2,X0,X1,X8,X32] :
( ~ hBOOL(hAPP(X32,X2))
| hBOOL(hAPP(X32,X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X32,X2,X8,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X32,X2,X8,X0),X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).
fof(f19410,plain,
spl0_876,
inference(avatar_split_clause,[],[f738,f19408]) ).
fof(f19408,plain,
( spl0_876
<=> ! [X32,X0,X8,X2,X1] :
( ~ hBOOL(hAPP(X32,X1))
| hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X32,X1,X8,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X32,X1,X8,X0),X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f738,axiom,
! [X2,X0,X1,X8,X32] :
( ~ hBOOL(hAPP(X32,X1))
| hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X32,X1,X8,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X32,X1,X8,X0),X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_0) ).
fof(f19406,plain,
spl0_875,
inference(avatar_split_clause,[],[f317,f19404]) ).
fof(f19404,plain,
( spl0_875
<=> ! [X10,X0,X20,X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X7,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool))
| c_Finite__Set_Osetprod(X20,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X10) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),c_Finite__Set_Osetprod(X20,X6,X0,X10)),c_Finite__Set_Osetprod(X20,X7,X0,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f317,axiom,
! [X10,X0,X6,X7,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X7,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool))
| c_Finite__Set_Osetprod(X20,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0,X10) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),c_Finite__Set_Osetprod(X20,X6,X0,X10)),c_Finite__Set_Osetprod(X20,X7,X0,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__Un__disjoint_0) ).
fof(f19088,plain,
spl0_874,
inference(avatar_split_clause,[],[f1177,f19086]) ).
fof(f19086,plain,
( spl0_874
<=> ! [X0,X8,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f1177,axiom,
! [X2,X0,X1,X8,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
fof(f19084,plain,
spl0_873,
inference(avatar_split_clause,[],[f1176,f19082]) ).
fof(f19082,plain,
( spl0_873
<=> ! [X2,X0,X8,X5,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f1176,axiom,
! [X2,X0,X1,X8,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
fof(f19080,plain,
spl0_872,
inference(avatar_split_clause,[],[f685,f19078]) ).
fof(f19078,plain,
( spl0_872
<=> ! [X0,X12,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f685,axiom,
! [X2,X0,X1,X5,X12] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
fof(f19076,plain,
spl0_871,
inference(avatar_split_clause,[],[f396,f19074]) ).
fof(f19074,plain,
( spl0_871
<=> ! [X2,X0,X8,X6,X1] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| c_lessequals(c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),c_Relation_OImage(X8,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f396,axiom,
! [X2,X0,X1,X8,X6] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| c_lessequals(c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),c_Relation_OImage(X8,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
fof(f19072,plain,
spl0_870,
inference(avatar_split_clause,[],[f368,f19070]) ).
fof(f19070,plain,
( spl0_870
<=> ! [X0,X12,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f368,axiom,
! [X2,X0,X1,X5,X12] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
fof(f19068,plain,
spl0_869,
inference(avatar_split_clause,[],[f367,f19066]) ).
fof(f19066,plain,
( spl0_869
<=> ! [X0,X12,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X5,X12,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f367,axiom,
! [X2,X0,X1,X5,X12] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X5,X12,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
fof(f18988,plain,
spl0_868,
inference(avatar_split_clause,[],[f995,f18986]) ).
fof(f18986,plain,
( spl0_868
<=> ! [X32,X0,X8,X2,X1] :
( ~ hBOOL(hAPP(X32,X2))
| hBOOL(hAPP(X32,X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X32,X2,X8,X0),X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f995,axiom,
! [X2,X0,X1,X8,X32] :
( ~ hBOOL(hAPP(X32,X2))
| hBOOL(hAPP(X32,X1))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X32,X2,X8,X0),X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).
fof(f18984,plain,
spl0_867,
inference(avatar_split_clause,[],[f994,f18982]) ).
fof(f18982,plain,
( spl0_867
<=> ! [X32,X0,X8,X2,X1] :
( ~ hBOOL(hAPP(X32,X1))
| hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X32,X1,X8,X0),X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f994,axiom,
! [X2,X0,X1,X8,X32] :
( ~ hBOOL(hAPP(X32,X1))
| hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X32,X1,X8,X0),X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_1) ).
fof(f18943,plain,
spl0_866,
inference(avatar_split_clause,[],[f986,f18941]) ).
fof(f18941,plain,
( spl0_866
<=> ! [X18,X10,X20,X0,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(X0),X18,X0,tc_fun(X0,X0),X10),X20,X10,X0,X0)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),X18),X6)),hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),X20),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f986,axiom,
! [X10,X0,X18,X6,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(X0),X18,X0,tc_fun(X0,X0),X10),X20,X10,X0,X0)),X6) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),X18),X6)),hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),X20),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__addf_0) ).
fof(f18844,plain,
spl0_865,
inference(avatar_split_clause,[],[f1389,f18842]) ).
fof(f18842,plain,
( spl0_865
<=> ! [X48,X0,X9,X8] :
( ~ c_lessequals(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),c_Relation_Orel__comp(X9,c_Transitive__Closure_Ortrancl(X9,X0),X0,X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f1389,plain,
! [X48,X0,X8,X9] :
( ~ c_lessequals(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),c_Relation_Orel__comp(X9,c_Transitive__Closure_Ortrancl(X9,X0),X0,X0,X0))) ),
inference(definition_unfolding,[],[f945,f1163,f1163]) ).
fof(f945,axiom,
! [X48,X0,X8,X9] :
( ~ c_lessequals(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),c_Transitive__Closure_Otrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),c_Transitive__Closure_Otrancl(X9,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).
fof(f18840,plain,
spl0_864,
inference(avatar_split_clause,[],[f946,f18838]) ).
fof(f18838,plain,
( spl0_864
<=> ! [X2,X0,X8,X6,X1] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) = c_Relation_OImage(X8,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f946,axiom,
! [X2,X0,X1,X8,X6] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) = c_Relation_OImage(X8,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).
fof(f18836,plain,
spl0_863,
inference(avatar_split_clause,[],[f397,f18834]) ).
fof(f18834,plain,
( spl0_863
<=> ! [X2,X11,X0,X5,X1] :
( ~ class_Ring__and__Field_Osemiring(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X11)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f397,axiom,
! [X2,X0,X11,X1,X5] :
( ~ class_Ring__and__Field_Osemiring(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X11)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
fof(f18720,plain,
spl0_862,
inference(avatar_split_clause,[],[f1382,f18718]) ).
fof(f18718,plain,
( spl0_862
<=> ! [X4,X0,X3,X15] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_Orel__comp(X15,c_Transitive__Closure_Ortrancl(X15,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X15,X3,X4,X0),X4,X0,X0)),c_Transitive__Closure_Ortrancl(X15,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f1382,plain,
! [X3,X0,X4,X15] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_Orel__comp(X15,c_Transitive__Closure_Ortrancl(X15,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X15,X3,X4,X0),X4,X0,X0)),c_Transitive__Closure_Ortrancl(X15,X0))) ),
inference(definition_unfolding,[],[f1064,f1163]) ).
fof(f1064,axiom,
! [X3,X0,X4,X15] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Otrancl(X15,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X15,X3,X4,X0),X4,X0,X0)),c_Transitive__Closure_Ortrancl(X15,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).
fof(f18716,plain,
spl0_861,
inference(avatar_split_clause,[],[f1381,f18714]) ).
fof(f18714,plain,
( spl0_861
<=> ! [X4,X0,X3,X15] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_Orel__comp(X15,c_Transitive__Closure_Ortrancl(X15,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X15,X3,X4,X0),X0,X0)),c_Transitive__Closure_Ortrancl(X15,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f1381,plain,
! [X3,X0,X4,X15] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_Orel__comp(X15,c_Transitive__Closure_Ortrancl(X15,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X15,X3,X4,X0),X0,X0)),c_Transitive__Closure_Ortrancl(X15,X0))) ),
inference(definition_unfolding,[],[f1063,f1163]) ).
fof(f1063,axiom,
! [X3,X0,X4,X15] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Otrancl(X15,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X15,X3,X4,X0),X0,X0)),c_Transitive__Closure_Ortrancl(X15,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).
fof(f18567,plain,
spl0_860,
inference(avatar_split_clause,[],[f1387,f18565]) ).
fof(f18565,plain,
( spl0_860
<=> ! [X15,X0,X2,X1] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X15,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Relation_Orel__comp(X15,c_Transitive__Closure_Ortrancl(X15,X0),X0,X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f1387,plain,
! [X2,X0,X1,X15] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X15,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Relation_Orel__comp(X15,c_Transitive__Closure_Ortrancl(X15,X0),X0,X0,X0))) ),
inference(definition_unfolding,[],[f1088,f1163]) ).
fof(f1088,axiom,
! [X2,X0,X1,X15] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X15,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Otrancl(X15,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclD_0) ).
fof(f18563,plain,
spl0_859,
inference(avatar_split_clause,[],[f1039,f18561]) ).
fof(f18561,plain,
( spl0_859
<=> ! [X13,X0,X14,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X14),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Oone__class_Oone(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X13,X0)),c_Power_Opower__class_Opower(X2,X14,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f1039,axiom,
! [X2,X0,X14,X13] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X14),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Oone__class_Oone(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X13,X0)),c_Power_Opower__class_Opower(X2,X14,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
fof(f18559,plain,
spl0_858,
inference(avatar_split_clause,[],[f1020,f18557]) ).
fof(f18557,plain,
( spl0_858
<=> ! [X5,X10,X2,X0,X8,X9,X25] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X5,X0,X10)),c_Relation_Orel__comp(X8,X9,X0,X25,X10)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X25)),c_Pair(X2,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X2,X5,X8,X9,X0,X10,X25),X0,X25)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f1020,axiom,
! [X2,X10,X0,X8,X9,X5,X25] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X5,X0,X10)),c_Relation_Orel__comp(X8,X9,X0,X25,X10)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X25)),c_Pair(X2,c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X2,X5,X8,X9,X0,X10,X25),X0,X25)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).
fof(f18555,plain,
spl0_857,
inference(avatar_split_clause,[],[f1019,f18553]) ).
fof(f18553,plain,
( spl0_857
<=> ! [X5,X10,X2,X0,X8,X9,X25] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X5,X0,X10)),c_Relation_Orel__comp(X8,X9,X0,X25,X10)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X25,X10)),c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X2,X5,X8,X9,X0,X10,X25),X5,X25,X10)),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f1019,axiom,
! [X2,X10,X0,X8,X9,X5,X25] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X5,X0,X10)),c_Relation_Orel__comp(X8,X9,X0,X25,X10)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X25,X10)),c_Pair(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1(X2,X5,X8,X9,X0,X10,X25),X5,X25,X10)),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).
fof(f18165,plain,
spl0_856,
inference(avatar_split_clause,[],[f1380,f18163]) ).
fof(f18163,plain,
( spl0_856
<=> ! [X4,X0,X3,X15] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_Orel__comp(X15,c_Transitive__Closure_Ortrancl(X15,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X15,X3,X4,X0),X4,X0,X0)),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f1380,plain,
! [X3,X0,X4,X15] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_Orel__comp(X15,c_Transitive__Closure_Ortrancl(X15,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X15,X3,X4,X0),X4,X0,X0)),X15)) ),
inference(definition_unfolding,[],[f1015,f1163]) ).
fof(f1015,axiom,
! [X3,X0,X4,X15] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Otrancl(X15,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1(X15,X3,X4,X0),X4,X0,X0)),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).
fof(f18135,plain,
spl0_855,
inference(avatar_split_clause,[],[f1379,f18133]) ).
fof(f18133,plain,
( spl0_855
<=> ! [X4,X0,X3,X15] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_Orel__comp(X15,c_Transitive__Closure_Ortrancl(X15,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X15,X3,X4,X0),X0,X0)),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f1379,plain,
! [X3,X0,X4,X15] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_Orel__comp(X15,c_Transitive__Closure_Ortrancl(X15,X0),X0,X0,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X15,X3,X4,X0),X0,X0)),X15)) ),
inference(definition_unfolding,[],[f1010,f1163]) ).
fof(f1010,axiom,
! [X3,X0,X4,X15] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Otrancl(X15,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1(X15,X3,X4,X0),X0,X0)),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).
fof(f18131,plain,
spl0_854,
inference(avatar_split_clause,[],[f1377,f18129]) ).
fof(f18129,plain,
( spl0_854
<=> ! [X0,X8,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X8,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X8,X0),X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f1377,plain,
! [X3,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X8,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X8,X0),X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ),
inference(definition_unfolding,[],[f1008,f1163]) ).
fof(f1008,axiom,
! [X3,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X8,X0),c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1(X8,X0),X0,X0)),c_Transitive__Closure_Otrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).
fof(f18127,plain,
spl0_853,
inference(avatar_split_clause,[],[f1057,f18125]) ).
fof(f18125,plain,
( spl0_853
<=> ! [X8,X63,X3,X32] :
( hBOOL(hAPP(X32,X3))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X8,t_a)))
| hBOOL(hAPP(hAPP(c_in(t_a),X63),c_Wellfounded_Oacc(X8,t_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X63,v_sko__Wellfounded__Xacc__Xinduct__1(X32,X8),t_a,t_a)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f1057,axiom,
! [X3,X8,X63,X32] :
( hBOOL(hAPP(X32,X3))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X8,t_a)))
| hBOOL(hAPP(hAPP(c_in(t_a),X63),c_Wellfounded_Oacc(X8,t_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X63,v_sko__Wellfounded__Xacc__Xinduct__1(X32,X8),t_a,t_a)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).
fof(f18123,plain,
spl0_852,
inference(avatar_split_clause,[],[f1055,f18121]) ).
fof(f18121,plain,
( spl0_852
<=> ! [X8,X63,X3,X32] :
( hBOOL(hAPP(X32,X3))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X8,t_a)))
| hBOOL(hAPP(hAPP(c_in(t_a),X63),c_Wellfounded_Oacc(X8,t_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X63,v_sko__Wellfounded__Xacc__Xinducts__1(X32,X8),t_a,t_a)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f1055,axiom,
! [X3,X8,X63,X32] :
( hBOOL(hAPP(X32,X3))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X8,t_a)))
| hBOOL(hAPP(hAPP(c_in(t_a),X63),c_Wellfounded_Oacc(X8,t_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X63,v_sko__Wellfounded__Xacc__Xinducts__1(X32,X8),t_a,t_a)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).
fof(f18119,plain,
spl0_851,
inference(avatar_split_clause,[],[f1037,f18117]) ).
fof(f18117,plain,
( spl0_851
<=> ! [X18,X4,X0,X3,X15] :
( ~ c_lessequals(hAPP(X18,X3),hAPP(X18,X4),tc_nat)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),X15))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Wellfounded_Omlex__prod(X18,X15,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f1037,axiom,
! [X3,X0,X18,X4,X15] :
( ~ c_lessequals(hAPP(X18,X3),hAPP(X18,X4),tc_nat)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),X15))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Wellfounded_Omlex__prod(X18,X15,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mlex__leq_0) ).
fof(f18115,plain,
spl0_850,
inference(avatar_split_clause,[],[f1002,f18113]) ).
fof(f18113,plain,
( spl0_850
<=> ! [X0,X8,X2,X1] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X2,X1,X8,X0),X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f1002,axiom,
! [X2,X0,X1,X8] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X2,X1,X8,X0),X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_0) ).
fof(f18111,plain,
spl0_849,
inference(avatar_split_clause,[],[f991,f18109]) ).
fof(f18109,plain,
( spl0_849
<=> ! [X0,X8,X23,X3] :
( X3 = X23
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X8,X3,X23,X0),X23,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f991,axiom,
! [X3,X0,X8,X23] :
( X3 = X23
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X8,X3,X23,X0),X23,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_1) ).
fof(f18107,plain,
spl0_848,
inference(avatar_split_clause,[],[f734,f18105]) ).
fof(f18105,plain,
( spl0_848
<=> ! [X18,X19,X0,X10,X2] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X19,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X2),X19))
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),c_Set_Oinsert(X2,X19,X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),hAPP(X18,X2)),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f734,axiom,
! [X2,X10,X0,X18,X19] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| ~ c_Finite__Set_Ofinite(X19,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X2),X19))
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),c_Set_Oinsert(X2,X19,X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),hAPP(X18,X2)),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__insert_0) ).
fof(f18039,plain,
( spl0_847
| ~ spl0_684
| ~ spl0_768 ),
inference(avatar_split_clause,[],[f17807,f15265,f12044,f18037]) ).
fof(f12044,plain,
( spl0_684
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f15265,plain,
( spl0_768
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f17807,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat)
| ~ spl0_684
| ~ spl0_768 ),
inference(superposition,[],[f12045,f15266]) ).
fof(f15266,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat) = X0
| ~ spl0_768 ),
inference(avatar_component_clause,[],[f15265]) ).
fof(f12045,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_684 ),
inference(avatar_component_clause,[],[f12044]) ).
fof(f17854,plain,
spl0_846,
inference(avatar_split_clause,[],[f1404,f17852]) ).
fof(f17852,plain,
( spl0_846
<=> ! [X9,X0,X8] :
( ~ c_Wellfounded_Owf(X9,X0)
| ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X8,X0,X0),X0,X0),c_Relation_ORange(X9,X0,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f1404,plain,
! [X0,X8,X9] :
( ~ c_Wellfounded_Owf(X9,X0)
| ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ORange(c_Relation_Oconverse(X8,X0,X0),X0,X0),c_Relation_ORange(X9,X0,X0),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f131,f1146]) ).
fof(f1146,axiom,
! [X10,X0,X8] : c_Relation_ODomain(X8,X0,X10) = c_Relation_ORange(c_Relation_Oconverse(X8,X0,X10),X10,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).
fof(f131,axiom,
! [X0,X8,X9] :
( ~ c_Wellfounded_Owf(X9,X0)
| ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(c_Relation_ODomain(X8,X0,X0),c_Relation_ORange(X9,X0,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Un_0) ).
fof(f17850,plain,
spl0_845,
inference(avatar_split_clause,[],[f1264,f17848]) ).
fof(f17848,plain,
( spl0_845
<=> ! [X4,X23,X3,X65] :
( X4 = X23
| X3 = X23
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X65))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X65),X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f1264,axiom,
! [X65,X3,X4,X23] :
( X4 = X23
| X3 = X23
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X65))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X65),X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
fof(f17846,plain,
spl0_844,
inference(avatar_split_clause,[],[f1263,f17844]) ).
fof(f17844,plain,
( spl0_844
<=> ! [X4,X23,X3,X65] :
( X4 = X23
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X65))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X65),X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f1263,axiom,
! [X65,X3,X4,X23] :
( X4 = X23
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X65))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X65),X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
fof(f17842,plain,
spl0_843,
inference(avatar_split_clause,[],[f1237,f17840]) ).
fof(f17840,plain,
( spl0_843
<=> ! [X4,X23,X3,X65] :
( X3 = X23
| X4 = X23
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X65))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X65),X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f1237,axiom,
! [X65,X3,X4,X23] :
( X3 = X23
| X4 = X23
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X65))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X65),X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).
fof(f17805,plain,
spl0_842,
inference(avatar_split_clause,[],[f1236,f17803]) ).
fof(f17803,plain,
( spl0_842
<=> ! [X4,X23,X3,X65] :
( X3 = X23
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X65))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X65),X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f1236,axiom,
! [X65,X3,X4,X23] :
( X3 = X23
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X65))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X65),X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).
fof(f17801,plain,
spl0_841,
inference(avatar_split_clause,[],[f998,f17799]) ).
fof(f17799,plain,
( spl0_841
<=> ! [X61,X60,X8] :
( X60 = X61
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),c_Transitive__Closure_Ortrancl(X8,t_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X60,X61,X8),t_a,t_a)),c_Transitive__Closure_Ortrancl(X8,t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f998,axiom,
! [X8,X60,X61] :
( X60 = X61
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),c_Transitive__Closure_Ortrancl(X8,t_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X60,X61,X8),t_a,t_a)),c_Transitive__Closure_Ortrancl(X8,t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_0) ).
fof(f17797,plain,
spl0_840,
inference(avatar_split_clause,[],[f982,f17795]) ).
fof(f17795,plain,
( spl0_840
<=> ! [X18,X10,X0,X6,X8] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),X18),X6)),X8) = hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X0),X18,X0,tc_fun(X0,X0),X10),X10,X0,X0),X8)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f982,axiom,
! [X10,X0,X18,X8,X6] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),X18),X6)),X8) = hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X0),X18,X0,tc_fun(X0,X0),X10),X10,X0,X0),X8)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__left__distrib_0) ).
fof(f17793,plain,
spl0_839,
inference(avatar_split_clause,[],[f611,f17791]) ).
fof(f17791,plain,
( spl0_839
<=> ! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Oone__class_Oone(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Power_Opower__class_Opower(X2,X14,X0))),c_Power_Opower__class_Opower(X2,X14,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f611,axiom,
! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Oone__class_Oone(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Power_Opower__class_Opower(X2,X14,X0))),c_Power_Opower__class_Opower(X2,X14,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
fof(f17600,plain,
( spl0_838
| ~ spl0_212
| ~ spl0_833 ),
inference(avatar_split_clause,[],[f17573,f17570,f2440,f17598]) ).
fof(f17598,plain,
( spl0_838
<=> ! [X0,X14,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X1,X14,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f2440,plain,
( spl0_212
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f17570,plain,
( spl0_833
<=> ! [X0,X14,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X1,X14,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f17573,plain,
( ! [X2,X0,X1,X14] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X1,X14,X0))) )
| ~ spl0_212
| ~ spl0_833 ),
inference(forward_demodulation,[],[f17571,f2442]) ).
fof(f2442,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2440]) ).
fof(f17571,plain,
( ! [X2,X0,X1,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X1,X14,X0))) )
| ~ spl0_833 ),
inference(avatar_component_clause,[],[f17570]) ).
fof(f17589,plain,
spl0_837,
inference(avatar_split_clause,[],[f1018,f17587]) ).
fof(f17587,plain,
( spl0_837
<=> ! [X18,X10,X20,X0,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Finite__Set_Osetprod(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(X0),X18,X0,tc_fun(X0,X0),X10),X20,X10,X0,X0),X6,X10,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Finite__Set_Osetprod(X18,X6,X10,X0)),c_Finite__Set_Osetprod(X20,X6,X10,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f1018,axiom,
! [X10,X0,X18,X6,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Finite__Set_Osetprod(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(X0),X18,X0,tc_fun(X0,X0),X10),X20,X10,X0,X0),X6,X10,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Finite__Set_Osetprod(X18,X6,X10,X0)),c_Finite__Set_Osetprod(X20,X6,X10,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__timesf_0) ).
fof(f17585,plain,
spl0_836,
inference(avatar_split_clause,[],[f992,f17583]) ).
fof(f17583,plain,
( spl0_836
<=> ! [X0,X8,X23,X3] :
( X3 = X23
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X8,X3,X23,X0),X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f992,axiom,
! [X3,X0,X8,X23] :
( X3 = X23
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X23,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1(X8,X3,X23,X0),X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_0) ).
fof(f17581,plain,
spl0_835,
inference(avatar_split_clause,[],[f990,f17579]) ).
fof(f17579,plain,
( spl0_835
<=> ! [X0,X8,X2,X1] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X2,X1,X8,X0),X1,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f990,axiom,
! [X2,X0,X1,X8] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1(X2,X1,X8,X0),X1,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_1) ).
fof(f17577,plain,
spl0_834,
inference(avatar_split_clause,[],[f580,f17575]) ).
fof(f17575,plain,
( spl0_834
<=> ! [X2,X0,X12,X5,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f580,axiom,
! [X2,X0,X1,X5,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f17572,plain,
spl0_833,
inference(avatar_split_clause,[],[f408,f17570]) ).
fof(f408,axiom,
! [X2,X0,X1,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X1,X14,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
fof(f17568,plain,
spl0_832,
inference(avatar_split_clause,[],[f164,f17566]) ).
fof(f17566,plain,
( spl0_832
<=> ! [X0,X29,X27,X28,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X28)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X29)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X28),X30)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f164,axiom,
! [X28,X0,X29,X27,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X28)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X29)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X28),X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f17406,plain,
( ~ spl0_33
| spl0_831
| ~ spl0_187
| ~ spl0_681 ),
inference(avatar_split_clause,[],[f17086,f11859,f2340,f17404,f1584]) ).
fof(f1584,plain,
( spl0_33
<=> class_Ring__and__Field_Odvd(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f17404,plain,
( spl0_831
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f2340,plain,
( spl0_187
<=> ! [X0,X1,X31] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X31),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f11859,plain,
( spl0_681
<=> ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f17086,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_nat)
| ~ class_Ring__and__Field_Odvd(tc_nat) )
| ~ spl0_187
| ~ spl0_681 ),
inference(superposition,[],[f2341,f11860]) ).
fof(f11860,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)) = X0
| ~ spl0_681 ),
inference(avatar_component_clause,[],[f11859]) ).
fof(f2341,plain,
( ! [X31,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X31),X0)
| ~ class_Ring__and__Field_Odvd(X0) )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f2340]) ).
fof(f17161,plain,
spl0_830,
inference(avatar_split_clause,[],[f1192,f17159]) ).
fof(f17159,plain,
( spl0_830
<=> ! [X18,X4,X3,X0,X10,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_Oinv__image(X8,X18,X10,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X10)),c_Pair(hAPP(X18,X3),hAPP(X18,X4),X10,X10)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f1192,axiom,
! [X3,X10,X0,X18,X8,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_Oinv__image(X8,X18,X10,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X10)),c_Pair(hAPP(X18,X3),hAPP(X18,X4),X10,X10)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).
fof(f17157,plain,
spl0_829,
inference(avatar_split_clause,[],[f1191,f17155]) ).
fof(f17155,plain,
( spl0_829
<=> ! [X18,X4,X3,X0,X10,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X10)),c_Pair(hAPP(X18,X3),hAPP(X18,X4),X10,X10)),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_Oinv__image(X8,X18,X10,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f1191,axiom,
! [X3,X10,X0,X18,X8,X4] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X10)),c_Pair(hAPP(X18,X3),hAPP(X18,X4),X10,X10)),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_Oinv__image(X8,X18,X10,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).
fof(f17153,plain,
spl0_828,
inference(avatar_split_clause,[],[f1000,f17151]) ).
fof(f17151,plain,
( spl0_828
<=> ! [X61,X60,X8] :
( X60 = X61
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),c_Transitive__Closure_Ortrancl(X8,t_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X60,X61,X8),X61,t_a,t_a)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f1000,axiom,
! [X8,X60,X61] :
( X60 = X61
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X60,X61,t_a,t_a)),c_Transitive__Closure_Ortrancl(X8,t_a)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(v_sko__Transitive__Closure__Xrtrancl__Xcases__1(X60,X61,X8),X61,t_a,t_a)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).
fof(f17149,plain,
spl0_827,
inference(avatar_split_clause,[],[f756,f17147]) ).
fof(f17147,plain,
( spl0_827
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f756,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
fof(f17078,plain,
spl0_826,
inference(avatar_split_clause,[],[f752,f17076]) ).
fof(f17076,plain,
( spl0_826
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f752,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
fof(f17074,plain,
spl0_825,
inference(avatar_split_clause,[],[f749,f17072]) ).
fof(f17072,plain,
( spl0_825
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f749,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
fof(f17070,plain,
spl0_824,
inference(avatar_split_clause,[],[f623,f17068]) ).
fof(f17068,plain,
( spl0_824
<=> ! [X5,X0,X12,X2,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,X12,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f623,axiom,
! [X2,X0,X1,X5,X12] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,X12,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
fof(f17066,plain,
spl0_823,
inference(avatar_split_clause,[],[f622,f17064]) ).
fof(f17064,plain,
( spl0_823
<=> ! [X5,X0,X12,X2,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,X12,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f622,axiom,
! [X2,X0,X1,X5,X12] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,X12,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).
fof(f17062,plain,
spl0_822,
inference(avatar_split_clause,[],[f219,f17060]) ).
fof(f17060,plain,
( spl0_822
<=> ! [X10,X9,X0,X33,X25,X8,X34] :
( ~ c_lessequals(X33,X8,tc_fun(tc_prod(X0,X10),tc_bool))
| ~ c_lessequals(X34,X9,tc_fun(tc_prod(X10,X25),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X33,X34,X0,X10,X25),c_Relation_Orel__comp(X8,X9,X0,X10,X25),tc_fun(tc_prod(X0,X25),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f219,axiom,
! [X10,X0,X8,X9,X34,X25,X33] :
( ~ c_lessequals(X33,X8,tc_fun(tc_prod(X0,X10),tc_bool))
| ~ c_lessequals(X34,X9,tc_fun(tc_prod(X10,X25),tc_bool))
| c_lessequals(c_Relation_Orel__comp(X33,X34,X0,X10,X25),c_Relation_Orel__comp(X8,X9,X0,X10,X25),tc_fun(tc_prod(X0,X25),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).
fof(f16572,plain,
( ~ spl0_33
| spl0_821
| ~ spl0_187
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f16450,f11692,f2340,f16570,f1584]) ).
fof(f16570,plain,
( spl0_821
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f11692,plain,
( spl0_680
<=> ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f16450,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Odvd(tc_nat) )
| ~ spl0_187
| ~ spl0_680 ),
inference(superposition,[],[f2341,f11693]) ).
fof(f11693,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) = X0
| ~ spl0_680 ),
inference(avatar_component_clause,[],[f11692]) ).
fof(f16568,plain,
spl0_820,
inference(avatar_split_clause,[],[f1363,f16566]) ).
fof(f16566,plain,
( spl0_820
<=> ! [X10,X0,X6,X7] : c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X0,X10),tc_bool)),X0,X10),X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X0,X10),X10,X0),c_Relation_ORange(c_Relation_Oconverse(X7,X0,X10),X10,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f1363,plain,
! [X10,X0,X6,X7] : c_Relation_ORange(c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X0,X10),tc_bool)),X0,X10),X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(c_Relation_Oconverse(X6,X0,X10),X10,X0),c_Relation_ORange(c_Relation_Oconverse(X7,X0,X10),X10,X0),tc_fun(X0,tc_bool)),
inference(definition_unfolding,[],[f595,f1146,f1146,f1146]) ).
fof(f595,axiom,
! [X10,X0,X6,X7] : c_Relation_ODomain(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X0,X10),tc_bool)),X0,X10) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ODomain(X6,X0,X10),c_Relation_ODomain(X7,X0,X10),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).
fof(f16564,plain,
spl0_819,
inference(avatar_split_clause,[],[f1271,f16562]) ).
fof(f16562,plain,
( spl0_819
<=> ! [X4,X23,X3,X65] :
( X3 = X23
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X65))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X65),X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f1271,axiom,
! [X65,X3,X4,X23] :
( X3 = X23
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X65))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X65),X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
fof(f16560,plain,
spl0_818,
inference(avatar_split_clause,[],[f1252,f16558]) ).
fof(f16558,plain,
( spl0_818
<=> ! [X4,X23,X3,X65] :
( X4 = X23
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X65))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X65),X23))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f1252,axiom,
! [X65,X3,X4,X23] :
( X4 = X23
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X65))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X65),X23))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).
fof(f16556,plain,
spl0_817,
inference(avatar_split_clause,[],[f1209,f16554]) ).
fof(f16554,plain,
( spl0_817
<=> ! [X1,X10,X0,X6,X2,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X10),X1),hAPP(X7,X2)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),c_Product__Type_OSigma(X6,X7,X0,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f1209,axiom,
! [X2,X10,X0,X1,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X10),X1),hAPP(X7,X2)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),c_Product__Type_OSigma(X6,X7,X0,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).
fof(f16552,plain,
spl0_816,
inference(avatar_split_clause,[],[f1187,f16550]) ).
fof(f16550,plain,
( spl0_816
<=> ! [X18,X4,X20,X0,X10,X8,X3] :
( hAPP(X18,X4) = hAPP(X20,X4)
| c_Recdef_Ocut(X18,X8,X3,X0,X10) != c_Recdef_Ocut(X20,X8,X3,X0,X10)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,X3,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f1187,axiom,
! [X3,X10,X0,X18,X8,X4,X20] :
( hAPP(X18,X4) = hAPP(X20,X4)
| c_Recdef_Ocut(X18,X8,X3,X0,X10) != c_Recdef_Ocut(X20,X8,X3,X0,X10)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,X3,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
fof(f16548,plain,
spl0_815,
inference(avatar_split_clause,[],[f1080,f16546]) ).
fof(f16546,plain,
( spl0_815
<=> ! [X0,X8,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(X0),X1),c_Wellfounded_Oacc(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X2,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f1080,axiom,
! [X2,X0,X1,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(X0),X1),c_Wellfounded_Oacc(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X2,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).
fof(f16544,plain,
spl0_814,
inference(avatar_split_clause,[],[f1058,f16542]) ).
fof(f16542,plain,
( spl0_814
<=> ! [X2,X4,X0,X8,X32] :
( hBOOL(hAPP(X32,X4))
| hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X32,X8,X0),X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f1058,axiom,
! [X2,X0,X8,X4,X32] :
( hBOOL(hAPP(X32,X4))
| hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X32,X8,X0),X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_1) ).
fof(f16540,plain,
spl0_813,
inference(avatar_split_clause,[],[f1052,f16538]) ).
fof(f16538,plain,
( spl0_813
<=> ! [X2,X4,X0,X8,X32] :
( hBOOL(hAPP(X32,X4))
| hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X32,X8,X0),X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f1052,axiom,
! [X2,X0,X8,X4,X32] :
( hBOOL(hAPP(X32,X4))
| hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X32,X8,X0),X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).
fof(f16536,plain,
spl0_812,
inference(avatar_split_clause,[],[f1045,f16534]) ).
fof(f16534,plain,
( spl0_812
<=> ! [X37,X4,X47,X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X37),X47))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X4),X47))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X47,X8,X0),X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f1045,axiom,
! [X0,X47,X8,X37,X4] :
( ~ c_Wellfounded_Owf(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X37),X47))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X4),X47))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X47,X8,X0),X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
fof(f16532,plain,
spl0_811,
inference(avatar_split_clause,[],[f1044,f16530]) ).
fof(f16530,plain,
( spl0_811
<=> ! [X4,X47,X0,X3,X15] :
( ~ c_Wellfounded_Owf(X15,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X47))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X4),X47))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X47,X15,X0),X0,X0)),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f1044,axiom,
! [X3,X0,X47,X4,X15] :
( ~ c_Wellfounded_Owf(X15,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X47))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X4),X47))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X47,X15,X0),X0,X0)),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).
fof(f16440,plain,
spl0_810,
inference(avatar_split_clause,[],[f923,f16438]) ).
fof(f16438,plain,
( spl0_810
<=> ! [X3,X4,X0,X23,X8,X10] :
( X4 = X23
| ~ c_Relation_Osingle__valued(X8,X0,X10)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X3,X4,X0,X10)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X3,X23,X0,X10)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f923,axiom,
! [X3,X10,X0,X8,X4,X23] :
( X4 = X23
| ~ c_Relation_Osingle__valued(X8,X0,X10)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X3,X4,X0,X10)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X3,X23,X0,X10)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).
fof(f16436,plain,
spl0_809,
inference(avatar_split_clause,[],[f834,f16434]) ).
fof(f16434,plain,
( spl0_809
<=> ! [X5,X0,X12,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f834,axiom,
! [X2,X0,X1,X5,X12] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f16432,plain,
spl0_808,
inference(avatar_split_clause,[],[f735,f16430]) ).
fof(f16430,plain,
( spl0_808
<=> ! [X18,X10,X0,X6,X2] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| c_Finite__Set_Osetprod(X18,c_Set_Oinsert(X2,X6,X0),X0,X10) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),hAPP(X18,X2)),c_Finite__Set_Osetprod(X18,X6,X0,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f735,axiom,
! [X2,X10,X0,X18,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| c_Finite__Set_Osetprod(X18,c_Set_Oinsert(X2,X6,X0),X0,X10) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X10),hAPP(X18,X2)),c_Finite__Set_Osetprod(X18,X6,X0,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__insert_0) ).
fof(f16428,plain,
spl0_807,
inference(avatar_split_clause,[],[f237,f16426]) ).
fof(f16426,plain,
( spl0_807
<=> ! [X10,X0,X6,X8,X7] :
( ~ c_lessequals(c_Relation_OImage(X8,X6,X10,X0),X7,tc_fun(X0,tc_bool))
| c_lessequals(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X10,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X8,X10,X0),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),X0,X10)),tc_fun(X10,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f237,axiom,
! [X10,X0,X8,X6,X7] :
( ~ c_lessequals(c_Relation_OImage(X8,X6,X10,X0),X7,tc_fun(X0,tc_bool))
| c_lessequals(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X10,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X8,X10,X0),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),X0,X10)),tc_fun(X10,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset__eq_0) ).
fof(f16424,plain,
spl0_806,
inference(avatar_split_clause,[],[f236,f16422]) ).
fof(f16422,plain,
( spl0_806
<=> ! [X10,X0,X6,X8,X7] :
( c_lessequals(c_Relation_OImage(X8,X6,X10,X0),X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X10,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X8,X10,X0),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),X0,X10)),tc_fun(X10,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f236,axiom,
! [X10,X0,X8,X6,X7] :
( c_lessequals(c_Relation_OImage(X8,X6,X10,X0),X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X10,tc_bool)),c_Relation_OImage(c_Relation_Oconverse(X8,X10,X0),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),X0,X10)),tc_fun(X10,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset__eq_1) ).
fof(f16115,plain,
( spl0_805
| ~ spl0_212
| ~ spl0_796 ),
inference(avatar_split_clause,[],[f15891,f15887,f2440,f16113]) ).
fof(f16113,plain,
( spl0_805
<=> ! [X18,X0,X3,X22] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_Finite__Set_Osetprod(X18,X22,X0,tc_nat)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),hAPP(X18,X3)))
| ~ c_Finite__Set_Ofinite(X22,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f15887,plain,
( spl0_796
<=> ! [X18,X0,X3,X22] :
( ~ c_Finite__Set_Ofinite(X22,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X22))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(X18,X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Osetprod(X18,X22,X0,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f15891,plain,
( ! [X3,X0,X18,X22] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_Finite__Set_Osetprod(X18,X22,X0,tc_nat)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),hAPP(X18,X3)))
| ~ c_Finite__Set_Ofinite(X22,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X22)) )
| ~ spl0_212
| ~ spl0_796 ),
inference(forward_demodulation,[],[f15890,f2442]) ).
fof(f15890,plain,
( ! [X3,X0,X18,X22] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),hAPP(X18,X3)))
| ~ c_Finite__Set_Ofinite(X22,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X22))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Osetprod(X18,X22,X0,tc_nat))) )
| ~ spl0_212
| ~ spl0_796 ),
inference(forward_demodulation,[],[f15888,f2442]) ).
fof(f15888,plain,
( ! [X3,X0,X18,X22] :
( ~ c_Finite__Set_Ofinite(X22,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X22))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(X18,X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Osetprod(X18,X22,X0,tc_nat))) )
| ~ spl0_796 ),
inference(avatar_component_clause,[],[f15887]) ).
fof(f16106,plain,
( spl0_804
| ~ spl0_212
| ~ spl0_794 ),
inference(avatar_split_clause,[],[f15881,f15878,f2440,f16104]) ).
fof(f16104,plain,
( spl0_804
<=> ! [X0,X14,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_Power_Opower__class_Opower(X2,X14,X0) != c_Power_Opower__class_Opower(X1,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f15878,plain,
( spl0_794
<=> ! [X0,X14,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| c_Power_Opower__class_Opower(X2,X14,X0) != c_Power_Opower__class_Opower(X1,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f15881,plain,
( ! [X2,X0,X1,X14] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_Power_Opower__class_Opower(X2,X14,X0) != c_Power_Opower__class_Opower(X1,X14,X0) )
| ~ spl0_212
| ~ spl0_794 ),
inference(forward_demodulation,[],[f15879,f2442]) ).
fof(f15879,plain,
( ! [X2,X0,X1,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| c_Power_Opower__class_Opower(X2,X14,X0) != c_Power_Opower__class_Opower(X1,X14,X0) )
| ~ spl0_794 ),
inference(avatar_component_clause,[],[f15878]) ).
fof(f15919,plain,
spl0_803,
inference(avatar_split_clause,[],[f1416,f15917]) ).
fof(f15917,plain,
( spl0_803
<=> ! [X22,X0,X15] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X22,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X15,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f1416,plain,
! [X0,X15,X22] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X22,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X15,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f1415,f459]) ).
fof(f459,axiom,
! [X10,X0,X15,X22,X25,X43] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X22,X43,tc_fun(tc_prod(X0,X25),tc_bool)),X15,X0,X25,X10) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X22,X15,X0,X25,X10),c_Relation_Orel__comp(X43,X15,X0,X25,X10),tc_fun(tc_prod(X0,X10),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).
fof(f1415,plain,
! [X0,X15,X22] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X22,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X15,X15,X0,X0,X0),c_Relation_Orel__comp(X22,X15,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f957,f584]) ).
fof(f584,axiom,
! [X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
fof(f957,axiom,
! [X0,X15,X22] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X15,X15,X0,X0,X0),c_Relation_Orel__comp(X22,X15,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).
fof(f15915,plain,
( spl0_802
| ~ spl0_228
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f4408,f3806,f2513,f15913]) ).
fof(f15913,plain,
( spl0_802
<=> ! [X0,X1] : hBOOL(hAPP(c_Relation_OId(X0),c_Pair(X1,X1,X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f2513,plain,
( spl0_228
<=> ! [X22,X0,X3] :
( hBOOL(hAPP(X22,X3))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f3806,plain,
( spl0_339
<=> ! [X2,X0] : hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X2,X0,X0)),c_Relation_OId(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f4408,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Relation_OId(X0),c_Pair(X1,X1,X0,X0)))
| ~ spl0_228
| ~ spl0_339 ),
inference(resolution,[],[f3807,f2514]) ).
fof(f2514,plain,
( ! [X3,X0,X22] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X22))
| hBOOL(hAPP(X22,X3)) )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f2513]) ).
fof(f3807,plain,
( ! [X2,X0] : hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X2,X0,X0)),c_Relation_OId(X0)))
| ~ spl0_339 ),
inference(avatar_component_clause,[],[f3806]) ).
fof(f15911,plain,
spl0_801,
inference(avatar_split_clause,[],[f1414,f15909]) ).
fof(f15909,plain,
( spl0_801
<=> ! [X22,X0,X15] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X22,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X15,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f1414,plain,
! [X0,X15,X22] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X22,c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X15,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f1413,f459]) ).
fof(f1413,plain,
! [X0,X15,X22] :
( c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X22,c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X15,X15,X0,X0,X0),c_Relation_Orel__comp(X22,X15,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
inference(forward_demodulation,[],[f956,f584]) ).
fof(f956,axiom,
! [X0,X15,X22] :
( ~ c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X15,X15,X0,X0,X0),c_Relation_Orel__comp(X22,X15,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).
fof(f15907,plain,
spl0_800,
inference(avatar_split_clause,[],[f1183,f15905]) ).
fof(f15905,plain,
( spl0_800
<=> ! [X4,X0,X3,X8] :
( ~ c_Relation_Oantisym(X8,X0)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,X3,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f1183,axiom,
! [X3,X0,X8,X4] :
( ~ c_Relation_Oantisym(X8,X0)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,X3,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__def_0) ).
fof(f15903,plain,
spl0_799,
inference(avatar_split_clause,[],[f1056,f15901]) ).
fof(f15901,plain,
( spl0_799
<=> ! [X4,X8,X3,X32] :
( hBOOL(hAPP(X32,X4))
| hBOOL(hAPP(X32,X3))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X8,t_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X4,v_sko__Wellfounded__Xacc__Xinducts__1(X32,X8),t_a,t_a)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f1056,axiom,
! [X3,X8,X4,X32] :
( hBOOL(hAPP(X32,X4))
| hBOOL(hAPP(X32,X3))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X8,t_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X4,v_sko__Wellfounded__Xacc__Xinducts__1(X32,X8),t_a,t_a)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).
fof(f15899,plain,
spl0_798,
inference(avatar_split_clause,[],[f1053,f15897]) ).
fof(f15897,plain,
( spl0_798
<=> ! [X4,X8,X3,X32] :
( hBOOL(hAPP(X32,X4))
| hBOOL(hAPP(X32,X3))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X8,t_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X4,v_sko__Wellfounded__Xacc__Xinduct__1(X32,X8),t_a,t_a)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f1053,axiom,
! [X3,X8,X4,X32] :
( hBOOL(hAPP(X32,X4))
| hBOOL(hAPP(X32,X3))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X8,t_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(t_a,t_a)),c_Pair(X4,v_sko__Wellfounded__Xacc__Xinduct__1(X32,X8),t_a,t_a)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).
fof(f15895,plain,
spl0_797,
inference(avatar_split_clause,[],[f1028,f15893]) ).
fof(f15893,plain,
( spl0_797
<=> ! [X18,X10,X0,X3,X8,X20] :
( c_Recdef_Ocut(X18,X8,X3,X0,X10) = c_Recdef_Ocut(X20,X8,X3,X0,X10)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X18,X20,X8,X3,X0,X10),X3,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f1028,axiom,
! [X3,X10,X0,X18,X8,X20] :
( c_Recdef_Ocut(X18,X8,X3,X0,X10) = c_Recdef_Ocut(X20,X8,X3,X0,X10)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_List_Osko__Recdef__Xcuts__eq__1__1(X18,X20,X8,X3,X0,X10),X3,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_1) ).
fof(f15889,plain,
spl0_796,
inference(avatar_split_clause,[],[f732,f15887]) ).
fof(f732,axiom,
! [X3,X0,X18,X22] :
( ~ c_Finite__Set_Ofinite(X22,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X22))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(X18,X3)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Osetprod(X18,X22,X0,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__pos__nat__iff_0) ).
fof(f15885,plain,
spl0_795,
inference(avatar_split_clause,[],[f657,f15883]) ).
fof(f15883,plain,
( spl0_795
<=> ! [X18,X10,X0,X3,X8,X20] :
( c_Recdef_Ocut(X18,X8,X3,X0,X10) = c_Recdef_Ocut(X20,X8,X3,X0,X10)
| hAPP(X18,c_List_Osko__Recdef__Xcuts__eq__1__1(X18,X20,X8,X3,X0,X10)) != hAPP(X20,c_List_Osko__Recdef__Xcuts__eq__1__1(X18,X20,X8,X3,X0,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f657,axiom,
! [X3,X10,X0,X18,X8,X20] :
( c_Recdef_Ocut(X18,X8,X3,X0,X10) = c_Recdef_Ocut(X20,X8,X3,X0,X10)
| hAPP(X18,c_List_Osko__Recdef__Xcuts__eq__1__1(X18,X20,X8,X3,X0,X10)) != hAPP(X20,c_List_Osko__Recdef__Xcuts__eq__1__1(X18,X20,X8,X3,X0,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_2) ).
fof(f15880,plain,
spl0_794,
inference(avatar_split_clause,[],[f594,f15878]) ).
fof(f594,axiom,
! [X2,X0,X1,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| c_Power_Opower__class_Opower(X2,X14,X0) != c_Power_Opower__class_Opower(X1,X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
fof(f15876,plain,
spl0_793,
inference(avatar_split_clause,[],[f521,f15874]) ).
fof(f15874,plain,
( spl0_793
<=> ! [X6,X0,X10,X15,X7] :
( ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X15,X10,X0),X0,X10)
| c_Relation_OImage(X15,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X10,tc_bool)),X10,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X15,X6,X10,X0),c_Relation_OImage(X15,X7,X10,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f521,axiom,
! [X10,X0,X6,X7,X15] :
( ~ c_Relation_Osingle__valued(c_Relation_Oconverse(X15,X10,X0),X0,X10)
| c_Relation_OImage(X15,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X10,tc_bool)),X10,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X15,X6,X10,X0),c_Relation_OImage(X15,X7,X10,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).
fof(f15872,plain,
spl0_792,
inference(avatar_split_clause,[],[f460,f15870]) ).
fof(f15870,plain,
( spl0_792
<=> ! [X15,X43,X0,X22,X10,X25] : c_Relation_Orel__comp(X15,c_Lattices_Oupper__semilattice__class_Osup(X22,X43,tc_fun(tc_prod(X25,X10),tc_bool)),X0,X25,X10) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X15,X22,X0,X25,X10),c_Relation_Orel__comp(X15,X43,X0,X25,X10),tc_fun(tc_prod(X0,X10),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f460,axiom,
! [X10,X0,X15,X22,X25,X43] : c_Relation_Orel__comp(X15,c_Lattices_Oupper__semilattice__class_Osup(X22,X43,tc_fun(tc_prod(X25,X10),tc_bool)),X0,X25,X10) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X15,X22,X0,X25,X10),c_Relation_Orel__comp(X15,X43,X0,X25,X10),tc_fun(tc_prod(X0,X10),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).
fof(f15868,plain,
( spl0_791
| ~ spl0_252
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3625,f3207,f3014,f15866]) ).
fof(f15866,plain,
( spl0_791
<=> ! [X0,X1] :
( c_Finite__Set_Ofinite(X0,X1)
| c_Finite__Set_Ocard(X0,X1) = c_Orderings_Obot__class_Obot(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f3014,plain,
( spl0_252
<=> ! [X14] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| c_Orderings_Obot__class_Obot(tc_nat) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f3207,plain,
( spl0_292
<=> ! [X6,X0] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_Finite__Set_Ocard(X6,X0)))
| c_Finite__Set_Ofinite(X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f3625,plain,
( ! [X0,X1] :
( c_Finite__Set_Ofinite(X0,X1)
| c_Finite__Set_Ocard(X0,X1) = c_Orderings_Obot__class_Obot(tc_nat) )
| ~ spl0_252
| ~ spl0_292 ),
inference(resolution,[],[f3208,f3015]) ).
fof(f3015,plain,
( ! [X14] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| c_Orderings_Obot__class_Obot(tc_nat) = X14 )
| ~ spl0_252 ),
inference(avatar_component_clause,[],[f3014]) ).
fof(f3208,plain,
( ! [X0,X6] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_Finite__Set_Ocard(X6,X0)))
| c_Finite__Set_Ofinite(X6,X0) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f3207]) ).
fof(f15864,plain,
spl0_790,
inference(avatar_split_clause,[],[f459,f15862]) ).
fof(f15862,plain,
( spl0_790
<=> ! [X43,X0,X22,X10,X25,X15] : c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X22,X43,tc_fun(tc_prod(X0,X25),tc_bool)),X15,X0,X25,X10) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X22,X15,X0,X25,X10),c_Relation_Orel__comp(X43,X15,X0,X25,X10),tc_fun(tc_prod(X0,X10),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f15607,plain,
( spl0_789
| ~ spl0_228
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3017,f2766,f2513,f15605]) ).
fof(f15605,plain,
( spl0_789
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f2766,plain,
( spl0_250
<=> ! [X0,X8,X3] :
( ~ c_Wellfounded_Owf(X8,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X3),c_Wellfounded_Oacc(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f3017,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2)) )
| ~ spl0_228
| ~ spl0_250 ),
inference(resolution,[],[f2767,f2514]) ).
fof(f2767,plain,
( ! [X3,X0,X8] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),c_Wellfounded_Oacc(X8,X0)))
| ~ c_Wellfounded_Owf(X8,X0) )
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2766]) ).
fof(f15439,plain,
( spl0_788
| ~ spl0_57
| ~ spl0_212
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2981,f2752,f2440,f1700,f15437]) ).
fof(f15437,plain,
( spl0_788
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f1700,plain,
( spl0_57
<=> ! [X14] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f2752,plain,
( spl0_247
<=> ! [X45,X46,X31] :
( ~ c_lessequals(X45,X46,tc_nat)
| ~ c_lessequals(X46,X31,tc_nat)
| c_lessequals(X45,X31,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f2981,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_57
| ~ spl0_212
| ~ spl0_247 ),
inference(forward_demodulation,[],[f2960,f2442]) ).
fof(f2960,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_57
| ~ spl0_247 ),
inference(resolution,[],[f2753,f1701]) ).
fof(f1701,plain,
( ! [X14] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1700]) ).
fof(f2753,plain,
( ! [X31,X46,X45] :
( ~ c_lessequals(X46,X31,tc_nat)
| ~ c_lessequals(X45,X46,tc_nat)
| c_lessequals(X45,X31,tc_nat) )
| ~ spl0_247 ),
inference(avatar_component_clause,[],[f2752]) ).
fof(f15435,plain,
spl0_787,
inference(avatar_split_clause,[],[f1385,f15433]) ).
fof(f15433,plain,
( spl0_787
<=> ! [X4,X0,X3,X15] :
( X3 = X4
| hBOOL(hAPP(hAPP(c_in(X0),X3),c_Relation_ORange(c_Relation_Oconverse(X15,X0,X0),X0,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X15,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f1385,plain,
! [X3,X0,X4,X15] :
( X3 = X4
| hBOOL(hAPP(hAPP(c_in(X0),X3),c_Relation_ORange(c_Relation_Oconverse(X15,X0,X0),X0,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X15,X0))) ),
inference(definition_unfolding,[],[f1078,f1146]) ).
fof(f1078,axiom,
! [X3,X0,X4,X15] :
( X3 = X4
| hBOOL(hAPP(hAPP(c_in(X0),X3),c_Relation_ODomain(X15,X0,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X15,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
fof(f15431,plain,
spl0_786,
inference(avatar_split_clause,[],[f1212,f15429]) ).
fof(f15429,plain,
( spl0_786
<=> ! [X10,X0,X8,X6,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_in(X10),X1),c_Relation_OImage(X8,X6,X0,X10)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f1212,axiom,
! [X2,X10,X0,X1,X8,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_in(X10),X1),c_Relation_OImage(X8,X6,X0,X10)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
fof(f15427,plain,
spl0_785,
inference(avatar_split_clause,[],[f1210,f15425]) ).
fof(f15425,plain,
( spl0_785
<=> ! [X0,X8,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Wellfounded_Oacc(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f1210,axiom,
! [X2,X0,X1,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Wellfounded_Oacc(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downward_0) ).
fof(f15423,plain,
spl0_784,
inference(avatar_split_clause,[],[f1001,f15421]) ).
fof(f15421,plain,
( spl0_784
<=> ! [X32,X0,X8,X2,X1] :
( ~ hBOOL(hAPP(X32,X1))
| hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X32,X1,X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f1001,axiom,
! [X2,X0,X1,X8,X32] :
( ~ hBOOL(hAPP(X32,X1))
| hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1(X32,X1,X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).
fof(f15419,plain,
spl0_783,
inference(avatar_split_clause,[],[f999,f15417]) ).
fof(f15417,plain,
( spl0_783
<=> ! [X32,X0,X8,X2,X1] :
( ~ hBOOL(hAPP(X32,X2))
| hBOOL(hAPP(X32,X1))
| hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X32,X2,X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f999,axiom,
! [X2,X0,X1,X8,X32] :
( ~ hBOOL(hAPP(X32,X2))
| hBOOL(hAPP(X32,X1))
| hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1(X32,X2,X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_2) ).
fof(f15415,plain,
spl0_782,
inference(avatar_split_clause,[],[f996,f15413]) ).
fof(f15413,plain,
( spl0_782
<=> ! [X32,X0,X8,X2,X1] :
( ~ hBOOL(hAPP(X32,X2))
| hBOOL(hAPP(X32,X1))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X32,X2,X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f996,axiom,
! [X2,X0,X1,X8,X32] :
( ~ hBOOL(hAPP(X32,X2))
| hBOOL(hAPP(X32,X1))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2(X32,X2,X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_3) ).
fof(f15411,plain,
spl0_781,
inference(avatar_split_clause,[],[f993,f15409]) ).
fof(f15409,plain,
( spl0_781
<=> ! [X32,X0,X8,X2,X1] :
( ~ hBOOL(hAPP(X32,X1))
| hBOOL(hAPP(X32,X2))
| hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X32,X1,X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f993,axiom,
! [X2,X0,X1,X8,X32] :
( ~ hBOOL(hAPP(X32,X1))
| hBOOL(hAPP(X32,X2))
| hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2(X32,X1,X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_2) ).
fof(f15407,plain,
spl0_780,
inference(avatar_split_clause,[],[f920,f15405]) ).
fof(f15405,plain,
( spl0_780
<=> ! [X0,X16,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X16))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f920,axiom,
! [X0,X16,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X16))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X16),X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
fof(f15403,plain,
spl0_779,
inference(avatar_split_clause,[],[f895,f15401]) ).
fof(f15401,plain,
( spl0_779
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f895,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
fof(f15399,plain,
spl0_778,
inference(avatar_split_clause,[],[f894,f15397]) ).
fof(f15397,plain,
( spl0_778
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f894,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
fof(f15368,plain,
spl0_777,
inference(avatar_split_clause,[],[f891,f15366]) ).
fof(f15366,plain,
( spl0_777
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f891,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f15364,plain,
spl0_776,
inference(avatar_split_clause,[],[f888,f15362]) ).
fof(f15362,plain,
( spl0_776
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f888,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
fof(f15360,plain,
spl0_775,
inference(avatar_split_clause,[],[f887,f15358]) ).
fof(f15358,plain,
( spl0_775
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f887,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
fof(f15356,plain,
spl0_774,
inference(avatar_split_clause,[],[f886,f15354]) ).
fof(f15354,plain,
( spl0_774
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f886,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
fof(f15352,plain,
spl0_773,
inference(avatar_split_clause,[],[f877,f15350]) ).
fof(f15350,plain,
( spl0_773
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f877,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f15348,plain,
spl0_772,
inference(avatar_split_clause,[],[f88,f15346]) ).
fof(f15346,plain,
( spl0_772
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f88,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
fof(f15344,plain,
spl0_771,
inference(avatar_split_clause,[],[f87,f15342]) ).
fof(f15342,plain,
( spl0_771
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f87,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
fof(f15340,plain,
spl0_770,
inference(avatar_split_clause,[],[f86,f15338]) ).
fof(f15338,plain,
( spl0_770
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f86,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
fof(f15336,plain,
spl0_769,
inference(avatar_split_clause,[],[f85,f15334]) ).
fof(f15334,plain,
( spl0_769
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f85,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
fof(f15267,plain,
( ~ spl0_21
| spl0_768
| ~ spl0_57
| ~ spl0_212
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2871,f2723,f2440,f1700,f15265,f1524]) ).
fof(f1524,plain,
( spl0_21
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f2723,plain,
( spl0_240
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X3,X4,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f2871,plain,
( ! [X0] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat) = X0
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_57
| ~ spl0_212
| ~ spl0_240 ),
inference(forward_demodulation,[],[f2846,f2442]) ).
fof(f2846,plain,
( ! [X0] :
( ~ class_Lattices_Oupper__semilattice(tc_nat)
| c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0 )
| ~ spl0_57
| ~ spl0_240 ),
inference(resolution,[],[f2724,f1701]) ).
fof(f2724,plain,
( ! [X3,X0,X4] :
( ~ c_lessequals(X3,X4,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = X4 )
| ~ spl0_240 ),
inference(avatar_component_clause,[],[f2723]) ).
fof(f14935,plain,
spl0_767,
inference(avatar_split_clause,[],[f1372,f14933]) ).
fof(f14933,plain,
( spl0_767
<=> ! [X0,X8,X10,X2] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Relation_ORange(c_Relation_Oconverse(X8,X0,X10),X10,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X2,X8,X0,X10),X0,X10)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f1372,plain,
! [X2,X10,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Relation_ORange(c_Relation_Oconverse(X8,X0,X10),X10,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X2,X8,X0,X10),X0,X10)),X8)) ),
inference(definition_unfolding,[],[f1049,f1146]) ).
fof(f1049,axiom,
! [X2,X10,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Relation_ODomain(X8,X0,X10)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,c_ATP__Linkup_Osko__Relation__XDomainE__1__1(X2,X8,X0,X10),X0,X10)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).
fof(f14931,plain,
spl0_766,
inference(avatar_split_clause,[],[f1371,f14929]) ).
fof(f14929,plain,
( spl0_766
<=> ! [X0,X8,X10,X2] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Relation_ORange(c_Relation_Oconverse(X8,X0,X10),X10,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X2,X8,X0,X10),X0,X10)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f1371,plain,
! [X2,X10,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Relation_ORange(c_Relation_Oconverse(X8,X0,X10),X10,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X2,X8,X0,X10),X0,X10)),X8)) ),
inference(definition_unfolding,[],[f1050,f1146]) ).
fof(f1050,axiom,
! [X2,X10,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Relation_ODomain(X8,X0,X10)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1(X2,X8,X0,X10),X0,X10)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).
fof(f14927,plain,
spl0_765,
inference(avatar_split_clause,[],[f1060,f14925]) ).
fof(f14925,plain,
( spl0_765
<=> ! [X4,X0,X3,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X4,X3,X0,X0),X8,tc_prod(X0,X0)),X0)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f1060,axiom,
! [X3,X0,X8,X4] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X4,X3,X0,X0),X8,tc_prod(X0,X0)),X0)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_2) ).
fof(f14923,plain,
spl0_764,
inference(avatar_split_clause,[],[f978,f14921]) ).
fof(f14921,plain,
( spl0_764
<=> ! [X13,X0,X14,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X14),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X2,X13,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f978,axiom,
! [X2,X0,X14,X13] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X14),X13))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X2,X13,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
fof(f14919,plain,
spl0_763,
inference(avatar_split_clause,[],[f977,f14917]) ).
fof(f14917,plain,
( spl0_763
<=> ! [X0,X14,X16,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X16,X0)),c_Power_Opower__class_Opower(X2,X14,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f977,axiom,
! [X2,X0,X16,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X16,X0)),c_Power_Opower__class_Opower(X2,X14,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
fof(f14915,plain,
( ~ spl0_21
| spl0_762
| ~ spl0_57
| ~ spl0_212
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2822,f2715,f2440,f1700,f14913,f1524]) ).
fof(f14913,plain,
( spl0_762
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f2715,plain,
( spl0_238
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X4,X3,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f2822,plain,
( ! [X0] :
( c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X0
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_57
| ~ spl0_212
| ~ spl0_238 ),
inference(forward_demodulation,[],[f2798,f2442]) ).
fof(f2798,plain,
( ! [X0] :
( ~ class_Lattices_Oupper__semilattice(tc_nat)
| c_Lattices_Oupper__semilattice__class_Osup(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 )
| ~ spl0_57
| ~ spl0_238 ),
inference(resolution,[],[f2716,f1701]) ).
fof(f2716,plain,
( ! [X3,X0,X4] :
( ~ c_lessequals(X4,X3,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = X3 )
| ~ spl0_238 ),
inference(avatar_component_clause,[],[f2715]) ).
fof(f14911,plain,
spl0_761,
inference(avatar_split_clause,[],[f935,f14909]) ).
fof(f14909,plain,
( spl0_761
<=> ! [X2,X0,X8,X10,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(X2,X1,X10,X0)),X8))
| hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),X10,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f935,axiom,
! [X2,X10,X0,X1,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(X2,X1,X10,X0)),X8))
| hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),X10,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
fof(f14907,plain,
spl0_760,
inference(avatar_split_clause,[],[f934,f14905]) ).
fof(f14905,plain,
( spl0_760
<=> ! [X2,X0,X8,X10,X1] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(X2,X1,X10,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),X10,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f934,axiom,
! [X2,X10,X0,X1,X8] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(X2,X1,X10,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),X10,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
fof(f14903,plain,
spl0_759,
inference(avatar_split_clause,[],[f933,f14901]) ).
fof(f14901,plain,
( spl0_759
<=> ! [X22,X0,X15] :
( ~ c_lessequals(X15,X22,tc_fun(X0,tc_bool))
| c_lessequals(hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X15),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X22),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f933,axiom,
! [X0,X15,X22] :
( ~ c_lessequals(X15,X22,tc_fun(X0,tc_bool))
| c_lessequals(hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X15),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X22),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_1) ).
fof(f14899,plain,
spl0_758,
inference(avatar_split_clause,[],[f932,f14897]) ).
fof(f14897,plain,
( spl0_758
<=> ! [X22,X0,X15] :
( c_lessequals(X15,X22,tc_fun(X0,tc_bool))
| ~ c_lessequals(hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X15),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X22),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f932,axiom,
! [X0,X15,X22] :
( c_lessequals(X15,X22,tc_fun(X0,tc_bool))
| ~ c_lessequals(hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X15),hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X22),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).
fof(f14895,plain,
spl0_757,
inference(avatar_split_clause,[],[f928,f14893]) ).
fof(f14893,plain,
( spl0_757
<=> ! [X18,X10,X0,X6,X8] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X8),hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),X18),X6)) = hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X0),X8),X18,X0,X0,X10)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f928,axiom,
! [X10,X0,X18,X8,X6] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X8),hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),X18),X6)) = hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X0),X8),X18,X0,X0,X10)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__right__distrib_0) ).
fof(f14891,plain,
spl0_756,
inference(avatar_split_clause,[],[f774,f14889]) ).
fof(f14889,plain,
( spl0_756
<=> ! [X2,X0,X12,X5,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X5,X12,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f774,axiom,
! [X2,X0,X1,X5,X12] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X5,X12,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
fof(f14887,plain,
spl0_755,
inference(avatar_split_clause,[],[f773,f14885]) ).
fof(f14885,plain,
( spl0_755
<=> ! [X5,X0,X12,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f773,axiom,
! [X2,X0,X1,X5,X12] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
fof(f14883,plain,
spl0_754,
inference(avatar_split_clause,[],[f736,f14881]) ).
fof(f14881,plain,
( spl0_754
<=> ! [X4,X0,X3,X8] :
( ~ c_Wellfounded_Oacyclic(X8,X0)
| c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X4,X3,X0,X0),X8,tc_prod(X0,X0)),X0)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f736,axiom,
! [X3,X0,X8,X4] :
( ~ c_Wellfounded_Oacyclic(X8,X0)
| c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X4,X3,X0,X0),X8,tc_prod(X0,X0)),X0)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).
fof(f14879,plain,
spl0_753,
inference(avatar_split_clause,[],[f726,f14877]) ).
fof(f14877,plain,
( spl0_753
<=> ! [X4,X0,X23,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X23)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f726,axiom,
! [X3,X0,X4,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X23)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
fof(f14875,plain,
spl0_752,
inference(avatar_split_clause,[],[f725,f14873]) ).
fof(f14873,plain,
( spl0_752
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f725,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
fof(f14871,plain,
( spl0_751
| ~ spl0_192
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2644,f2453,f2360,f14869]) ).
fof(f14869,plain,
( spl0_751
<=> ! [X0,X1] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f2360,plain,
( spl0_192
<=> ! [X6,X0] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f2453,plain,
( spl0_215
<=> ! [X0,X24,X19] :
( ~ c_Finite__Set_Ofinite(X24,X0)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X19,X24,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f2644,plain,
( ! [X0,X1] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X1) )
| ~ spl0_192
| ~ spl0_215 ),
inference(superposition,[],[f2454,f2361]) ).
fof(f2361,plain,
( ! [X0,X6] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f2360]) ).
fof(f2454,plain,
( ! [X0,X19,X24] :
( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X19,X24,tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(X24,X0) )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f2453]) ).
fof(f14867,plain,
spl0_750,
inference(avatar_split_clause,[],[f724,f14865]) ).
fof(f14865,plain,
( spl0_750
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f724,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f14746,plain,
( spl0_749
| ~ spl0_441
| ~ spl0_593
| ~ spl0_746 ),
inference(avatar_split_clause,[],[f14073,f14069,f9289,f5544,f14744]) ).
fof(f14744,plain,
( spl0_749
<=> ! [X0,X8] : c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_Orel__comp(X8,c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f5544,plain,
( spl0_441
<=> ! [X0,X8] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X8,X0),X8,X0,X0,X0) = c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f9289,plain,
( spl0_593
<=> ! [X15,X43,X0,X64,X22,X10,X25] : c_Relation_Orel__comp(c_Relation_Orel__comp(X15,X22,X0,X64,X25),X43,X0,X25,X10) = c_Relation_Orel__comp(X15,c_Relation_Orel__comp(X22,X43,X64,X25,X10),X0,X64,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f14069,plain,
( spl0_746
<=> ! [X0,X8] : c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_Orel__comp(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X8,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f14073,plain,
( ! [X0,X8] : c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_Orel__comp(X8,c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool))
| ~ spl0_441
| ~ spl0_593
| ~ spl0_746 ),
inference(forward_demodulation,[],[f14072,f5545]) ).
fof(f5545,plain,
( ! [X0,X8] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X8,X0),X8,X0,X0,X0) = c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)
| ~ spl0_441 ),
inference(avatar_component_clause,[],[f5544]) ).
fof(f14072,plain,
( ! [X0,X8] : c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_Orel__comp(X8,c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X8,X0),X8,X0,X0,X0),X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool))
| ~ spl0_593
| ~ spl0_746 ),
inference(forward_demodulation,[],[f14070,f9290]) ).
fof(f9290,plain,
( ! [X10,X0,X15,X22,X25,X43,X64] : c_Relation_Orel__comp(c_Relation_Orel__comp(X15,X22,X0,X64,X25),X43,X0,X25,X10) = c_Relation_Orel__comp(X15,c_Relation_Orel__comp(X22,X43,X64,X25,X10),X0,X64,X10)
| ~ spl0_593 ),
inference(avatar_component_clause,[],[f9289]) ).
fof(f14070,plain,
( ! [X0,X8] : c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_Orel__comp(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X8,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool))
| ~ spl0_746 ),
inference(avatar_component_clause,[],[f14069]) ).
fof(f14519,plain,
( spl0_748
| ~ spl0_45
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2641,f2449,f1644,f14517]) ).
fof(f14517,plain,
( spl0_748
<=> ! [X0] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f1644,plain,
( spl0_45
<=> class_Lattices_Oboolean__algebra(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f2449,plain,
( spl0_214
<=> ! [X0,X3] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f2641,plain,
( ! [X0] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X0)) = X0
| ~ spl0_45
| ~ spl0_214 ),
inference(resolution,[],[f2450,f1646]) ).
fof(f1646,plain,
( class_Lattices_Oboolean__algebra(tc_bool)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f1644]) ).
fof(f2450,plain,
( ! [X3,X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3)) = X3 )
| ~ spl0_214 ),
inference(avatar_component_clause,[],[f2449]) ).
fof(f14352,plain,
( spl0_747
| ~ spl0_212
| ~ spl0_735 ),
inference(avatar_split_clause,[],[f14027,f14024,f2440,f14350]) ).
fof(f14350,plain,
( spl0_747
<=> ! [X2,X0,X14] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),c_Power_Opower__class_Opower(X2,X14,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f14024,plain,
( spl0_735
<=> ! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),c_Power_Opower__class_Opower(X2,X14,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f14027,plain,
( ! [X2,X0,X14] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),c_Power_Opower__class_Opower(X2,X14,X0))) )
| ~ spl0_212
| ~ spl0_735 ),
inference(forward_demodulation,[],[f14025,f2442]) ).
fof(f14025,plain,
( ! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),c_Power_Opower__class_Opower(X2,X14,X0))) )
| ~ spl0_735 ),
inference(avatar_component_clause,[],[f14024]) ).
fof(f14071,plain,
spl0_746,
inference(avatar_split_clause,[],[f1361,f14069]) ).
fof(f1361,plain,
! [X0,X8] : c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_Orel__comp(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X8,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),
inference(definition_unfolding,[],[f958,f1163,f1163]) ).
fof(f958,axiom,
! [X0,X8] : c_Transitive__Closure_Otrancl(X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(X8,X0),X8,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).
fof(f14067,plain,
spl0_745,
inference(avatar_split_clause,[],[f1194,f14065]) ).
fof(f14065,plain,
( spl0_745
<=> ! [X0,X8,X2,X1] :
( ~ c_Relation_Osym(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X2,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f1194,axiom,
! [X2,X0,X1,X8] :
( ~ c_Relation_Osym(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X2,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symD_0) ).
fof(f14063,plain,
( spl0_744
| ~ spl0_19
| ~ spl0_208
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2628,f2440,f2424,f1514,f14061]) ).
fof(f14061,plain,
( spl0_744
<=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f1514,plain,
( spl0_19
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f2424,plain,
( spl0_208
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f2628,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat)) = X0
| ~ spl0_19
| ~ spl0_208
| ~ spl0_212 ),
inference(forward_demodulation,[],[f2627,f2442]) ).
fof(f2627,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = X0
| ~ spl0_19
| ~ spl0_208 ),
inference(resolution,[],[f2425,f1516]) ).
fof(f1516,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f1514]) ).
fof(f2425,plain,
( ! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 )
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f2424]) ).
fof(f14059,plain,
spl0_743,
inference(avatar_split_clause,[],[f1182,f14057]) ).
fof(f14057,plain,
( spl0_743
<=> ! [X0,X8,X3,X2] :
( ~ c_Wellfounded_Owf(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X3,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X2,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f1182,axiom,
! [X2,X3,X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X3,X0,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X2,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).
fof(f14055,plain,
spl0_742,
inference(avatar_split_clause,[],[f1172,f14053]) ).
fof(f14053,plain,
( spl0_742
<=> ! [X0,X8,X10,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(X1,X2,X10,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),c_Relation_Oconverse(X8,X10,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f1172,axiom,
! [X2,X10,X0,X1,X8] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(X1,X2,X10,X0)),X8))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),c_Relation_Oconverse(X8,X10,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).
fof(f14051,plain,
spl0_741,
inference(avatar_split_clause,[],[f1071,f14049]) ).
fof(f14049,plain,
( spl0_741
<=> ! [X2,X0,X8,X10,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(X1,X2,X10,X0)),c_Relation_Oconverse(X8,X0,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f1071,axiom,
! [X2,X10,X0,X1,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(X1,X2,X10,X0)),c_Relation_Oconverse(X8,X0,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseI_0) ).
fof(f14047,plain,
spl0_740,
inference(avatar_split_clause,[],[f1047,f14045]) ).
fof(f14045,plain,
( spl0_740
<=> ! [X10,X0,X6,X8,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_OImage(X8,X6,X10,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X6,X1,X8,X10,X0),X1,X10,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f1047,axiom,
! [X10,X0,X1,X8,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_OImage(X8,X6,X10,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X6,X1,X8,X10,X0),X1,X10,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).
fof(f14043,plain,
spl0_739,
inference(avatar_split_clause,[],[f1046,f14041]) ).
fof(f14041,plain,
( spl0_739
<=> ! [X10,X0,X6,X8,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_OImage(X8,X6,X10,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X6,X1,X8,X10,X0),X1,X10,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f1046,axiom,
! [X10,X0,X1,X8,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_OImage(X8,X6,X10,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X6,X1,X8,X10,X0),X1,X10,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).
fof(f14039,plain,
spl0_738,
inference(avatar_split_clause,[],[f942,f14037]) ).
fof(f14037,plain,
( spl0_738
<=> ! [X15,X0,X3,X22] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X3),c_Transitive__Closure_Ortrancl(X22,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X3),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f942,axiom,
! [X3,X0,X15,X22] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X3),c_Transitive__Closure_Ortrancl(X22,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X3),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).
fof(f14035,plain,
spl0_737,
inference(avatar_split_clause,[],[f941,f14033]) ).
fof(f14033,plain,
( spl0_737
<=> ! [X15,X0,X3,X22] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X3),c_Transitive__Closure_Ortrancl(X15,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X3),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f941,axiom,
! [X3,X0,X15,X22] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X3),c_Transitive__Closure_Ortrancl(X15,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X3),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).
fof(f14031,plain,
spl0_736,
inference(avatar_split_clause,[],[f897,f14029]) ).
fof(f14029,plain,
( spl0_736
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f897,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f14026,plain,
spl0_735,
inference(avatar_split_clause,[],[f733,f14024]) ).
fof(f733,axiom,
! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),c_Power_Opower__class_Opower(X2,X14,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).
fof(f14022,plain,
spl0_734,
inference(avatar_split_clause,[],[f689,f14020]) ).
fof(f14020,plain,
( spl0_734
<=> ! [X18,X0,X10,X2,X7] : c_Set_Ovimage(X18,c_Set_Oinsert(X2,X7,X10),X0,X10) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X18,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),X0,X10),c_Set_Ovimage(X18,X7,X0,X10),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f689,axiom,
! [X2,X10,X0,X18,X7] : c_Set_Ovimage(X18,c_Set_Oinsert(X2,X7,X10),X0,X10) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X18,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),X0,X10),c_Set_Ovimage(X18,X7,X0,X10),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
fof(f14018,plain,
( spl0_733
| ~ spl0_19
| ~ spl0_207
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2626,f2440,f2420,f1514,f14016]) ).
fof(f14016,plain,
( spl0_733
<=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f2420,plain,
( spl0_207
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f2626,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0) = X0
| ~ spl0_19
| ~ spl0_207
| ~ spl0_212 ),
inference(forward_demodulation,[],[f2625,f2442]) ).
fof(f2625,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X0) = X0
| ~ spl0_19
| ~ spl0_207 ),
inference(resolution,[],[f2421,f1516]) ).
fof(f2421,plain,
( ! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) = X2 )
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f2420]) ).
fof(f14014,plain,
spl0_732,
inference(avatar_split_clause,[],[f127,f14012]) ).
fof(f14012,plain,
( spl0_732
<=> ! [X22,X0,X15] :
( ~ c_Wellfounded_Owf(X15,X0)
| ~ c_Wellfounded_Owf(X22,X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_lessequals(c_Relation_Orel__comp(X15,X22,X0,X0,X0),X15,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f127,axiom,
! [X0,X15,X22] :
( ~ c_Wellfounded_Owf(X15,X0)
| ~ c_Wellfounded_Owf(X22,X0)
| c_Wellfounded_Owf(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ c_lessequals(c_Relation_Orel__comp(X15,X22,X0,X0,X0),X15,tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).
fof(f14010,plain,
spl0_731,
inference(avatar_split_clause,[],[f101,f14008]) ).
fof(f14008,plain,
( spl0_731
<=> ! [X0,X6,X21,X7] :
( ~ c_lessequals(X21,X6,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X21,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f101,axiom,
! [X21,X0,X6,X7] :
( ~ c_lessequals(X21,X6,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X21,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
fof(f14006,plain,
spl0_730,
inference(avatar_split_clause,[],[f100,f14004]) ).
fof(f14004,plain,
( spl0_730
<=> ! [X0,X6,X21,X7] :
( c_lessequals(X21,X6,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X21,tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f100,axiom,
! [X21,X0,X6,X7] :
( c_lessequals(X21,X6,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X21,tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
fof(f13680,plain,
( spl0_729
| ~ spl0_41
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2620,f2412,f1624,f13678]) ).
fof(f13678,plain,
( spl0_729
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f1624,plain,
( spl0_41
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f2412,plain,
( spl0_205
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f2620,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool)
| ~ spl0_41
| ~ spl0_205 ),
inference(resolution,[],[f2413,f1626]) ).
fof(f1626,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f1624]) ).
fof(f2413,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0) )
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f2412]) ).
fof(f12945,plain,
( spl0_728
| ~ spl0_21
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2619,f2412,f1524,f12943]) ).
fof(f12943,plain,
( spl0_728
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f2619,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_nat)
| ~ spl0_21
| ~ spl0_205 ),
inference(resolution,[],[f2413,f1526]) ).
fof(f1526,plain,
( class_Lattices_Oupper__semilattice(tc_nat)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f1524]) ).
fof(f12670,plain,
( spl0_727
| ~ spl0_367
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f12666,f12663,f4546,f12668]) ).
fof(f12668,plain,
( spl0_727
<=> ! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f4546,plain,
( spl0_367
<=> ! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X15,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f12663,plain,
( spl0_726
<=> ! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f12666,plain,
( ! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0)
| ~ spl0_367
| ~ spl0_726 ),
inference(forward_demodulation,[],[f12664,f4547]) ).
fof(f4547,plain,
( ! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X15,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_367 ),
inference(avatar_component_clause,[],[f4546]) ).
fof(f12664,plain,
( ! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),X0,X0,X0)
| ~ spl0_726 ),
inference(avatar_component_clause,[],[f12663]) ).
fof(f12665,plain,
spl0_726,
inference(avatar_split_clause,[],[f1347,f12663]) ).
fof(f1347,plain,
! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),X0,X0,X0),
inference(definition_unfolding,[],[f1030,f1163]) ).
fof(f1030,axiom,
! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).
fof(f12661,plain,
spl0_725,
inference(avatar_split_clause,[],[f981,f12659]) ).
fof(f12659,plain,
( spl0_725
<=> ! [X18,X10,X0,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X10)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),c_HOL_Ozero__class_Ozero(X10)),c_Finite__Set_Osetprod(X18,X6,X0,X10)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),c_HOL_Ozero__class_Ozero(X10)),hAPP(X18,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1(X6,X18,X0,X10)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f981,axiom,
! [X10,X0,X18,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X10)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),c_HOL_Ozero__class_Ozero(X10)),c_Finite__Set_Osetprod(X18,X6,X0,X10)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),c_HOL_Ozero__class_Ozero(X10)),hAPP(X18,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1(X6,X18,X0,X10)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__pos_1) ).
fof(f12657,plain,
spl0_724,
inference(avatar_split_clause,[],[f740,f12655]) ).
fof(f12655,plain,
( spl0_724
<=> ! [X0,X8,X6,X2] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X2),c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f740,axiom,
! [X2,X0,X8,X6] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X2),c_Relation_OImage(X8,c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
fof(f12653,plain,
( spl0_723
| ~ spl0_42
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2594,f2384,f1629,f12651]) ).
fof(f12651,plain,
( spl0_723
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f1629,plain,
( spl0_42
<=> class_Lattices_Olower__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f2384,plain,
( spl0_198
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2594,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool)
| ~ spl0_42
| ~ spl0_198 ),
inference(resolution,[],[f2385,f1631]) ).
fof(f1631,plain,
( class_Lattices_Olower__semilattice(tc_bool)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f1629]) ).
fof(f2385,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f2384]) ).
fof(f12649,plain,
spl0_722,
inference(avatar_split_clause,[],[f716,f12647]) ).
fof(f12647,plain,
( spl0_722
<=> ! [X10,X53,X0,X6,X33,X8] :
( ~ c_lessequals(X53,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X33,X8,tc_fun(tc_prod(X0,X10),tc_bool))
| c_lessequals(c_Relation_OImage(X33,X53,X0,X10),c_Relation_OImage(X8,X6,X0,X10),tc_fun(X10,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f716,axiom,
! [X10,X0,X8,X6,X53,X33] :
( ~ c_lessequals(X53,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X33,X8,tc_fun(tc_prod(X0,X10),tc_bool))
| c_lessequals(c_Relation_OImage(X33,X53,X0,X10),c_Relation_OImage(X8,X6,X0,X10),tc_fun(X10,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__mono_0) ).
fof(f12645,plain,
spl0_721,
inference(avatar_split_clause,[],[f680,f12643]) ).
fof(f12643,plain,
( spl0_721
<=> ! [X44,X0,X6,X21,X7] :
( ~ c_lessequals(X6,X21,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X44,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X21,X44,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f680,axiom,
! [X21,X0,X6,X44,X7] :
( ~ c_lessequals(X6,X21,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X44,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X21,X44,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
fof(f12641,plain,
spl0_720,
inference(avatar_split_clause,[],[f605,f12639]) ).
fof(f12639,plain,
( spl0_720
<=> ! [X6,X0,X7] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f605,axiom,
! [X0,X6,X7] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Un_0) ).
fof(f12637,plain,
spl0_719,
inference(avatar_split_clause,[],[f587,f12635]) ).
fof(f12635,plain,
( spl0_719
<=> ! [X6,X0,X7] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f587,axiom,
! [X0,X6,X7] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Int_0) ).
fof(f12633,plain,
spl0_718,
inference(avatar_split_clause,[],[f523,f12631]) ).
fof(f12631,plain,
( spl0_718
<=> ! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X14,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Power_Opower__class_Opower(X2,X14,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f523,axiom,
! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X14,X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Power_Opower__class_Opower(X2,X14,X0)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
fof(f12629,plain,
spl0_717,
inference(avatar_split_clause,[],[f507,f12627]) ).
fof(f12627,plain,
( spl0_717
<=> ! [X0,X6,X21,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X21,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f507,axiom,
! [X21,X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X21,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
fof(f12625,plain,
spl0_716,
inference(avatar_split_clause,[],[f506,f12623]) ).
fof(f506,axiom,
! [X21,X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X6,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
fof(f12621,plain,
spl0_715,
inference(avatar_split_clause,[],[f475,f12619]) ).
fof(f12619,plain,
( spl0_715
<=> ! [X44,X0,X6,X21,X7] :
( ~ c_lessequals(X6,X21,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X44,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X21,X44,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f475,axiom,
! [X21,X0,X6,X44,X7] :
( ~ c_lessequals(X6,X21,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X44,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X21,X44,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
fof(f12617,plain,
spl0_714,
inference(avatar_split_clause,[],[f424,f12615]) ).
fof(f12615,plain,
( spl0_714
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f424,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
fof(f12613,plain,
spl0_713,
inference(avatar_split_clause,[],[f423,f12611]) ).
fof(f12611,plain,
( spl0_713
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f423,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
fof(f12609,plain,
( spl0_712
| ~ spl0_22
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2593,f2384,f1529,f12607]) ).
fof(f1529,plain,
( spl0_22
<=> class_Lattices_Olower__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f2593,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_nat)
| ~ spl0_22
| ~ spl0_198 ),
inference(resolution,[],[f2385,f1531]) ).
fof(f1531,plain,
( class_Lattices_Olower__semilattice(tc_nat)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1529]) ).
fof(f12605,plain,
spl0_711,
inference(avatar_split_clause,[],[f264,f12603]) ).
fof(f12603,plain,
( spl0_711
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X2,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f264,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X2,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
fof(f12601,plain,
spl0_710,
inference(avatar_split_clause,[],[f263,f12599]) ).
fof(f12599,plain,
( spl0_710
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X2,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f263,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X2,X1,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
fof(f12597,plain,
spl0_709,
inference(avatar_split_clause,[],[f251,f12595]) ).
fof(f12595,plain,
( spl0_709
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f251,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X5))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
fof(f12593,plain,
spl0_708,
inference(avatar_split_clause,[],[f205,f12591]) ).
fof(f12591,plain,
( spl0_708
<=> ! [X0,X6,X21,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f205,axiom,
! [X21,X0,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X6,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
fof(f12589,plain,
spl0_707,
inference(avatar_split_clause,[],[f204,f12587]) ).
fof(f204,axiom,
! [X21,X0,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_fun(X0,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X21,X6,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
fof(f12585,plain,
spl0_706,
inference(avatar_split_clause,[],[f182,f12583]) ).
fof(f12583,plain,
( spl0_706
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X1,X5,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f182,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X1,X5,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
fof(f12581,plain,
spl0_705,
inference(avatar_split_clause,[],[f155,f12579]) ).
fof(f12579,plain,
( spl0_705
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f155,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
fof(f12577,plain,
spl0_704,
inference(avatar_split_clause,[],[f154,f12575]) ).
fof(f12575,plain,
( spl0_704
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f154,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
fof(f12573,plain,
spl0_703,
inference(avatar_split_clause,[],[f99,f12571]) ).
fof(f12571,plain,
( spl0_703
<=> ! [X6,X0,X10,X15,X7] : c_lessequals(c_Relation_OImage(X15,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X10,tc_bool)),X10,X0),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X15,X6,X10,X0),c_Relation_OImage(X15,X7,X10,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f99,axiom,
! [X10,X0,X6,X7,X15] : c_lessequals(c_Relation_OImage(X15,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X10,tc_bool)),X10,X0),c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(X15,X6,X10,X0),c_Relation_OImage(X15,X7,X10,X0),tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
fof(f12569,plain,
spl0_702,
inference(avatar_split_clause,[],[f59,f12567]) ).
fof(f12567,plain,
( spl0_702
<=> ! [X22,X0,X15] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X15,X0),c_Transitive__Closure_Ortrancl(X22,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f59,axiom,
! [X0,X15,X22] : c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X15,X0),c_Transitive__Closure_Ortrancl(X22,X0),tc_fun(tc_prod(X0,X0),tc_bool)),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0),tc_fun(tc_prod(X0,X0),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).
fof(f12565,plain,
( spl0_701
| ~ spl0_48
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2585,f2372,f1659,f12563]) ).
fof(f12563,plain,
( spl0_701
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f1659,plain,
( spl0_48
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f2372,plain,
( spl0_195
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f2585,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = X0
| ~ spl0_48
| ~ spl0_195 ),
inference(resolution,[],[f2373,f1661]) ).
fof(f1661,plain,
( class_Lattices_Olattice(tc_bool)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1659]) ).
fof(f2373,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) = X3 )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f2372]) ).
fof(f12282,plain,
( spl0_700
| ~ spl0_36
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2584,f2372,f1599,f12280]) ).
fof(f12280,plain,
( spl0_700
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f1599,plain,
( spl0_36
<=> class_Lattices_Olattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f2584,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_36
| ~ spl0_195 ),
inference(resolution,[],[f2373,f1601]) ).
fof(f1601,plain,
( class_Lattices_Olattice(tc_nat)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1599]) ).
fof(f12106,plain,
spl0_699,
inference(avatar_split_clause,[],[f1362,f12104]) ).
fof(f12104,plain,
( spl0_699
<=> ! [X0,X8,X10,X2,X1] : c_Relation_ORange(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X2,X1,X0,X10),X8,tc_prod(X0,X10)),X0,X10),X10,X0) = c_Set_Oinsert(X2,c_Relation_ORange(c_Relation_Oconverse(X8,X0,X10),X10,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f1362,plain,
! [X2,X10,X0,X1,X8] : c_Relation_ORange(c_Relation_Oconverse(c_Set_Oinsert(c_Pair(X2,X1,X0,X10),X8,tc_prod(X0,X10)),X0,X10),X10,X0) = c_Set_Oinsert(X2,c_Relation_ORange(c_Relation_Oconverse(X8,X0,X10),X10,X0),X0),
inference(definition_unfolding,[],[f17,f1146,f1146]) ).
fof(f17,axiom,
! [X2,X10,X0,X1,X8] : c_Relation_ODomain(c_Set_Oinsert(c_Pair(X2,X1,X0,X10),X8,tc_prod(X0,X10)),X0,X10) = c_Set_Oinsert(X2,c_Relation_ODomain(X8,X0,X10),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__insert_0) ).
fof(f12102,plain,
spl0_698,
inference(avatar_split_clause,[],[f1229,f12100]) ).
fof(f12100,plain,
( spl0_698
<=> ! [X18,X4,X0,X3,X15] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X18,X3)),hAPP(X18,X4)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Wellfounded_Omlex__prod(X18,X15,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f1229,axiom,
! [X3,X0,X18,X4,X15] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X18,X3)),hAPP(X18,X4)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Wellfounded_Omlex__prod(X18,X15,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mlex__less_0) ).
fof(f12098,plain,
spl0_697,
inference(avatar_split_clause,[],[f1062,f12096]) ).
fof(f12096,plain,
( spl0_697
<=> ! [X0,X8,X10,X2] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Relation_ORange(X8,X10,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X2,X8,X0,X10),X2,X10,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f1062,axiom,
! [X2,X10,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Relation_ORange(X8,X10,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1(X2,X8,X0,X10),X2,X10,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).
fof(f12094,plain,
spl0_696,
inference(avatar_split_clause,[],[f1061,f12092]) ).
fof(f12092,plain,
( spl0_696
<=> ! [X0,X8,X10,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_ORange(X8,X10,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,X8,X0,X10),X1,X10,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f1061,axiom,
! [X10,X0,X1,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_ORange(X8,X10,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X0)),c_Pair(c_ATP__Linkup_Osko__Relation__XRangeE__1__1(X1,X8,X0,X10),X1,X10,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).
fof(f12090,plain,
( spl0_695
| ~ spl0_48
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2560,f2364,f1659,f12088]) ).
fof(f12088,plain,
( spl0_695
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f2364,plain,
( spl0_193
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f2560,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool) = X0
| ~ spl0_48
| ~ spl0_193 ),
inference(resolution,[],[f2365,f1661]) ).
fof(f2365,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) = X3 )
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f2364]) ).
fof(f12086,plain,
spl0_694,
inference(avatar_split_clause,[],[f1059,f12084]) ).
fof(f12084,plain,
( spl0_694
<=> ! [X4,X0,X3,X8] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X4,X3,X0,X0),X8,tc_prod(X0,X0)),X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f1059,axiom,
! [X3,X0,X8,X4] :
( ~ c_Wellfounded_Owf(c_Set_Oinsert(c_Pair(X4,X3,X0,X0),X8,tc_prod(X0,X0)),X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).
fof(f12082,plain,
spl0_693,
inference(avatar_split_clause,[],[f1006,f12080]) ).
fof(f12080,plain,
( spl0_693
<=> ! [X4,X32,X0,X8,X2] :
( ~ c_Wellfounded_Owf(X8,X0)
| hBOOL(hAPP(X32,X2))
| hBOOL(hAPP(X32,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X32,X8,X0),X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f1006,axiom,
! [X2,X0,X8,X4,X32] :
( ~ c_Wellfounded_Owf(X8,X0)
| hBOOL(hAPP(X32,X2))
| hBOOL(hAPP(X32,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X32,X8,X0),X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_0) ).
fof(f12078,plain,
spl0_692,
inference(avatar_split_clause,[],[f1005,f12076]) ).
fof(f12076,plain,
( spl0_692
<=> ! [X15,X62,X4,X0,X32] :
( ~ c_Wellfounded_Owf(X15,X0)
| hBOOL(hAPP(X32,X62))
| hBOOL(hAPP(X32,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X32,X15,X0),X0,X0)),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f1005,axiom,
! [X0,X62,X4,X15,X32] :
( ~ c_Wellfounded_Owf(X15,X0)
| hBOOL(hAPP(X32,X62))
| hBOOL(hAPP(X32,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X32,X15,X0),X0,X0)),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).
fof(f12074,plain,
spl0_691,
inference(avatar_split_clause,[],[f1004,f12072]) ).
fof(f12072,plain,
( spl0_691
<=> ! [X37,X4,X0,X8,X32] :
( ~ c_Wellfounded_Owf(X8,X0)
| hBOOL(hAPP(X32,X37))
| hBOOL(hAPP(X32,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X32,X8,X0),X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f1004,axiom,
! [X0,X8,X37,X4,X32] :
( ~ c_Wellfounded_Owf(X8,X0)
| hBOOL(hAPP(X32,X37))
| hBOOL(hAPP(X32,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X32,X8,X0),X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_0) ).
fof(f12070,plain,
spl0_690,
inference(avatar_split_clause,[],[f1003,f12068]) ).
fof(f12068,plain,
( spl0_690
<=> ! [X4,X32,X0,X8,X2] :
( ~ c_Wellfounded_Owf(X8,X0)
| hBOOL(hAPP(X32,X2))
| hBOOL(hAPP(X32,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X32,X8,X0),X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f1003,axiom,
! [X2,X0,X8,X4,X32] :
( ~ c_Wellfounded_Owf(X8,X0)
| hBOOL(hAPP(X32,X2))
| hBOOL(hAPP(X32,X4))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X32,X8,X0),X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).
fof(f12066,plain,
spl0_689,
inference(avatar_split_clause,[],[f737,f12064]) ).
fof(f12064,plain,
( spl0_689
<=> ! [X4,X0,X3,X8] :
( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X4,X3,X0,X0),X8,tc_prod(X0,X0)),X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f737,axiom,
! [X3,X0,X8,X4] :
( ~ c_Wellfounded_Oacyclic(c_Set_Oinsert(c_Pair(X4,X3,X0,X0),X8,tc_prod(X0,X0)),X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).
fof(f12062,plain,
spl0_688,
inference(avatar_split_clause,[],[f688,f12060]) ).
fof(f12060,plain,
( spl0_688
<=> ! [X6,X0,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = X6
| ~ c_lessequals(X6,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f688,axiom,
! [X3,X0,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = X6
| ~ c_lessequals(X6,c_Set_Oinsert(X3,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
fof(f12058,plain,
spl0_687,
inference(avatar_split_clause,[],[f434,f12056]) ).
fof(f12056,plain,
( spl0_687
<=> ! [X42,X41,X0,X10,X21] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X41,X42,tc_fun(X0,tc_bool)),X21,X0,X10) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X41,X21,X0,X10),c_Product__Type_OSigma(X42,X21,X0,X10),tc_fun(tc_prod(X0,X10),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f434,axiom,
! [X21,X41,X10,X0,X42] : c_Product__Type_OSigma(c_Lattices_Oupper__semilattice__class_Osup(X41,X42,tc_fun(X0,tc_bool)),X21,X0,X10) = c_Lattices_Oupper__semilattice__class_Osup(c_Product__Type_OSigma(X41,X21,X0,X10),c_Product__Type_OSigma(X42,X21,X0,X10),tc_fun(tc_prod(X0,X10),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).
fof(f12054,plain,
spl0_686,
inference(avatar_split_clause,[],[f336,f12052]) ).
fof(f12052,plain,
( spl0_686
<=> ! [X2,X0,X12,X5,X1] :
( X1 = X12
| X1 = X5
| c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X5,c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f336,axiom,
! [X2,X0,X1,X5,X12] :
( X1 = X12
| X1 = X5
| c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X5,c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
fof(f12050,plain,
spl0_685,
inference(avatar_split_clause,[],[f334,f12048]) ).
fof(f12048,plain,
( spl0_685
<=> ! [X0,X12,X5,X2,X1] :
( X2 = X5
| X1 = X5
| c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X5,c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f334,axiom,
! [X2,X0,X1,X5,X12] :
( X2 = X5
| X1 = X5
| c_Set_Oinsert(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) != c_Set_Oinsert(X5,c_Set_Oinsert(X12,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
fof(f12046,plain,
( spl0_684
| ~ spl0_36
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2559,f2364,f1599,f12044]) ).
fof(f2559,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_36
| ~ spl0_193 ),
inference(resolution,[],[f2365,f1601]) ).
fof(f12042,plain,
spl0_683,
inference(avatar_split_clause,[],[f230,f12040]) ).
fof(f12040,plain,
( spl0_683
<=> ! [X15,X10,X0,X6,X22] : c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X10,X0),tc_bool)),X6,X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X15,X6,X10,X0),c_Relation_OImage(X22,X6,X10,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f230,axiom,
! [X10,X0,X6,X15,X22] : c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X10,X0),tc_bool)),X6,X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X15,X6,X10,X0),c_Relation_OImage(X22,X6,X10,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Image_0) ).
fof(f12038,plain,
spl0_682,
inference(avatar_split_clause,[],[f126,f12036]) ).
fof(f12036,plain,
( spl0_682
<=> ! [X0,X14,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X1,X14,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f126,axiom,
! [X2,X0,X1,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X1,X14,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
fof(f11861,plain,
( spl0_681
| ~ spl0_28
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2548,f2332,f1559,f11859]) ).
fof(f1559,plain,
( spl0_28
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f2332,plain,
( spl0_185
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oone__class_Oone(X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f2548,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)) = X0
| ~ spl0_28
| ~ spl0_185 ),
inference(resolution,[],[f2333,f1561]) ).
fof(f1561,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f1559]) ).
fof(f2333,plain,
( ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oone__class_Oone(X0)) = X2 )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f2332]) ).
fof(f11694,plain,
( spl0_680
| ~ spl0_14
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f2545,f2320,f1489,f11692]) ).
fof(f1489,plain,
( spl0_14
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f2320,plain,
( spl0_182
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f2545,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) = X0
| ~ spl0_14
| ~ spl0_182 ),
inference(resolution,[],[f2321,f1491]) ).
fof(f1491,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f1489]) ).
fof(f2321,plain,
( ! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X3) = X3 )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f2320]) ).
fof(f11508,plain,
( spl0_679
| ~ spl0_212
| ~ spl0_653 ),
inference(avatar_split_clause,[],[f11357,f11353,f2440,f11506]) ).
fof(f11506,plain,
( spl0_679
<=> ! [X18,X0,X3,X19] :
( hAPP(hAPP(c_Finite__Set_Osetsum(X0,tc_nat),X18),X19) != c_Orderings_Obot__class_Obot(tc_nat)
| hAPP(X18,X3) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ c_Finite__Set_Ofinite(X19,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f11353,plain,
( spl0_653
<=> ! [X18,X0,X3,X19] :
( ~ c_Finite__Set_Ofinite(X19,X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(X18,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X19))
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,tc_nat),X18),X19) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f11357,plain,
( ! [X3,X0,X18,X19] :
( hAPP(hAPP(c_Finite__Set_Osetsum(X0,tc_nat),X18),X19) != c_Orderings_Obot__class_Obot(tc_nat)
| hAPP(X18,X3) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ c_Finite__Set_Ofinite(X19,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X19)) )
| ~ spl0_212
| ~ spl0_653 ),
inference(forward_demodulation,[],[f11356,f2442]) ).
fof(f11356,plain,
( ! [X3,X0,X18,X19] :
( hAPP(X18,X3) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ c_Finite__Set_Ofinite(X19,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X19))
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,tc_nat),X18),X19) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ~ spl0_212
| ~ spl0_653 ),
inference(forward_demodulation,[],[f11354,f2442]) ).
fof(f11354,plain,
( ! [X3,X0,X18,X19] :
( ~ c_Finite__Set_Ofinite(X19,X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(X18,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X19))
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,tc_nat),X18),X19) != c_HOL_Ozero__class_Ozero(tc_nat) )
| ~ spl0_653 ),
inference(avatar_component_clause,[],[f11353]) ).
fof(f11471,plain,
spl0_678,
inference(avatar_split_clause,[],[f1410,f11469]) ).
fof(f11469,plain,
( spl0_678
<=> ! [X0,X8] : c_Relation_Oconverse(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0,X0) = c_Relation_Orel__comp(c_Relation_Oconverse(X8,X0,X0),c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X8,X0),X0,X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f1410,plain,
! [X0,X8] : c_Relation_Oconverse(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0,X0) = c_Relation_Orel__comp(c_Relation_Oconverse(X8,X0,X0),c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X8,X0),X0,X0),X0,X0,X0),
inference(forward_demodulation,[],[f1358,f1159]) ).
fof(f1159,axiom,
! [X0,X8] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X8,X0,X0),X0) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X8,X0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
fof(f1358,plain,
! [X0,X8] : c_Relation_Oconverse(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0,X0) = c_Relation_Orel__comp(c_Relation_Oconverse(X8,X0,X0),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X8,X0,X0),X0),X0,X0,X0),
inference(definition_unfolding,[],[f1140,f1163,f1163]) ).
fof(f1140,axiom,
! [X0,X8] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X8,X0),X0,X0) = c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X8,X0,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
fof(f11467,plain,
( spl0_677
| ~ spl0_64
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f2160,f2066,f1728,f11465]) ).
fof(f11465,plain,
( spl0_677
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Wellfounded_Omlex__prod(X2,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f1728,plain,
( spl0_64
<=> ! [X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Oacyclic(X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f2066,plain,
( spl0_146
<=> ! [X18,X0,X15] :
( ~ c_Wellfounded_Owf(X15,X0)
| c_Wellfounded_Owf(c_Wellfounded_Omlex__prod(X18,X15,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f2160,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Wellfounded_Omlex__prod(X2,X0,X1),X1) )
| ~ spl0_64
| ~ spl0_146 ),
inference(resolution,[],[f2067,f1729]) ).
fof(f1729,plain,
( ! [X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Oacyclic(X8,X0) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1728]) ).
fof(f2067,plain,
( ! [X0,X18,X15] :
( c_Wellfounded_Owf(c_Wellfounded_Omlex__prod(X18,X15,X0),X0)
| ~ c_Wellfounded_Owf(X15,X0) )
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f2066]) ).
fof(f11463,plain,
spl0_676,
inference(avatar_split_clause,[],[f1373,f11461]) ).
fof(f11461,plain,
( spl0_676
<=> ! [X0,X8,X10,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X0),X2),c_Relation_ORange(c_Relation_Oconverse(X8,X0,X10),X10,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f1373,plain,
! [X2,X10,X0,X1,X8] :
( hBOOL(hAPP(hAPP(c_in(X0),X2),c_Relation_ORange(c_Relation_Oconverse(X8,X0,X10),X10,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),X8)) ),
inference(definition_unfolding,[],[f1221,f1146]) ).
fof(f1221,axiom,
! [X2,X10,X0,X1,X8] :
( hBOOL(hAPP(hAPP(c_in(X0),X2),c_Relation_ODomain(X8,X0,X10)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainI_0) ).
fof(f11459,plain,
spl0_675,
inference(avatar_split_clause,[],[f1369,f11457]) ).
fof(f11457,plain,
( spl0_675
<=> ! [X10,X0,X9,X8] :
( ~ c_lessequals(X8,X9,tc_fun(tc_prod(X0,X10),tc_bool))
| c_lessequals(c_Relation_ORange(c_Relation_Oconverse(X8,X0,X10),X10,X0),c_Relation_ORange(c_Relation_Oconverse(X9,X0,X10),X10,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f1369,plain,
! [X10,X0,X8,X9] :
( ~ c_lessequals(X8,X9,tc_fun(tc_prod(X0,X10),tc_bool))
| c_lessequals(c_Relation_ORange(c_Relation_Oconverse(X8,X0,X10),X10,X0),c_Relation_ORange(c_Relation_Oconverse(X9,X0,X10),X10,X0),tc_fun(X0,tc_bool)) ),
inference(definition_unfolding,[],[f687,f1146,f1146]) ).
fof(f687,axiom,
! [X10,X0,X8,X9] :
( ~ c_lessequals(X8,X9,tc_fun(tc_prod(X0,X10),tc_bool))
| c_lessequals(c_Relation_ODomain(X8,X0,X10),c_Relation_ODomain(X9,X0,X10),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__mono_0) ).
fof(f11455,plain,
spl0_674,
inference(avatar_split_clause,[],[f1231,f11453]) ).
fof(f11453,plain,
( spl0_674
<=> ! [X18,X4,X0,X3] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X18,X3)),hAPP(X18,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Wellfounded_Omeasure(X18,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f1231,axiom,
! [X3,X0,X18,X4] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X18,X3)),hAPP(X18,X4)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Wellfounded_Omeasure(X18,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__measure_0) ).
fof(f11451,plain,
spl0_673,
inference(avatar_split_clause,[],[f1230,f11449]) ).
fof(f11449,plain,
( spl0_673
<=> ! [X18,X4,X0,X3] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X18,X3)),hAPP(X18,X4)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Wellfounded_Omeasure(X18,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f1230,axiom,
! [X3,X0,X18,X4] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(X18,X3)),hAPP(X18,X4)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Wellfounded_Omeasure(X18,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__measure_1) ).
fof(f11447,plain,
spl0_672,
inference(avatar_split_clause,[],[f1222,f11445]) ).
fof(f11445,plain,
( spl0_672
<=> ! [X6,X7,X0,X10,X2,X1] :
( hBOOL(hAPP(hAPP(c_in(X10),X1),hAPP(X7,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),c_Product__Type_OSigma(X6,X7,X0,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f1222,axiom,
! [X2,X10,X0,X1,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X10),X1),hAPP(X7,X2)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),c_Product__Type_OSigma(X6,X7,X0,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
fof(f11443,plain,
spl0_671,
inference(avatar_split_clause,[],[f1108,f11441]) ).
fof(f11441,plain,
( spl0_671
<=> ! [X18,X10,X0,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hAPP(X18,X3) != c_HOL_Ozero__class_Ozero(X10)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Finite__Set_Osetprod(X18,X6,X0,X10) = c_HOL_Ozero__class_Ozero(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f1108,axiom,
! [X3,X10,X0,X18,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| hAPP(X18,X3) != c_HOL_Ozero__class_Ozero(X10)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Finite__Set_Osetprod(X18,X6,X0,X10) = c_HOL_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__zero_0) ).
fof(f11439,plain,
spl0_670,
inference(avatar_split_clause,[],[f1043,f11437]) ).
fof(f11437,plain,
( spl0_670
<=> ! [X18,X10,X0,X6] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X10)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Osetprod(X18,X6,X0,X10) != c_HOL_Ozero__class_Ozero(X10)
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1(X6,X18,X0,X10)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f1043,axiom,
! [X10,X0,X18,X6] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X10)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Osetprod(X18,X6,X0,X10) != c_HOL_Ozero__class_Ozero(X10)
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1(X6,X18,X0,X10)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__zero__iff_0) ).
fof(f11435,plain,
spl0_669,
inference(avatar_split_clause,[],[f1022,f11433]) ).
fof(f11433,plain,
( spl0_669
<=> ! [X18,X10,X0,X6] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),hAPP(hAPP(c_Finite__Set_Osetsum(X10,tc_nat),X18),X6)) = hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),c_COMBB(c_Nat_Osemiring__1__class_Oof__nat(X0),X18,tc_nat,X0,X10)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f1022,axiom,
! [X10,X0,X18,X6] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),hAPP(hAPP(c_Finite__Set_Osetsum(X10,tc_nat),X18),X6)) = hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),c_COMBB(c_Nat_Osemiring__1__class_Oof__nat(X0),X18,tc_nat,X0,X10)),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__setsum_0) ).
fof(f11431,plain,
spl0_668,
inference(avatar_split_clause,[],[f829,f11429]) ).
fof(f11429,plain,
( spl0_668
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f829,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f11427,plain,
spl0_667,
inference(avatar_split_clause,[],[f828,f11425]) ).
fof(f11425,plain,
( spl0_667
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f828,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f11415,plain,
spl0_666,
inference(avatar_split_clause,[],[f827,f11413]) ).
fof(f11413,plain,
( spl0_666
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f827,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f11411,plain,
spl0_665,
inference(avatar_split_clause,[],[f826,f11409]) ).
fof(f11409,plain,
( spl0_665
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f826,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f11407,plain,
spl0_664,
inference(avatar_split_clause,[],[f825,f11405]) ).
fof(f11405,plain,
( spl0_664
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f825,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f11403,plain,
spl0_663,
inference(avatar_split_clause,[],[f824,f11401]) ).
fof(f11401,plain,
( spl0_663
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f824,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f11399,plain,
spl0_662,
inference(avatar_split_clause,[],[f808,f11397]) ).
fof(f11397,plain,
( spl0_662
<=> ! [X0,X6,X3,X7] :
( X6 = X7
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X7))
| c_Set_Oinsert(X3,X6,X0) != c_Set_Oinsert(X3,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f808,axiom,
! [X3,X0,X6,X7] :
( X6 = X7
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X7))
| c_Set_Oinsert(X3,X6,X0) != c_Set_Oinsert(X3,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
fof(f11395,plain,
spl0_661,
inference(avatar_split_clause,[],[f798,f11393]) ).
fof(f11393,plain,
( spl0_661
<=> ! [X5,X0,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X5),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f798,axiom,
! [X0,X6,X7,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),X5),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
fof(f11391,plain,
spl0_660,
inference(avatar_split_clause,[],[f783,f11389]) ).
fof(f11389,plain,
( spl0_660
<=> ! [X5,X0,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X5),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f783,axiom,
! [X0,X6,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X5),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
fof(f11387,plain,
spl0_659,
inference(avatar_split_clause,[],[f477,f11385]) ).
fof(f11385,plain,
( spl0_659
<=> ! [X10,X0,X9,X8] : c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(tc_prod(X10,X0),tc_bool)),X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X8,X10,X0),c_Relation_Oconverse(X9,X10,X0),tc_fun(tc_prod(X0,X10),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f477,axiom,
! [X10,X0,X8,X9] : c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(tc_prod(X10,X0),tc_bool)),X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(X8,X10,X0),c_Relation_Oconverse(X9,X10,X0),tc_fun(tc_prod(X0,X10),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Un_0) ).
fof(f11383,plain,
spl0_658,
inference(avatar_split_clause,[],[f371,f11381]) ).
fof(f11381,plain,
( spl0_658
<=> ! [X0,X6,X2,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X0) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Set_Oinsert(X2,X7,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f371,axiom,
! [X2,X0,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X0) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Set_Oinsert(X2,X7,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
fof(f11379,plain,
spl0_657,
inference(avatar_split_clause,[],[f370,f11377]) ).
fof(f11377,plain,
( spl0_657
<=> ! [X0,X21,X2,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X21))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X7,X0),X21,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f370,axiom,
! [X2,X21,X0,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X21))
| c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X7,X0),X21,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
fof(f11369,plain,
spl0_656,
inference(avatar_split_clause,[],[f305,f11367]) ).
fof(f11367,plain,
( spl0_656
<=> ! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Power_Opower__class_Opower(X2,X14,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f305,axiom,
! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Power_Opower__class_Opower(X2,X14,X0)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
fof(f11365,plain,
spl0_655,
inference(avatar_split_clause,[],[f281,f11363]) ).
fof(f11363,plain,
( spl0_655
<=> ! [X2,X0,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Oone__class_Oone(X0))),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f281,axiom,
! [X2,X0,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Oone__class_Oone(X0))),X16) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(f11361,plain,
spl0_654,
inference(avatar_split_clause,[],[f280,f11359]) ).
fof(f11359,plain,
( spl0_654
<=> ! [X2,X0,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X16)),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Oone__class_Oone(X0))),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f280,axiom,
! [X2,X0,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X16)),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Oone__class_Oone(X0))),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(f11355,plain,
spl0_653,
inference(avatar_split_clause,[],[f43,f11353]) ).
fof(f43,axiom,
! [X3,X0,X18,X19] :
( ~ c_Finite__Set_Ofinite(X19,X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(X18,X3)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X19))
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,tc_nat),X18),X19) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__eq__0__iff_0) ).
fof(f11351,plain,
spl0_652,
inference(avatar_split_clause,[],[f26,f11349]) ).
fof(f11349,plain,
( spl0_652
<=> ! [X13,X0,X14,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X14,X13,tc_nat)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_Power_Opower__class_Opower(X2,X13,X0),c_Power_Opower__class_Opower(X2,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f26,axiom,
! [X2,X0,X14,X13] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X14,X13,tc_nat)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_Power_Opower__class_Opower(X2,X13,X0),c_Power_Opower__class_Opower(X2,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
fof(f10766,plain,
( spl0_651
| ~ spl0_288
| ~ spl0_544 ),
inference(avatar_split_clause,[],[f8383,f7759,f3171,f10764]) ).
fof(f10764,plain,
( spl0_651
<=> ! [X0,X1] : c_Nitpick_Orefl_H(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f3171,plain,
( spl0_288
<=> ! [X0,X8] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X8,X0,X0),X0) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X8,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f7759,plain,
( spl0_544
<=> ! [X0,X1] : c_Nitpick_Orefl_H(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f8383,plain,
( ! [X0,X1] : c_Nitpick_Orefl_H(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1)
| ~ spl0_288
| ~ spl0_544 ),
inference(superposition,[],[f7760,f3172]) ).
fof(f3172,plain,
( ! [X0,X8] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X8,X0,X0),X0) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X8,X0),X0,X0)
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f3171]) ).
fof(f7760,plain,
( ! [X0,X1] : c_Nitpick_Orefl_H(c_Transitive__Closure_Ortrancl(X0,X1),X1)
| ~ spl0_544 ),
inference(avatar_component_clause,[],[f7759]) ).
fof(f10756,plain,
spl0_650,
inference(avatar_split_clause,[],[f1370,f10754]) ).
fof(f10754,plain,
( spl0_650
<=> ! [X48,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f1370,plain,
! [X48,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ),
inference(definition_unfolding,[],[f1083,f1163]) ).
fof(f1083,axiom,
! [X48,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),c_Transitive__Closure_Otrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).
fof(f10752,plain,
spl0_649,
inference(avatar_split_clause,[],[f1073,f10750]) ).
fof(f10750,plain,
( spl0_649
<=> ! [X15,X18,X10,X0,X3,X2] :
( hAPP(X18,X3) = hAPP(c_Recdef_Ocut(X18,X15,X2,X0,X10),X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X2,X0,X0)),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f1073,axiom,
! [X2,X3,X10,X0,X18,X15] :
( hAPP(X18,X3) = hAPP(c_Recdef_Ocut(X18,X15,X2,X0,X10),X3)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X2,X0,X0)),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).
fof(f10748,plain,
spl0_648,
inference(avatar_split_clause,[],[f1054,f10746]) ).
fof(f10746,plain,
( spl0_648
<=> ! [X0,X8,X3] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),c_Wellfounded_Oacc(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X8,X3,X0),X3,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f1054,axiom,
! [X3,X0,X8] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),c_Wellfounded_Oacc(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X8,X3,X0),X3,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).
fof(f10744,plain,
spl0_647,
inference(avatar_split_clause,[],[f1051,f10742]) ).
fof(f10742,plain,
( spl0_647
<=> ! [X0,X3,X15] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),c_Wellfounded_Oacc(X15,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X15,X3,X0),X3,X0,X0)),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f1051,axiom,
! [X3,X0,X15] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),c_Wellfounded_Oacc(X15,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X15,X3,X0),X3,X0,X0)),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
fof(f10740,plain,
( spl0_646
| ~ spl0_288
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f6005,f5596,f3171,f10738]) ).
fof(f10738,plain,
( spl0_646
<=> ! [X0,X1] : ~ c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f5596,plain,
( spl0_443
<=> ! [X0,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f6005,plain,
( ! [X0,X1] : ~ c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1)
| ~ spl0_288
| ~ spl0_443 ),
inference(superposition,[],[f5597,f3172]) ).
fof(f5597,plain,
( ! [X0,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X0,X1),X1)
| ~ spl0_443 ),
inference(avatar_component_clause,[],[f5596]) ).
fof(f10736,plain,
spl0_645,
inference(avatar_split_clause,[],[f1040,f10734]) ).
fof(f10734,plain,
( spl0_645
<=> ! [X18,X10,X0,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X10)
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1(X6,X18,X0,X10)),X6))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),c_HOL_Ozero__class_Ozero(X10)),c_Finite__Set_Osetprod(X18,X6,X0,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f1040,axiom,
! [X10,X0,X18,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X10)
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1(X6,X18,X0,X10)),X6))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X10),c_HOL_Ozero__class_Ozero(X10)),c_Finite__Set_Osetprod(X18,X6,X0,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__pos_0) ).
fof(f10732,plain,
spl0_644,
inference(avatar_split_clause,[],[f989,f10730]) ).
fof(f10730,plain,
( spl0_644
<=> ! [X5,X10,X0,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X6,X7,X5,X0,X10)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),X5),c_Product__Type_OSigma(X6,X7,X0,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f989,axiom,
! [X10,X0,X6,X7,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1(X6,X7,X5,X0,X10)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),X5),c_Product__Type_OSigma(X6,X7,X0,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaE_0) ).
fof(f10728,plain,
spl0_643,
inference(avatar_split_clause,[],[f988,f10726]) ).
fof(f10726,plain,
( spl0_643
<=> ! [X18,X10,X0,X6] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X10)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Osetprod(X18,X6,X0,X10) != c_HOL_Ozero__class_Ozero(X10)
| c_HOL_Ozero__class_Ozero(X10) = hAPP(X18,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1(X6,X18,X0,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f988,axiom,
! [X10,X0,X18,X6] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X10)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Osetprod(X18,X6,X0,X10) != c_HOL_Ozero__class_Ozero(X10)
| c_HOL_Ozero__class_Ozero(X10) = hAPP(X18,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1(X6,X18,X0,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__zero__iff_1) ).
fof(f10724,plain,
spl0_642,
inference(avatar_split_clause,[],[f955,f10722]) ).
fof(f10722,plain,
( spl0_642
<=> ! [X32,X0,X8,X2] :
( hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X32,X8,X0)),c_Wellfounded_Oacc(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f955,axiom,
! [X2,X0,X8,X32] :
( hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X32,X8,X0)),c_Wellfounded_Oacc(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_0) ).
fof(f10720,plain,
spl0_641,
inference(avatar_split_clause,[],[f950,f10718]) ).
fof(f10718,plain,
( spl0_641
<=> ! [X32,X0,X8,X2] :
( hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X32,X8,X0)),c_Wellfounded_Oacc(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f950,axiom,
! [X2,X0,X8,X32] :
( hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X32,X8,X0)),c_Wellfounded_Oacc(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).
fof(f10716,plain,
spl0_640,
inference(avatar_split_clause,[],[f775,f10714]) ).
fof(f10714,plain,
( spl0_640
<=> ! [X18,X0,X6,X10,X7] : c_Set_Ovimage(X18,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X10,tc_bool)),X0,X10) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X18,X6,X0,X10),c_Set_Ovimage(X18,X7,X0,X10),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f775,axiom,
! [X10,X0,X18,X6,X7] : c_Set_Ovimage(X18,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X10,tc_bool)),X0,X10) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X18,X6,X0,X10),c_Set_Ovimage(X18,X7,X0,X10),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
fof(f10712,plain,
spl0_639,
inference(avatar_split_clause,[],[f722,f10710]) ).
fof(f10710,plain,
( spl0_639
<=> ! [X0,X29,X27,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X30)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f722,axiom,
! [X0,X29,X27,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f10708,plain,
spl0_638,
inference(avatar_split_clause,[],[f721,f10706]) ).
fof(f10706,plain,
( spl0_638
<=> ! [X0,X29,X27,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X29)),X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f721,axiom,
! [X0,X29,X27,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X29),X30)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X29)),X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(f10704,plain,
spl0_637,
inference(avatar_split_clause,[],[f719,f10702]) ).
fof(f10702,plain,
( spl0_637
<=> ! [X0,X29,X27,X28] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X28)),X29) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X29)),X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f719,axiom,
! [X28,X0,X29,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X28)),X29) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X27),X29)),X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f10700,plain,
spl0_636,
inference(avatar_split_clause,[],[f718,f10698]) ).
fof(f10698,plain,
( spl0_636
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f718,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f10696,plain,
( spl0_635
| ~ spl0_288
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f5853,f5548,f3171,f10694]) ).
fof(f10694,plain,
( spl0_635
<=> ! [X0,X1] : ~ c_Relation_Oirrefl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f5548,plain,
( spl0_442
<=> ! [X0,X1] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f5853,plain,
( ! [X0,X1] : ~ c_Relation_Oirrefl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X0,X1),X1,X1),X1)
| ~ spl0_288
| ~ spl0_442 ),
inference(superposition,[],[f5549,f3172]) ).
fof(f5549,plain,
( ! [X0,X1] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Ortrancl(X0,X1),X1)
| ~ spl0_442 ),
inference(avatar_component_clause,[],[f5548]) ).
fof(f10692,plain,
spl0_634,
inference(avatar_split_clause,[],[f614,f10690]) ).
fof(f10690,plain,
( spl0_634
<=> ! [X22,X0,X15] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X15,X0),c_Transitive__Closure_Ortrancl(X22,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f614,axiom,
! [X0,X15,X22] : c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool)),X0) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X15,X0),c_Transitive__Closure_Ortrancl(X22,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).
fof(f10688,plain,
spl0_633,
inference(avatar_split_clause,[],[f610,f10686]) ).
fof(f10686,plain,
( spl0_633
<=> ! [X18,X0,X6,X10,X7] : c_Set_Ovimage(X18,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X10,tc_bool)),X0,X10) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X18,X6,X0,X10),c_Set_Ovimage(X18,X7,X0,X10),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f610,axiom,
! [X10,X0,X18,X6,X7] : c_Set_Ovimage(X18,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X10,tc_bool)),X0,X10) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X18,X6,X0,X10),c_Set_Ovimage(X18,X7,X0,X10),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
fof(f10684,plain,
spl0_632,
inference(avatar_split_clause,[],[f529,f10682]) ).
fof(f10682,plain,
( spl0_632
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f529,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
fof(f10680,plain,
spl0_631,
inference(avatar_split_clause,[],[f528,f10678]) ).
fof(f10678,plain,
( spl0_631
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f528,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X5),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
fof(f10676,plain,
spl0_630,
inference(avatar_split_clause,[],[f527,f10674]) ).
fof(f10674,plain,
( spl0_630
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f527,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
fof(f10672,plain,
spl0_629,
inference(avatar_split_clause,[],[f399,f10670]) ).
fof(f10670,plain,
( spl0_629
<=> ! [X22,X0,X15] :
( c_Transitive__Closure_Ortrancl(X15,X0) = c_Transitive__Closure_Ortrancl(X22,X0)
| ~ c_lessequals(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool))
| ~ c_lessequals(X22,c_Transitive__Closure_Ortrancl(X15,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f399,axiom,
! [X0,X15,X22] :
( c_Transitive__Closure_Ortrancl(X15,X0) = c_Transitive__Closure_Ortrancl(X22,X0)
| ~ c_lessequals(X15,X22,tc_fun(tc_prod(X0,X0),tc_bool))
| ~ c_lessequals(X22,c_Transitive__Closure_Ortrancl(X15,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).
fof(f10668,plain,
spl0_628,
inference(avatar_split_clause,[],[f284,f10666]) ).
fof(f10666,plain,
( spl0_628
<=> ! [X0,X6,X3,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X7))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f284,axiom,
! [X3,X0,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X7))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
fof(f10664,plain,
spl0_627,
inference(avatar_split_clause,[],[f231,f10662]) ).
fof(f10662,plain,
( spl0_627
<=> ! [X6,X0,X10,X15,X7] : c_Relation_OImage(X15,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X10,tc_bool)),X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X15,X6,X10,X0),c_Relation_OImage(X15,X7,X10,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f231,axiom,
! [X10,X0,X6,X7,X15] : c_Relation_OImage(X15,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X10,tc_bool)),X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(X15,X6,X10,X0),c_Relation_OImage(X15,X7,X10,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).
fof(f10660,plain,
spl0_626,
inference(avatar_split_clause,[],[f228,f10658]) ).
fof(f10658,plain,
( spl0_626
<=> ! [X0,X12,X5,X2] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f228,axiom,
! [X2,X0,X5,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f10656,plain,
spl0_625,
inference(avatar_split_clause,[],[f227,f10654]) ).
fof(f10654,plain,
( spl0_625
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f227,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f10648,plain,
spl0_624,
inference(avatar_split_clause,[],[f226,f10646]) ).
fof(f10646,plain,
( spl0_624
<=> ! [X0,X12,X5,X2] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f226,axiom,
! [X2,X0,X5,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(f10644,plain,
spl0_623,
inference(avatar_split_clause,[],[f225,f10642]) ).
fof(f10642,plain,
( spl0_623
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f225,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f10640,plain,
spl0_622,
inference(avatar_split_clause,[],[f224,f10638]) ).
fof(f10638,plain,
( spl0_622
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f224,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f10636,plain,
spl0_621,
inference(avatar_split_clause,[],[f223,f10634]) ).
fof(f10634,plain,
( spl0_621
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f223,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f10632,plain,
spl0_620,
inference(avatar_split_clause,[],[f113,f10630]) ).
fof(f10630,plain,
( spl0_620
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f113,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
fof(f10628,plain,
spl0_619,
inference(avatar_split_clause,[],[f112,f10626]) ).
fof(f10626,plain,
( spl0_619
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f112,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
fof(f10624,plain,
spl0_618,
inference(avatar_split_clause,[],[f102,f10622]) ).
fof(f10622,plain,
( spl0_618
<=> ! [X18,X10,X0,X6,X7] :
( ~ class_Ring__and__Field_Odvd(X10)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X7,X0)
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Ring__and__Field_Odvd__class_Odvd(c_Finite__Set_Osetprod(X18,X6,X0,X10),c_Finite__Set_Osetprod(X18,X7,X0,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f102,axiom,
! [X10,X0,X18,X6,X7] :
( ~ class_Ring__and__Field_Odvd(X10)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| ~ c_Finite__Set_Ofinite(X7,X0)
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Ring__and__Field_Odvd__class_Odvd(c_Finite__Set_Osetprod(X18,X6,X0,X10),c_Finite__Set_Osetprod(X18,X7,X0,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__dvd__setprod__subset_0) ).
fof(f10552,plain,
( ~ spl0_13
| ~ spl0_617
| ~ spl0_101
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2488,f2440,f1877,f10549,f1484]) ).
fof(f1484,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f10549,plain,
( spl0_617
<=> c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f1877,plain,
( spl0_101
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f2488,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| ~ spl0_101
| ~ spl0_212 ),
inference(superposition,[],[f1878,f2442]) ).
fof(f1878,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f1877]) ).
fof(f10440,plain,
( spl0_616
| ~ spl0_99
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2485,f2440,f1869,f10438]) ).
fof(f10438,plain,
( spl0_616
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f1869,plain,
( spl0_99
<=> ! [X16] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),c_HOL_Ozero__class_Ozero(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f2485,plain,
( ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat)))
| ~ spl0_99
| ~ spl0_212 ),
inference(superposition,[],[f1870,f2442]) ).
fof(f1870,plain,
( ! [X16] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1869]) ).
fof(f10284,plain,
spl0_615,
inference(avatar_split_clause,[],[f1228,f10282]) ).
fof(f10282,plain,
( spl0_615
<=> ! [X0,X8,X6,X2] :
( ~ c_Relation_Orefl__on(X6,X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X2,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f1228,axiom,
! [X2,X0,X8,X6] :
( ~ c_Relation_Orefl__on(X6,X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X2,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).
fof(f10280,plain,
spl0_614,
inference(avatar_split_clause,[],[f1227,f10278]) ).
fof(f10278,plain,
( spl0_614
<=> ! [X3,X4,X0,X6,X8] :
( ~ c_Relation_Orefl__on(X6,X8,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f1227,axiom,
! [X3,X0,X8,X6,X4] :
( ~ c_Relation_Orefl__on(X6,X8,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
fof(f10276,plain,
spl0_613,
inference(avatar_split_clause,[],[f1226,f10274]) ).
fof(f10274,plain,
( spl0_613
<=> ! [X3,X4,X0,X6,X8] :
( ~ c_Relation_Orefl__on(X6,X8,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X4),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f1226,axiom,
! [X3,X0,X8,X6,X4] :
( ~ c_Relation_Orefl__on(X6,X8,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X4),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
fof(f10272,plain,
spl0_612,
inference(avatar_split_clause,[],[f1223,f10270]) ).
fof(f10270,plain,
( spl0_612
<=> ! [X1,X10,X0,X6,X2,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),c_Product__Type_OSigma(X6,X7,X0,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f1223,axiom,
! [X2,X10,X0,X1,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),c_Product__Type_OSigma(X6,X7,X0,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
fof(f10268,plain,
spl0_611,
inference(avatar_split_clause,[],[f1217,f10266]) ).
fof(f10266,plain,
( spl0_611
<=> ! [X3,X4,X0,X6,X8] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f1217,axiom,
! [X3,X0,X8,X6,X4] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
fof(f10264,plain,
spl0_610,
inference(avatar_split_clause,[],[f1216,f10262]) ).
fof(f10262,plain,
( spl0_610
<=> ! [X3,X4,X0,X6,X8] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X4),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f1216,axiom,
! [X3,X0,X8,X6,X4] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X4),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
fof(f10256,plain,
spl0_609,
inference(avatar_split_clause,[],[f1101,f10254]) ).
fof(f10254,plain,
( spl0_609
<=> ! [X22,X0,X15] :
( X15 = X22
| hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X15) != hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f1101,axiom,
! [X0,X15,X22] :
( X15 = X22
| hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X15) != hAPP(c_COMBC(c_in(X0),X0,tc_fun(X0,tc_bool),tc_bool),X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).
fof(f10252,plain,
spl0_608,
inference(avatar_split_clause,[],[f1027,f10250]) ).
fof(f10250,plain,
( spl0_608
<=> ! [X6,X0,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X5),c_Relation_OId__on(X6,X0)))
| c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X6,X5,X0),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X6,X5,X0),X0,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f1027,axiom,
! [X0,X6,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X5),c_Relation_OId__on(X6,X0)))
| c_Pair(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X6,X5,X0),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X6,X5,X0),X0,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_1) ).
fof(f10248,plain,
spl0_607,
inference(avatar_split_clause,[],[f1025,f10246]) ).
fof(f10246,plain,
( spl0_607
<=> ! [X18,X10,X0,X6] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Finite__Set_Osetprod(X18,X6,X10,tc_nat)) = c_Finite__Set_Osetprod(c_COMBB(c_Nat_Osemiring__1__class_Oof__nat(X0),X18,tc_nat,X0,X10),X6,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f1025,axiom,
! [X10,X0,X18,X6] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Finite__Set_Osetprod(X18,X6,X10,tc_nat)) = c_Finite__Set_Osetprod(c_COMBB(c_Nat_Osemiring__1__class_Oof__nat(X0),X18,tc_nat,X0,X10),X6,X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__setprod_0) ).
fof(f10244,plain,
spl0_606,
inference(avatar_split_clause,[],[f697,f10242]) ).
fof(f10242,plain,
( spl0_606
<=> ! [X4,X51,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X4),X51,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Power_Opower__class_Opower(X3,X51,X0)),c_Power_Opower__class_Opower(X4,X51,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f697,axiom,
! [X51,X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X4),X51,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Power_Opower__class_Opower(X3,X51,X0)),c_Power_Opower__class_Opower(X4,X51,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
fof(f10240,plain,
spl0_605,
inference(avatar_split_clause,[],[f696,f10238]) ).
fof(f10238,plain,
( spl0_605
<=> ! [X0,X14,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X14,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X1,X14,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f696,axiom,
! [X2,X0,X1,X14] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X14,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X1,X14,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
fof(f10236,plain,
spl0_604,
inference(avatar_split_clause,[],[f660,f10234]) ).
fof(f10234,plain,
( spl0_604
<=> ! [X4,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X3,X4,tc_nat)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X1))
| c_lessequals(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X1,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f660,axiom,
! [X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X3,X4,tc_nat)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X1))
| c_lessequals(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X1,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
fof(f10232,plain,
spl0_603,
inference(avatar_split_clause,[],[f659,f10230]) ).
fof(f10230,plain,
( spl0_603
<=> ! [X4,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X3,X4,tc_nat)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X1))
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X1,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f659,axiom,
! [X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X3,X4,tc_nat)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X1))
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X1,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).
fof(f10228,plain,
spl0_602,
inference(avatar_split_clause,[],[f535,f10226]) ).
fof(f10226,plain,
( spl0_602
<=> ! [X10,X0,X6,X7] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X10,X0),tc_bool)),X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X10,X0),c_Relation_ORange(X7,X10,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f535,axiom,
! [X10,X0,X6,X7] : c_Relation_ORange(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(tc_prod(X10,X0),tc_bool)),X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_ORange(X6,X10,X0),c_Relation_ORange(X7,X10,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).
fof(f10224,plain,
spl0_601,
inference(avatar_split_clause,[],[f524,f10222]) ).
fof(f10222,plain,
( spl0_601
<=> ! [X5,X0,X12,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X12,X0)
| c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f524,axiom,
! [X2,X0,X1,X5,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X12,X0)
| c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
fof(f10220,plain,
spl0_600,
inference(avatar_split_clause,[],[f203,f10218]) ).
fof(f10218,plain,
( spl0_600
<=> ! [X5,X0,X12,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,X12,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f203,axiom,
! [X2,X0,X1,X5,X12] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,X12,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X12),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f10214,plain,
spl0_599,
inference(avatar_split_clause,[],[f135,f10212]) ).
fof(f10212,plain,
( spl0_599
<=> ! [X9,X0,X6,X8,X7] :
( ~ c_Relation_Orefl__on(X6,X8,X0)
| ~ c_Relation_Orefl__on(X7,X9,X0)
| c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f135,axiom,
! [X0,X8,X6,X9,X7] :
( ~ c_Relation_Orefl__on(X6,X8,X0)
| ~ c_Relation_Orefl__on(X7,X9,X0)
| c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).
fof(f9311,plain,
spl0_598,
inference(avatar_split_clause,[],[f1364,f9309]) ).
fof(f9309,plain,
( spl0_598
<=> ! [X0,X8,X3] :
( ~ c_Wellfounded_Oacyclic(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f1364,plain,
! [X3,X0,X8] :
( ~ c_Wellfounded_Oacyclic(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0))) ),
inference(definition_unfolding,[],[f1012,f1163]) ).
fof(f1012,axiom,
! [X3,X0,X8] :
( ~ c_Wellfounded_Oacyclic(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__def_0) ).
fof(f9307,plain,
spl0_597,
inference(avatar_split_clause,[],[f1262,f9305]) ).
fof(f9305,plain,
( spl0_597
<=> ! [X4,X0,X23,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X23),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X23),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f1262,axiom,
! [X3,X0,X4,X23] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X23),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X23),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f9303,plain,
spl0_596,
inference(avatar_split_clause,[],[f1261,f9301]) ).
fof(f9301,plain,
( spl0_596
<=> ! [X4,X0,X23,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X23))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f1261,axiom,
! [X3,X0,X4,X23] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X23))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f9299,plain,
( spl0_595
| ~ spl0_106
| ~ spl0_143
| ~ spl0_171
| ~ spl0_547 ),
inference(avatar_split_clause,[],[f8444,f7773,f2242,f2054,f1897,f9297]) ).
fof(f9297,plain,
( spl0_595
<=> ! [X0] : c_Equiv__Relations_Oequiv(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f1897,plain,
( spl0_106
<=> ! [X0] : c_Relation_OId(X0) = c_Relation_Oconverse(c_Relation_OId(X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f2054,plain,
( spl0_143
<=> ! [X10,X0,X15] : c_Relation_Orel__comp(X15,c_Relation_OId(X10),X0,X10,X10) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f2242,plain,
( spl0_171
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ORange(c_Relation_OId(X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f7773,plain,
( spl0_547
<=> ! [X0,X8] :
( c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(X8,X0,X0),X0,X0),X8,X0)
| c_Relation_Orel__comp(c_Relation_Oconverse(X8,X0,X0),X8,X0,X0,X0) != X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f8444,plain,
( ! [X0] : c_Equiv__Relations_Oequiv(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Relation_OId(X0),X0)
| ~ spl0_106
| ~ spl0_143
| ~ spl0_171
| ~ spl0_547 ),
inference(forward_demodulation,[],[f8443,f2243]) ).
fof(f2243,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ORange(c_Relation_OId(X0),X0,X0)
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f2242]) ).
fof(f8443,plain,
( ! [X0] : c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0)
| ~ spl0_106
| ~ spl0_143
| ~ spl0_547 ),
inference(trivial_inequality_removal,[],[f8442]) ).
fof(f8442,plain,
( ! [X0] :
( c_Relation_OId(X0) != c_Relation_OId(X0)
| c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0) )
| ~ spl0_106
| ~ spl0_143
| ~ spl0_547 ),
inference(forward_demodulation,[],[f8437,f2055]) ).
fof(f2055,plain,
( ! [X10,X0,X15] : c_Relation_Orel__comp(X15,c_Relation_OId(X10),X0,X10,X10) = X15
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f2054]) ).
fof(f8437,plain,
( ! [X0] :
( c_Relation_OId(X0) != c_Relation_Orel__comp(c_Relation_OId(X0),c_Relation_OId(X0),X0,X0,X0)
| c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0) )
| ~ spl0_106
| ~ spl0_547 ),
inference(superposition,[],[f7774,f1898]) ).
fof(f1898,plain,
( ! [X0] : c_Relation_OId(X0) = c_Relation_Oconverse(c_Relation_OId(X0),X0,X0)
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1897]) ).
fof(f7774,plain,
( ! [X0,X8] :
( c_Relation_Orel__comp(c_Relation_Oconverse(X8,X0,X0),X8,X0,X0,X0) != X8
| c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(X8,X0,X0),X0,X0),X8,X0) )
| ~ spl0_547 ),
inference(avatar_component_clause,[],[f7773]) ).
fof(f9295,plain,
spl0_594,
inference(avatar_split_clause,[],[f1219,f9293]) ).
fof(f9293,plain,
( spl0_594
<=> ! [X2,X0,X8,X10,X1] :
( hBOOL(hAPP(hAPP(c_in(X10),X1),c_Relation_ORange(X8,X0,X10)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f1219,axiom,
! [X2,X10,X0,X1,X8] :
( hBOOL(hAPP(hAPP(c_in(X10),X1),c_Relation_ORange(X8,X0,X10)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X10)),c_Pair(X2,X1,X0,X10)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeI_0) ).
fof(f9291,plain,
spl0_593,
inference(avatar_split_clause,[],[f1138,f9289]) ).
fof(f1138,axiom,
! [X10,X0,X15,X22,X25,X43,X64] : c_Relation_Orel__comp(c_Relation_Orel__comp(X15,X22,X0,X64,X25),X43,X0,X25,X10) = c_Relation_Orel__comp(X15,c_Relation_Orel__comp(X22,X43,X64,X25,X10),X0,X64,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).
fof(f9287,plain,
spl0_592,
inference(avatar_split_clause,[],[f976,f9285]) ).
fof(f9285,plain,
( spl0_592
<=> ! [X18,X10,X0,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),X6) = c_HOL_Ozero__class_Ozero(X10)
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(X6,X18,X0,X10)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f976,axiom,
! [X10,X0,X18,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),X6) = c_HOL_Ozero__class_Ozero(X10)
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(X6,X18,X0,X10)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__0_H_0) ).
fof(f9283,plain,
spl0_591,
inference(avatar_split_clause,[],[f940,f9281]) ).
fof(f9281,plain,
( spl0_591
<=> ! [X10,X0,X6,X8,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_OImage(X8,X6,X10,X0)))
| hBOOL(hAPP(hAPP(c_in(X10),c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X6,X1,X8,X10,X0)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f940,axiom,
! [X10,X0,X1,X8,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_OImage(X8,X6,X10,X0)))
| hBOOL(hAPP(hAPP(c_in(X10),c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X6,X1,X8,X10,X0)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).
fof(f9279,plain,
spl0_590,
inference(avatar_split_clause,[],[f939,f9277]) ).
fof(f9277,plain,
( spl0_590
<=> ! [X10,X0,X6,X8,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_OImage(X8,X6,X10,X0)))
| hBOOL(hAPP(hAPP(c_in(X10),c_ATP__Linkup_Osko__Relation__XImageE__1__1(X6,X1,X8,X10,X0)),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f939,axiom,
! [X10,X0,X1,X8,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Relation_OImage(X8,X6,X10,X0)))
| hBOOL(hAPP(hAPP(c_in(X10),c_ATP__Linkup_Osko__Relation__XImageE__1__1(X6,X1,X8,X10,X0)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).
fof(f9275,plain,
spl0_589,
inference(avatar_split_clause,[],[f490,f9273]) ).
fof(f9273,plain,
( spl0_589
<=> ! [X0,X6,X21,X7] :
( ~ c_lessequals(X21,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X21,X7,tc_fun(X0,tc_bool))
| c_lessequals(X21,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f490,axiom,
! [X21,X0,X6,X7] :
( ~ c_lessequals(X21,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X21,X7,tc_fun(X0,tc_bool))
| c_lessequals(X21,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
fof(f9271,plain,
spl0_588,
inference(avatar_split_clause,[],[f448,f9269]) ).
fof(f9269,plain,
( spl0_588
<=> ! [X0,X21,X2,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X2),X21))
| c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X7,X0),X21,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f448,axiom,
! [X2,X21,X0,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X2),X21))
| c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X7,X0),X21,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
fof(f9267,plain,
spl0_587,
inference(avatar_split_clause,[],[f447,f9265]) ).
fof(f9265,plain,
( spl0_587
<=> ! [X0,X6,X2,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Set_Oinsert(X2,X7,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f447,axiom,
! [X2,X0,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Set_Oinsert(X2,X7,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
fof(f9263,plain,
spl0_586,
inference(avatar_split_clause,[],[f381,f9261]) ).
fof(f9261,plain,
( spl0_586
<=> ! [X0,X6,X21,X7] :
( ~ c_lessequals(X6,X21,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X21,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X21,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f381,axiom,
! [X21,X0,X6,X7] :
( ~ c_lessequals(X6,X21,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X21,tc_fun(X0,tc_bool))
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X21,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
fof(f9259,plain,
spl0_585,
inference(avatar_split_clause,[],[f270,f9257]) ).
fof(f9257,plain,
( spl0_585
<=> ! [X0,X6,X21,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X21,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f270,axiom,
! [X21,X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X21,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
fof(f9255,plain,
( spl0_584
| ~ spl0_166
| ~ spl0_519 ),
inference(avatar_split_clause,[],[f7549,f7063,f2222,f9253]) ).
fof(f9253,plain,
( spl0_584
<=> ! [X0] : c_Nitpick_Orefl_H(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f2222,plain,
( spl0_166
<=> ! [X0,X3] : hBOOL(hAPP(hAPP(c_in(X0),X3),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f7063,plain,
( spl0_519
<=> ! [X0,X8] :
( c_Nitpick_Orefl_H(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X8,X0),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X8,X0),X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f7549,plain,
( ! [X0] : c_Nitpick_Orefl_H(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_166
| ~ spl0_519 ),
inference(resolution,[],[f7064,f2223]) ).
fof(f2223,plain,
( ! [X3,X0] : hBOOL(hAPP(hAPP(c_in(X0),X3),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))))
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f2222]) ).
fof(f7064,plain,
( ! [X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X8,X0),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X8,X0),X0,X0)),X8))
| c_Nitpick_Orefl_H(X8,X0) )
| ~ spl0_519 ),
inference(avatar_component_clause,[],[f7063]) ).
fof(f9251,plain,
spl0_583,
inference(avatar_split_clause,[],[f269,f9249]) ).
fof(f9249,plain,
( spl0_583
<=> ! [X0,X6,X21,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f269,axiom,
! [X21,X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
fof(f9247,plain,
spl0_582,
inference(avatar_split_clause,[],[f141,f9245]) ).
fof(f9245,plain,
( spl0_582
<=> ! [X0,X6,X21,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f141,axiom,
! [X21,X0,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Lattices_Olower__semilattice__class_Oinf(X6,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
fof(f9243,plain,
spl0_581,
inference(avatar_split_clause,[],[f140,f9241]) ).
fof(f9241,plain,
( spl0_581
<=> ! [X0,X6,X21,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X21,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f140,axiom,
! [X21,X0,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X21,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X7,X21,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
fof(f9146,plain,
( spl0_580
| ~ spl0_165
| ~ spl0_518 ),
inference(avatar_split_clause,[],[f7534,f7059,f2218,f9144]) ).
fof(f9144,plain,
( spl0_580
<=> ! [X0] : c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f2218,plain,
( spl0_165
<=> ! [X5,X0] : ~ hBOOL(hAPP(hAPP(c_in(X0),X5),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f7059,plain,
( spl0_518
<=> ! [X0,X8] :
( c_Relation_Oirrefl(X8,X0)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X8,X0),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X8,X0),X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f7534,plain,
( ! [X0] : c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_165
| ~ spl0_518 ),
inference(resolution,[],[f7060,f2219]) ).
fof(f2219,plain,
( ! [X0,X5] : ~ hBOOL(hAPP(hAPP(c_in(X0),X5),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f2218]) ).
fof(f7060,plain,
( ! [X0,X8] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X8,X0),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X8,X0),X0,X0)),X8))
| c_Relation_Oirrefl(X8,X0) )
| ~ spl0_518 ),
inference(avatar_component_clause,[],[f7059]) ).
fof(f8606,plain,
spl0_579,
inference(avatar_split_clause,[],[f1353,f8604]) ).
fof(f8604,plain,
( spl0_579
<=> ! [X0,X8] : c_Relation_ORange(c_Relation_Oconverse(X8,X0,X0),X0,X0) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f1353,plain,
! [X0,X8] : c_Relation_ORange(c_Relation_Oconverse(X8,X0,X0),X0,X0) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0,X0),X0,X0),
inference(definition_unfolding,[],[f1107,f1146,f1146,f1163]) ).
fof(f1107,axiom,
! [X0,X8] : c_Relation_ODomain(X8,X0,X0) = c_Relation_ODomain(c_Transitive__Closure_Otrancl(X8,X0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).
fof(f8602,plain,
spl0_578,
inference(avatar_split_clause,[],[f1215,f8600]) ).
fof(f8600,plain,
( spl0_578
<=> ! [X6,X0,X3] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),c_Relation_OId__on(X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f1215,axiom,
! [X3,X0,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),c_Relation_OId__on(X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
fof(f8598,plain,
spl0_577,
inference(avatar_split_clause,[],[f1214,f8596]) ).
fof(f8596,plain,
( spl0_577
<=> ! [X4,X0,X6,X3] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_OId__on(X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f1214,axiom,
! [X3,X0,X6,X4] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_OId__on(X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
fof(f8594,plain,
spl0_576,
inference(avatar_split_clause,[],[f1201,f8592]) ).
fof(f8592,plain,
( spl0_576
<=> ! [X0,X16,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X16)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f1201,axiom,
! [X0,X16,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X16)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
fof(f8590,plain,
spl0_575,
inference(avatar_split_clause,[],[f1200,f8588]) ).
fof(f8588,plain,
( spl0_575
<=> ! [X0,X16,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X16)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f1200,axiom,
! [X0,X16,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X16)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
fof(f8586,plain,
spl0_574,
inference(avatar_split_clause,[],[f1129,f8584]) ).
fof(f8584,plain,
( spl0_574
<=> ! [X9,X0,X8,X10,X25] : c_Relation_Oconverse(c_Relation_Orel__comp(X8,X9,X10,X25,X0),X10,X0) = c_Relation_Orel__comp(c_Relation_Oconverse(X9,X25,X0),c_Relation_Oconverse(X8,X10,X25),X0,X25,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f1129,axiom,
! [X10,X0,X8,X9,X25] : c_Relation_Oconverse(c_Relation_Orel__comp(X8,X9,X10,X25,X0),X10,X0) = c_Relation_Orel__comp(c_Relation_Oconverse(X9,X25,X0),c_Relation_Oconverse(X8,X10,X25),X0,X25,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).
fof(f8582,plain,
spl0_573,
inference(avatar_split_clause,[],[f984,f8580]) ).
fof(f8580,plain,
( spl0_573
<=> ! [X18,X10,X0,X6,X45] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X45),X6))
| c_Ring__and__Field_Odvd__class_Odvd(hAPP(X18,X45),c_Finite__Set_Osetprod(X18,X6,X0,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f984,axiom,
! [X10,X0,X18,X6,X45] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X45),X6))
| c_Ring__and__Field_Odvd__class_Odvd(hAPP(X18,X45),c_Finite__Set_Osetprod(X18,X6,X0,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__setprod_0) ).
fof(f8578,plain,
spl0_572,
inference(avatar_split_clause,[],[f925,f8576]) ).
fof(f8576,plain,
( spl0_572
<=> ! [X18,X10,X0,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| hAPP(X18,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(X6,X18,X0,X10)) != c_HOL_Ozero__class_Ozero(X10)
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),X6) = c_HOL_Ozero__class_Ozero(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f925,axiom,
! [X10,X0,X18,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X10)
| hAPP(X18,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1(X6,X18,X0,X10)) != c_HOL_Ozero__class_Ozero(X10)
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),X6) = c_HOL_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__0_H_1) ).
fof(f8574,plain,
spl0_571,
inference(avatar_split_clause,[],[f922,f8572]) ).
fof(f8572,plain,
( spl0_571
<=> ! [X0,X14,X16,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X14 = X16
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| c_Power_Opower__class_Opower(X2,X14,X0) != c_Power_Opower__class_Opower(X2,X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f922,axiom,
! [X2,X0,X16,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X14 = X16
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),X2))
| c_Power_Opower__class_Opower(X2,X14,X0) != c_Power_Opower__class_Opower(X2,X16,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
fof(f8570,plain,
( spl0_570
| ~ spl0_61
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f8526,f8465,f1716,f8568]) ).
fof(f8568,plain,
( spl0_570
<=> ! [X0,X1] : c_Relation_Oirrefl(c_Wellfounded_Omeasure(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f1716,plain,
( spl0_61
<=> ! [X18,X0] : c_Wellfounded_Owf(c_Wellfounded_Omeasure(X18,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f8465,plain,
( spl0_550
<=> ! [X0,X1] :
( c_Relation_Oirrefl(X0,X1)
| ~ c_Wellfounded_Owf(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f8526,plain,
( ! [X0,X1] : c_Relation_Oirrefl(c_Wellfounded_Omeasure(X0,X1),X1)
| ~ spl0_61
| ~ spl0_550 ),
inference(resolution,[],[f8466,f1717]) ).
fof(f1717,plain,
( ! [X0,X18] : c_Wellfounded_Owf(c_Wellfounded_Omeasure(X18,X0),X0)
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f1716]) ).
fof(f8466,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Relation_Oirrefl(X0,X1) )
| ~ spl0_550 ),
inference(avatar_component_clause,[],[f8465]) ).
fof(f8566,plain,
spl0_569,
inference(avatar_split_clause,[],[f707,f8564]) ).
fof(f8564,plain,
( spl0_569
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f707,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
fof(f8562,plain,
spl0_568,
inference(avatar_split_clause,[],[f633,f8560]) ).
fof(f8560,plain,
( spl0_568
<=> ! [X6,X0,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f633,axiom,
! [X0,X6,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).
fof(f8558,plain,
spl0_567,
inference(avatar_split_clause,[],[f632,f8556]) ).
fof(f8556,plain,
( spl0_567
<=> ! [X6,X0,X7] :
( ~ c_lessequals(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f632,axiom,
! [X0,X6,X7] :
( ~ c_lessequals(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).
fof(f8554,plain,
spl0_566,
inference(avatar_split_clause,[],[f559,f8552]) ).
fof(f8552,plain,
( spl0_566
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f559,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f8550,plain,
spl0_565,
inference(avatar_split_clause,[],[f509,f8548]) ).
fof(f8548,plain,
( spl0_565
<=> ! [X0,X6,X3,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X7))
| c_lessequals(c_Set_Oinsert(X3,X6,X0),X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f509,axiom,
! [X3,X0,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X7))
| c_lessequals(c_Set_Oinsert(X3,X6,X0),X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
fof(f8546,plain,
spl0_564,
inference(avatar_split_clause,[],[f476,f8544]) ).
fof(f8544,plain,
( spl0_564
<=> ! [X18,X0,X10,X2,X1] :
( hAPP(X18,X2) = X1
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Set_Ovimage(X18,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),X0,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f476,axiom,
! [X2,X10,X0,X18,X1] :
( hAPP(X18,X2) = X1
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Set_Ovimage(X18,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),X0,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
fof(f8542,plain,
spl0_563,
inference(avatar_split_clause,[],[f458,f8540]) ).
fof(f8540,plain,
( spl0_563
<=> ! [X6,X0] :
( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X6
| c_Finite__Set_Ocard(X6,X0) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f458,axiom,
! [X0,X6] :
( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = X6
| c_Finite__Set_Ocard(X6,X0) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).
fof(f8538,plain,
spl0_562,
inference(avatar_split_clause,[],[f443,f8536]) ).
fof(f8536,plain,
( spl0_562
<=> ! [X0,X6,X3,X7] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ c_lessequals(X6,c_Set_Oinsert(X3,X7,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f443,axiom,
! [X3,X0,X6,X7] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| ~ c_lessequals(X6,c_Set_Oinsert(X3,X7,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
fof(f8534,plain,
spl0_561,
inference(avatar_split_clause,[],[f429,f8532]) ).
fof(f8532,plain,
( spl0_561
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f429,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
fof(f8530,plain,
spl0_560,
inference(avatar_split_clause,[],[f428,f8528]) ).
fof(f8528,plain,
( spl0_560
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f428,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
fof(f8520,plain,
spl0_559,
inference(avatar_split_clause,[],[f404,f8518]) ).
fof(f8518,plain,
( spl0_559
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3) = X4
| c_Orderings_Otop__class_Otop(X0) != c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0)
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f404,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3) = X4
| c_Orderings_Otop__class_Otop(X0) != c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0)
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__unique_0) ).
fof(f8516,plain,
spl0_558,
inference(avatar_split_clause,[],[f349,f8514]) ).
fof(f8514,plain,
( spl0_558
<=> ! [X9,X0,X8] :
( ~ c_lessequals(X8,c_Transitive__Closure_Ortrancl(X9,X0),tc_fun(tc_prod(X0,X0),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X8,X0),c_Transitive__Closure_Ortrancl(X9,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f349,axiom,
! [X0,X8,X9] :
( ~ c_lessequals(X8,c_Transitive__Closure_Ortrancl(X9,X0),tc_fun(tc_prod(X0,X0),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X8,X0),c_Transitive__Closure_Ortrancl(X9,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
fof(f8512,plain,
spl0_557,
inference(avatar_split_clause,[],[f216,f8510]) ).
fof(f8510,plain,
( spl0_557
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f216,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f8508,plain,
spl0_556,
inference(avatar_split_clause,[],[f111,f8506]) ).
fof(f8506,plain,
( spl0_556
<=> ! [X0,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0))),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f111,axiom,
! [X0,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X16),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0))),X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(f8504,plain,
spl0_555,
inference(avatar_split_clause,[],[f49,f8502]) ).
fof(f8502,plain,
( spl0_555
<=> ! [X6,X0,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f49,axiom,
! [X0,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).
fof(f8500,plain,
spl0_554,
inference(avatar_split_clause,[],[f48,f8498]) ).
fof(f8498,plain,
( spl0_554
<=> ! [X6,X0,X7] :
( c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f48,axiom,
! [X0,X6,X7] :
( c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
fof(f8496,plain,
spl0_553,
inference(avatar_split_clause,[],[f33,f8494]) ).
fof(f8494,plain,
( spl0_553
<=> ! [X0,X6,X2,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X6,X0),c_Set_Oinsert(X2,X7,X0),tc_fun(X0,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f33,axiom,
! [X2,X0,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X2,X6,X0),c_Set_Oinsert(X2,X7,X0),tc_fun(X0,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
fof(f8492,plain,
spl0_552,
inference(avatar_split_clause,[],[f32,f8490]) ).
fof(f8490,plain,
( spl0_552
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X1,X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f32,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X1,X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f8488,plain,
spl0_551,
inference(avatar_split_clause,[],[f31,f8486]) ).
fof(f8486,plain,
( spl0_551
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f31,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f8467,plain,
( spl0_550
| ~ spl0_398
| ~ spl0_518 ),
inference(avatar_split_clause,[],[f7523,f7059,f4960,f8465]) ).
fof(f4960,plain,
( spl0_398
<=> ! [X2,X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X2,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f7523,plain,
( ! [X0,X1] :
( c_Relation_Oirrefl(X0,X1)
| ~ c_Wellfounded_Owf(X0,X1) )
| ~ spl0_398
| ~ spl0_518 ),
inference(resolution,[],[f7060,f4961]) ).
fof(f4961,plain,
( ! [X2,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X2,X0,X0)),X8))
| ~ c_Wellfounded_Owf(X8,X0) )
| ~ spl0_398 ),
inference(avatar_component_clause,[],[f4960]) ).
fof(f8436,plain,
( spl0_549
| ~ spl0_212
| ~ spl0_546 ),
inference(avatar_split_clause,[],[f7771,f7768,f2440,f8434]) ).
fof(f8434,plain,
( spl0_549
<=> ! [X0,X14] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f7768,plain,
( spl0_546
<=> ! [X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f7771,plain,
( ! [X0,X14] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14))) )
| ~ spl0_212
| ~ spl0_546 ),
inference(forward_demodulation,[],[f7769,f2442]) ).
fof(f7769,plain,
( ! [X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14))) )
| ~ spl0_546 ),
inference(avatar_component_clause,[],[f7768]) ).
fof(f8432,plain,
( spl0_548
| ~ spl0_212
| ~ spl0_545 ),
inference(avatar_split_clause,[],[f7766,f7763,f2440,f8430]) ).
fof(f8430,plain,
( spl0_548
<=> ! [X0,X14] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f7763,plain,
( spl0_545
<=> ! [X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f7766,plain,
( ! [X0,X14] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14))) )
| ~ spl0_212
| ~ spl0_545 ),
inference(forward_demodulation,[],[f7764,f2442]) ).
fof(f7764,plain,
( ! [X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14))) )
| ~ spl0_545 ),
inference(avatar_component_clause,[],[f7763]) ).
fof(f7775,plain,
spl0_547,
inference(avatar_split_clause,[],[f1368,f7773]) ).
fof(f1368,plain,
! [X0,X8] :
( c_Equiv__Relations_Oequiv(c_Relation_ORange(c_Relation_Oconverse(X8,X0,X0),X0,X0),X8,X0)
| c_Relation_Orel__comp(c_Relation_Oconverse(X8,X0,X0),X8,X0,X0,X0) != X8 ),
inference(definition_unfolding,[],[f1143,f1146]) ).
fof(f1143,axiom,
! [X0,X8] :
( c_Equiv__Relations_Oequiv(c_Relation_ODomain(X8,X0,X0),X8,X0)
| c_Relation_Orel__comp(c_Relation_Oconverse(X8,X0,X0),X8,X0,X0,X0) != X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__equivI_0) ).
fof(f7770,plain,
spl0_546,
inference(avatar_split_clause,[],[f1042,f7768]) ).
fof(f1042,axiom,
! [X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
fof(f7765,plain,
spl0_545,
inference(avatar_split_clause,[],[f1041,f7763]) ).
fof(f1041,axiom,
! [X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
fof(f7761,plain,
( spl0_544
| ~ spl0_370
| ~ spl0_519 ),
inference(avatar_split_clause,[],[f7542,f7063,f4558,f7759]) ).
fof(f4558,plain,
( spl0_370
<=> ! [X2,X0,X8] : hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X2,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f7542,plain,
( ! [X0,X1] : c_Nitpick_Orefl_H(c_Transitive__Closure_Ortrancl(X0,X1),X1)
| ~ spl0_370
| ~ spl0_519 ),
inference(resolution,[],[f7064,f4559]) ).
fof(f4559,plain,
( ! [X2,X0,X8] : hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X2,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0)))
| ~ spl0_370 ),
inference(avatar_component_clause,[],[f4558]) ).
fof(f7757,plain,
spl0_543,
inference(avatar_split_clause,[],[f1026,f7755]) ).
fof(f7755,plain,
( spl0_543
<=> ! [X6,X0,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X6,X5,X0)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X5),c_Relation_OId__on(X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f1026,axiom,
! [X0,X6,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X6,X5,X0)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X5),c_Relation_OId__on(X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).
fof(f7753,plain,
spl0_542,
inference(avatar_split_clause,[],[f1021,f7751]) ).
fof(f7751,plain,
( spl0_542
<=> ! [X48,X0] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),c_Relation_OId(X0)))
| c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X48,X0),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X48,X0),X0,X0) = X48 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f1021,axiom,
! [X48,X0] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),c_Relation_OId(X0)))
| c_Pair(c_ATP__Linkup_Osko__Relation__XIdE__1__1(X48,X0),c_ATP__Linkup_Osko__Relation__XIdE__1__1(X48,X0),X0,X0) = X48 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdE_0) ).
fof(f7749,plain,
spl0_541,
inference(avatar_split_clause,[],[f987,f7747]) ).
fof(f7747,plain,
( spl0_541
<=> ! [X18,X0,X10,X19] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| c_HOL_Oone__class_Oone(X10) = c_Finite__Set_Osetprod(X18,X19,X0,X10)
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1(X19,X18,X0,X10)),X19)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f987,axiom,
! [X10,X0,X18,X19] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| c_HOL_Oone__class_Oone(X10) = c_Finite__Set_Osetprod(X18,X19,X0,X10)
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1(X19,X18,X0,X10)),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__1_H_0) ).
fof(f7745,plain,
spl0_540,
inference(avatar_split_clause,[],[f954,f7743]) ).
fof(f7743,plain,
( spl0_540
<=> ! [X0,X8,X3] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),c_Wellfounded_Oacc(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X8,X3,X0)),c_Wellfounded_Oacc(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f954,axiom,
! [X3,X0,X8] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),c_Wellfounded_Oacc(X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X8,X3,X0)),c_Wellfounded_Oacc(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
fof(f7741,plain,
spl0_539,
inference(avatar_split_clause,[],[f951,f7739]) ).
fof(f7739,plain,
( spl0_539
<=> ! [X0,X3,X15] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),c_Wellfounded_Oacc(X15,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X15,X3,X0)),c_Wellfounded_Oacc(X15,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f951,axiom,
! [X3,X0,X15] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),c_Wellfounded_Oacc(X15,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X15,X3,X0)),c_Wellfounded_Oacc(X15,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
fof(f7737,plain,
spl0_538,
inference(avatar_split_clause,[],[f890,f7735]) ).
fof(f7735,plain,
( spl0_538
<=> ! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),c_Power_Opower__class_Opower(X2,X14,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f890,axiom,
! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),c_Power_Opower__class_Opower(X2,X14,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
fof(f7733,plain,
spl0_537,
inference(avatar_split_clause,[],[f631,f7731]) ).
fof(f7731,plain,
( spl0_537
<=> ! [X2,X0,X8,X10,X1] : c_Relation_ORange(c_Set_Oinsert(c_Pair(X2,X1,X10,X0),X8,tc_prod(X10,X0)),X10,X0) = c_Set_Oinsert(X1,c_Relation_ORange(X8,X10,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f631,axiom,
! [X2,X10,X0,X1,X8] : c_Relation_ORange(c_Set_Oinsert(c_Pair(X2,X1,X10,X0),X8,tc_prod(X10,X0)),X10,X0) = c_Set_Oinsert(X1,c_Relation_ORange(X8,X10,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__insert_0) ).
fof(f7729,plain,
spl0_536,
inference(avatar_split_clause,[],[f425,f7727]) ).
fof(f7727,plain,
( spl0_536
<=> ! [X18,X10,X0,X6] : c_Set_Ovimage(X18,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X10,tc_bool)),X6),X0,X10) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),c_Set_Ovimage(X18,X6,X0,X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f425,axiom,
! [X10,X0,X18,X6] : c_Set_Ovimage(X18,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X10,tc_bool)),X6),X0,X10) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),c_Set_Ovimage(X18,X6,X0,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
fof(f7725,plain,
spl0_535,
inference(avatar_split_clause,[],[f398,f7723]) ).
fof(f7723,plain,
( spl0_535
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X23,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X23,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f398,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X23,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X23,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
fof(f7721,plain,
spl0_534,
inference(avatar_split_clause,[],[f289,f7719]) ).
fof(f7719,plain,
( spl0_534
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X23,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f289,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X23,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
fof(f7715,plain,
spl0_533,
inference(avatar_split_clause,[],[f254,f7713]) ).
fof(f7713,plain,
( spl0_533
<=> ! [X0,X14,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_Power_Opower__class_Opower(X2,X14,X0),c_Power_Opower__class_Opower(X1,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f254,axiom,
! [X2,X0,X1,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_Power_Opower__class_Opower(X2,X14,X0),c_Power_Opower__class_Opower(X1,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
fof(f7711,plain,
spl0_532,
inference(avatar_split_clause,[],[f252,f7709]) ).
fof(f7709,plain,
( spl0_532
<=> ! [X13,X0,X14,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X14,X13,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X2,X0)
| c_lessequals(c_Power_Opower__class_Opower(X2,X14,X0),c_Power_Opower__class_Opower(X2,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f252,axiom,
! [X2,X0,X14,X13] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X14,X13,tc_nat)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X2,X0)
| c_lessequals(c_Power_Opower__class_Opower(X2,X14,X0),c_Power_Opower__class_Opower(X2,X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing_0) ).
fof(f7707,plain,
spl0_531,
inference(avatar_split_clause,[],[f98,f7705]) ).
fof(f7705,plain,
( spl0_531
<=> ! [X2,X0,X14] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Power_Opower__class_Opower(X2,X14,X0)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Power_Opower__class_Opower(X2,X14,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f98,axiom,
! [X2,X0,X14] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Power_Opower__class_Opower(X2,X14,X0)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_Power_Opower__class_Opower(X2,X14,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).
fof(f7567,plain,
( spl0_530
| ~ spl0_339
| ~ spl0_519 ),
inference(avatar_split_clause,[],[f7541,f7063,f3806,f7565]) ).
fof(f7565,plain,
( spl0_530
<=> ! [X0] : c_Nitpick_Orefl_H(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f7541,plain,
( ! [X0] : c_Nitpick_Orefl_H(c_Relation_OId(X0),X0)
| ~ spl0_339
| ~ spl0_519 ),
inference(resolution,[],[f7064,f3807]) ).
fof(f7331,plain,
( spl0_529
| ~ spl0_212
| ~ spl0_498 ),
inference(avatar_split_clause,[],[f6972,f6969,f2440,f7329]) ).
fof(f7329,plain,
( spl0_529
<=> ! [X0,X14] :
( c_Orderings_Obot__class_Obot(tc_nat) = X14
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f6969,plain,
( spl0_498
<=> ! [X0,X14] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f6972,plain,
( ! [X0,X14] :
( c_Orderings_Obot__class_Obot(tc_nat) = X14
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0) )
| ~ spl0_212
| ~ spl0_498 ),
inference(forward_demodulation,[],[f6970,f2442]) ).
fof(f6970,plain,
( ! [X0,X14] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0) )
| ~ spl0_498 ),
inference(avatar_component_clause,[],[f6969]) ).
fof(f7149,plain,
( spl0_528
| ~ spl0_166
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f5324,f4960,f2222,f7147]) ).
fof(f7147,plain,
( spl0_528
<=> ! [X0] : ~ c_Wellfounded_Owf(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f5324,plain,
( ! [X0] : ~ c_Wellfounded_Owf(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_166
| ~ spl0_398 ),
inference(resolution,[],[f4961,f2223]) ).
fof(f7097,plain,
spl0_527,
inference(avatar_split_clause,[],[f1411,f7095]) ).
fof(f7095,plain,
( spl0_527
<=> ! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f1411,plain,
! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),
inference(forward_demodulation,[],[f1032,f1355]) ).
fof(f1355,plain,
! [X0,X8] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X8,X0),X8,X0,X0,X0) = c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),
inference(definition_unfolding,[],[f1162,f1163]) ).
fof(f1162,axiom,
! [X0,X8] : c_Transitive__Closure_Otrancl(X8,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X8,X0),X8,X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
fof(f1032,axiom,
! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X8,X0),X8,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).
fof(f7093,plain,
spl0_526,
inference(avatar_split_clause,[],[f1407,f7091]) ).
fof(f7091,plain,
( spl0_526
<=> ! [X37,X65,X3] :
( X3 = X37
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X37,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X65),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f1407,plain,
! [X65,X3,X37] :
( X3 = X37
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X37,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X65),X3))) ),
inference(duplicate_literal_removal,[],[f1270]) ).
fof(f1270,axiom,
! [X65,X3,X37] :
( X3 = X37
| X3 = X37
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X37,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X65),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_4) ).
fof(f7089,plain,
spl0_525,
inference(avatar_split_clause,[],[f1406,f7087]) ).
fof(f7087,plain,
( spl0_525
<=> ! [X4,X65,X3] :
( X3 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X65),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f1406,plain,
! [X65,X3,X4] :
( X3 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X65),X3))) ),
inference(duplicate_literal_removal,[],[f1258]) ).
fof(f1258,axiom,
! [X65,X3,X4] :
( X3 = X4
| X3 = X4
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X65),X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
fof(f7085,plain,
spl0_524,
inference(avatar_split_clause,[],[f1359,f7083]) ).
fof(f7083,plain,
( spl0_524
<=> ! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f1359,plain,
! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),
inference(definition_unfolding,[],[f1029,f1163]) ).
fof(f1029,axiom,
! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(X8,X0),c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).
fof(f7081,plain,
spl0_523,
inference(avatar_split_clause,[],[f1098,f7079]) ).
fof(f7079,plain,
( spl0_523
<=> ! [X18,X0,X10,X2,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),hAPP(X18,X2)),X7))
| hBOOL(hAPP(hAPP(c_in(X10),X2),c_Set_Ovimage(X18,X7,X10,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f1098,axiom,
! [X2,X10,X0,X18,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),hAPP(X18,X2)),X7))
| hBOOL(hAPP(hAPP(c_in(X10),X2),c_Set_Ovimage(X18,X7,X10,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).
fof(f7077,plain,
spl0_522,
inference(avatar_split_clause,[],[f1096,f7075]) ).
fof(f7075,plain,
( spl0_522
<=> ! [X18,X10,X0,X6,X2] :
( hBOOL(hAPP(hAPP(c_in(X10),hAPP(X18,X2)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Set_Ovimage(X18,X6,X0,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f1096,axiom,
! [X2,X10,X0,X18,X6] :
( hBOOL(hAPP(hAPP(c_in(X10),hAPP(X18,X2)),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Set_Ovimage(X18,X6,X0,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
fof(f7073,plain,
( spl0_521
| ~ spl0_165
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f5311,f4956,f2218,f7071]) ).
fof(f7071,plain,
( spl0_521
<=> ! [X0] : ~ c_Nitpick_Orefl_H(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f4956,plain,
( spl0_397
<=> ! [X0,X8,X3] :
( ~ c_Nitpick_Orefl_H(X8,X0)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f5311,plain,
( ! [X0] : ~ c_Nitpick_Orefl_H(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_165
| ~ spl0_397 ),
inference(resolution,[],[f4957,f2219]) ).
fof(f4957,plain,
( ! [X3,X0,X8] :
( hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),X8))
| ~ c_Nitpick_Orefl_H(X8,X0) )
| ~ spl0_397 ),
inference(avatar_component_clause,[],[f4956]) ).
fof(f7069,plain,
spl0_520,
inference(avatar_split_clause,[],[f1082,f7067]) ).
fof(f7067,plain,
( spl0_520
<=> ! [X48,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),c_Transitive__Closure_Ortrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f1082,axiom,
! [X48,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),X8))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),c_Transitive__Closure_Ortrancl(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
fof(f7065,plain,
spl0_519,
inference(avatar_split_clause,[],[f1038,f7063]) ).
fof(f1038,axiom,
! [X0,X8] :
( c_Nitpick_Orefl_H(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X8,X0),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X8,X0),X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
fof(f7061,plain,
spl0_518,
inference(avatar_split_clause,[],[f1035,f7059]) ).
fof(f1035,axiom,
! [X0,X8] :
( c_Relation_Oirrefl(X8,X0)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X8,X0),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(X8,X0),X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_1) ).
fof(f7057,plain,
spl0_517,
inference(avatar_split_clause,[],[f1033,f7055]) ).
fof(f7055,plain,
( spl0_517
<=> ! [X6,X0,X8] :
( ~ c_Relation_Orefl__on(X6,X8,X0)
| c_lessequals(X8,c_Relation_Orel__comp(c_Relation_Oconverse(X8,X0,X0),X8,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f1033,axiom,
! [X0,X8,X6] :
( ~ c_Relation_Orefl__on(X6,X8,X0)
| c_lessequals(X8,c_Relation_Orel__comp(c_Relation_Oconverse(X8,X0,X0),X8,X0,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
fof(f7053,plain,
spl0_516,
inference(avatar_split_clause,[],[f952,f7051]) ).
fof(f7051,plain,
( spl0_516
<=> ! [X32,X0,X8,X2] :
( hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X32,X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f952,axiom,
! [X2,X0,X8,X32] :
( hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X32,X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).
fof(f7049,plain,
spl0_515,
inference(avatar_split_clause,[],[f948,f7047]) ).
fof(f7047,plain,
( spl0_515
<=> ! [X32,X0,X8,X2] :
( hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X32,X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f948,axiom,
! [X2,X0,X8,X32] :
( hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X32,X8,X0)))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Wellfounded_Oacc(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_2) ).
fof(f7045,plain,
spl0_514,
inference(avatar_split_clause,[],[f943,f7043]) ).
fof(f7043,plain,
( spl0_514
<=> ! [X18,X0,X10,X19] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| c_HOL_Oone__class_Oone(X10) = c_Finite__Set_Osetprod(X18,X19,X0,X10)
| hAPP(X18,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1(X19,X18,X0,X10)) != c_HOL_Oone__class_Oone(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f943,axiom,
! [X10,X0,X18,X19] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X10)
| c_HOL_Oone__class_Oone(X10) = c_Finite__Set_Osetprod(X18,X19,X0,X10)
| hAPP(X18,c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1(X19,X18,X0,X10)) != c_HOL_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__1_H_1) ).
fof(f7041,plain,
spl0_513,
inference(avatar_split_clause,[],[f937,f7039]) ).
fof(f7039,plain,
( spl0_513
<=> ! [X47,X0,X3,X15] :
( ~ c_Wellfounded_Owf(X15,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X47))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X47,X15,X0)),X47)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f937,axiom,
! [X3,X0,X47,X15] :
( ~ c_Wellfounded_Owf(X15,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X47))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X47,X15,X0)),X47)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).
fof(f7037,plain,
spl0_512,
inference(avatar_split_clause,[],[f936,f7035]) ).
fof(f7035,plain,
( spl0_512
<=> ! [X37,X47,X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X37),X47))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X47,X8,X0)),X47)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f936,axiom,
! [X0,X47,X8,X37] :
( ~ c_Wellfounded_Owf(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X37),X47))
| hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X47,X8,X0)),X47)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
fof(f7033,plain,
spl0_511,
inference(avatar_split_clause,[],[f823,f7031]) ).
fof(f7031,plain,
( spl0_511
<=> ! [X4,X0,X23,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X23,X4,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X23),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f823,axiom,
! [X3,X0,X4,X23] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X23,X4,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X23),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f7029,plain,
( spl0_510
| ~ spl0_166
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f5308,f4947,f2222,f7027]) ).
fof(f7027,plain,
( spl0_510
<=> ! [X0] : ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f4947,plain,
( spl0_395
<=> ! [X0,X8,X3] :
( ~ c_Relation_Oirrefl(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f5308,plain,
( ! [X0] : ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_166
| ~ spl0_395 ),
inference(resolution,[],[f4948,f2223]) ).
fof(f4948,plain,
( ! [X3,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),X8))
| ~ c_Relation_Oirrefl(X8,X0) )
| ~ spl0_395 ),
inference(avatar_component_clause,[],[f4947]) ).
fof(f7025,plain,
spl0_509,
inference(avatar_split_clause,[],[f822,f7023]) ).
fof(f7023,plain,
( spl0_509
<=> ! [X4,X0,X23,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X23),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X23),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f822,axiom,
! [X3,X0,X4,X23] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X23),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X23),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f7021,plain,
spl0_508,
inference(avatar_split_clause,[],[f821,f7019]) ).
fof(f7019,plain,
( spl0_508
<=> ! [X4,X0,X23,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X23))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f821,axiom,
! [X3,X0,X4,X23] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X23))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f7017,plain,
spl0_507,
inference(avatar_split_clause,[],[f820,f7015]) ).
fof(f7015,plain,
( spl0_507
<=> ! [X4,X0,X23,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X23,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f820,axiom,
! [X3,X0,X4,X23] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X23,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f7013,plain,
spl0_506,
inference(avatar_split_clause,[],[f797,f7011]) ).
fof(f7011,plain,
( spl0_506
<=> ! [X0,X6,X2,X1] :
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Set_Oinsert(X1,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f797,axiom,
! [X2,X0,X1,X6] :
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),c_Set_Oinsert(X1,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
fof(f7009,plain,
spl0_505,
inference(avatar_split_clause,[],[f787,f7007]) ).
fof(f7007,plain,
( spl0_505
<=> ! [X0,X6,X52,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X52),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X52),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f787,axiom,
! [X0,X6,X7,X52] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X52),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X52),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
fof(f7005,plain,
spl0_504,
inference(avatar_split_clause,[],[f606,f7003]) ).
fof(f7003,plain,
( spl0_504
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f606,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup_0) ).
fof(f7001,plain,
spl0_503,
inference(avatar_split_clause,[],[f588,f6999]) ).
fof(f6999,plain,
( spl0_503
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f588,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf_0) ).
fof(f6997,plain,
spl0_502,
inference(avatar_split_clause,[],[f560,f6995]) ).
fof(f6995,plain,
( spl0_502
<=> ! [X2,X0,X14,X16,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_lessequals(X16,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X14,X0),X1,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X16,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f560,axiom,
! [X2,X0,X1,X16,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_lessequals(X16,X14,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X14,X0),X1,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X16,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__dvd_0) ).
fof(f6993,plain,
spl0_501,
inference(avatar_split_clause,[],[f505,f6991]) ).
fof(f6991,plain,
( spl0_501
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f505,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
fof(f6989,plain,
spl0_500,
inference(avatar_split_clause,[],[f504,f6987]) ).
fof(f6987,plain,
( spl0_500
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X3,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0),c_Lattices_Oupper__semilattice__class_Osup(X23,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f504,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X3,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0),c_Lattices_Oupper__semilattice__class_Osup(X23,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
fof(f6976,plain,
spl0_499,
inference(avatar_split_clause,[],[f496,f6974]) ).
fof(f6974,plain,
( spl0_499
<=> ! [X4,X0,X14,X16,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_lessequals(X14,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X3,X14,X0),c_Power_Opower__class_Opower(X4,X16,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f496,axiom,
! [X3,X0,X16,X14,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_lessequals(X14,X16,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X3,X14,X0),c_Power_Opower__class_Opower(X4,X16,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__le_0) ).
fof(f6971,plain,
spl0_498,
inference(avatar_split_clause,[],[f479,f6969]) ).
fof(f479,axiom,
! [X0,X14] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
fof(f6967,plain,
spl0_497,
inference(avatar_split_clause,[],[f445,f6965]) ).
fof(f6965,plain,
( spl0_497
<=> ! [X18,X10,X0,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Ovimage(X18,X6,X10,X0),c_Set_Ovimage(X18,X7,X10,X0),tc_fun(X10,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f445,axiom,
! [X10,X0,X18,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Ovimage(X18,X6,X10,X0),c_Set_Ovimage(X18,X7,X10,X0),tc_fun(X10,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
fof(f6963,plain,
spl0_496,
inference(avatar_split_clause,[],[f348,f6961]) ).
fof(f6961,plain,
( spl0_496
<=> ! [X6,X0,X3] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_Set_Oinsert(X3,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f348,axiom,
! [X3,X0,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X6))
| c_Finite__Set_Ocard(X6,X0) = c_Finite__Set_Ocard(c_Set_Oinsert(X3,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_0) ).
fof(f6959,plain,
spl0_495,
inference(avatar_split_clause,[],[f344,f6957]) ).
fof(f6957,plain,
( spl0_495
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f344,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f6955,plain,
spl0_494,
inference(avatar_split_clause,[],[f343,f6953]) ).
fof(f6953,plain,
( spl0_494
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f343,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f6951,plain,
spl0_493,
inference(avatar_split_clause,[],[f342,f6949]) ).
fof(f6949,plain,
( spl0_493
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X2,X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f342,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X2,X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f6947,plain,
spl0_492,
inference(avatar_split_clause,[],[f341,f6945]) ).
fof(f6945,plain,
( spl0_492
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f341,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f6943,plain,
spl0_491,
inference(avatar_split_clause,[],[f340,f6941]) ).
fof(f6941,plain,
( spl0_491
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X2,X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f340,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X2,X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f6939,plain,
spl0_490,
inference(avatar_split_clause,[],[f339,f6937]) ).
fof(f6937,plain,
( spl0_490
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f339,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f6934,plain,
spl0_489,
inference(avatar_split_clause,[],[f277,f6932]) ).
fof(f6932,plain,
( spl0_489
<=> ! [X6,X0,X7] :
( ~ c_Finite__Set_Ofinite(X7,X0)
| X6 = X7
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(X7,X0),c_Finite__Set_Ocard(X6,X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f277,axiom,
! [X0,X6,X7] :
( ~ c_Finite__Set_Ofinite(X7,X0)
| X6 = X7
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Finite__Set_Ocard(X7,X0),c_Finite__Set_Ocard(X6,X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__seteq_0) ).
fof(f6930,plain,
spl0_488,
inference(avatar_split_clause,[],[f207,f6928]) ).
fof(f6928,plain,
( spl0_488
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X23,X0),X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0),c_Lattices_Olower__semilattice__class_Oinf(X23,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f207,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X23,X0),X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0),c_Lattices_Olower__semilattice__class_Oinf(X23,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
fof(f6926,plain,
spl0_487,
inference(avatar_split_clause,[],[f206,f6924]) ).
fof(f6924,plain,
( spl0_487
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X23,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f206,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X23,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
fof(f6922,plain,
spl0_486,
inference(avatar_split_clause,[],[f13,f6920]) ).
fof(f6920,plain,
( spl0_486
<=> ! [X9,X0,X8] :
( ~ c_lessequals(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X8,X0),c_Transitive__Closure_Ortrancl(X9,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f13,axiom,
! [X0,X8,X9] :
( ~ c_lessequals(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool))
| c_lessequals(c_Transitive__Closure_Ortrancl(X8,X0),c_Transitive__Closure_Ortrancl(X9,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).
fof(f6620,plain,
( spl0_485
| ~ spl0_397
| ~ spl0_440 ),
inference(avatar_split_clause,[],[f6057,f5540,f4956,f6618]) ).
fof(f6618,plain,
( spl0_485
<=> ! [X0,X1] : ~ c_Nitpick_Orefl_H(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X0),X1),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f5540,plain,
( spl0_440
<=> ! [X37,X65,X3] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X37,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X65),X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f6057,plain,
( ! [X0,X1] : ~ c_Nitpick_Orefl_H(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X0),X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_397
| ~ spl0_440 ),
inference(resolution,[],[f5541,f4957]) ).
fof(f5541,plain,
( ! [X65,X3,X37] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X37,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X65),X3)))
| ~ spl0_440 ),
inference(avatar_component_clause,[],[f5540]) ).
fof(f6598,plain,
( spl0_484
| ~ spl0_212
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f6363,f6360,f2440,f6596]) ).
fof(f6596,plain,
( spl0_484
<=> ! [X6,X0] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_Finite__Set_Ocard(X6,X0)))
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f6360,plain,
( spl0_466
<=> ! [X6,X0] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f6363,plain,
( ! [X0,X6] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_Finite__Set_Ocard(X6,X0)))
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_212
| ~ spl0_466 ),
inference(forward_demodulation,[],[f6361,f2442]) ).
fof(f6361,plain,
( ! [X0,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(X6,X0))) )
| ~ spl0_466 ),
inference(avatar_component_clause,[],[f6360]) ).
fof(f6573,plain,
( spl0_483
| ~ spl0_212
| ~ spl0_462 ),
inference(avatar_split_clause,[],[f6346,f6343,f2440,f6571]) ).
fof(f6571,plain,
( spl0_483
<=> ! [X0] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)))
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f6343,plain,
( spl0_462
<=> ! [X0] :
( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f6346,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)))
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) )
| ~ spl0_212
| ~ spl0_462 ),
inference(forward_demodulation,[],[f6344,f2442]) ).
fof(f6344,plain,
( ! [X0] :
( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0))) )
| ~ spl0_462 ),
inference(avatar_component_clause,[],[f6343]) ).
fof(f6427,plain,
( spl0_482
| ~ spl0_397
| ~ spl0_438 ),
inference(avatar_split_clause,[],[f5999,f5532,f4956,f6425]) ).
fof(f6425,plain,
( spl0_482
<=> ! [X0,X1] : ~ c_Nitpick_Orefl_H(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X0),X1),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f5532,plain,
( spl0_438
<=> ! [X4,X65,X3] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X65),X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f5999,plain,
( ! [X0,X1] : ~ c_Nitpick_Orefl_H(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X0),X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_397
| ~ spl0_438 ),
inference(resolution,[],[f5533,f4957]) ).
fof(f5533,plain,
( ! [X65,X3,X4] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X65),X3)))
| ~ spl0_438 ),
inference(avatar_component_clause,[],[f5532]) ).
fof(f6423,plain,
spl0_481,
inference(avatar_split_clause,[],[f1405,f6421]) ).
fof(f6421,plain,
( spl0_481
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f1405,plain,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ),
inference(duplicate_literal_removal,[],[f210]) ).
fof(f210,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f6419,plain,
spl0_480,
inference(avatar_split_clause,[],[f1367,f6417]) ).
fof(f6417,plain,
( spl0_480
<=> ! [X0,X8] :
( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X8,X0,X0),X0)
| c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f1367,plain,
! [X0,X8] :
( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X8,X0,X0),X0)
| c_Wellfounded_Owf(c_Relation_Oconverse(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0,X0),X0) ),
inference(definition_unfolding,[],[f1115,f1163]) ).
fof(f1115,axiom,
! [X0,X8] :
( ~ c_Wellfounded_Owf(c_Relation_Oconverse(X8,X0,X0),X0)
| c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X8,X0),X0,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
fof(f6415,plain,
spl0_479,
inference(avatar_split_clause,[],[f1244,f6413]) ).
fof(f6413,plain,
( spl0_479
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f1244,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
fof(f6411,plain,
spl0_478,
inference(avatar_split_clause,[],[f953,f6409]) ).
fof(f6409,plain,
( spl0_478
<=> ! [X32,X8,X3] :
( hBOOL(hAPP(X32,X3))
| ~ hBOOL(hAPP(X32,v_sko__Wellfounded__Xacc__Xinduct__1(X32,X8)))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X8,t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f953,axiom,
! [X3,X8,X32] :
( hBOOL(hAPP(X32,X3))
| ~ hBOOL(hAPP(X32,v_sko__Wellfounded__Xacc__Xinduct__1(X32,X8)))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X8,t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).
fof(f6407,plain,
spl0_477,
inference(avatar_split_clause,[],[f949,f6405]) ).
fof(f6405,plain,
( spl0_477
<=> ! [X32,X8,X3] :
( hBOOL(hAPP(X32,X3))
| ~ hBOOL(hAPP(X32,v_sko__Wellfounded__Xacc__Xinducts__1(X32,X8)))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X8,t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f949,axiom,
! [X3,X8,X32] :
( hBOOL(hAPP(X32,X3))
| ~ hBOOL(hAPP(X32,v_sko__Wellfounded__Xacc__Xinducts__1(X32,X8)))
| ~ hBOOL(hAPP(hAPP(c_in(t_a),X3),c_Wellfounded_Oacc(X8,t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).
fof(f6403,plain,
spl0_476,
inference(avatar_split_clause,[],[f849,f6401]) ).
fof(f6401,plain,
( spl0_476
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f849,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).
fof(f6399,plain,
spl0_475,
inference(avatar_split_clause,[],[f848,f6397]) ).
fof(f6397,plain,
( spl0_475
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f848,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).
fof(f6395,plain,
spl0_474,
inference(avatar_split_clause,[],[f833,f6393]) ).
fof(f6393,plain,
( spl0_474
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f833,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
fof(f6391,plain,
spl0_473,
inference(avatar_split_clause,[],[f832,f6389]) ).
fof(f6389,plain,
( spl0_473
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f832,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
fof(f6387,plain,
spl0_472,
inference(avatar_split_clause,[],[f806,f6385]) ).
fof(f6385,plain,
( spl0_472
<=> ! [X5,X0,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f806,axiom,
! [X0,X6,X7,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
fof(f6383,plain,
spl0_471,
inference(avatar_split_clause,[],[f805,f6381]) ).
fof(f6381,plain,
( spl0_471
<=> ! [X5,X0,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X5),X7))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f805,axiom,
! [X0,X6,X7,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),X5),X7))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
fof(f6379,plain,
spl0_470,
inference(avatar_split_clause,[],[f801,f6377]) ).
fof(f6377,plain,
( spl0_470
<=> ! [X6,X5,X0] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X5),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f801,axiom,
! [X0,X6,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X5),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).
fof(f6375,plain,
spl0_469,
inference(avatar_split_clause,[],[f800,f6373]) ).
fof(f6373,plain,
( spl0_469
<=> ! [X6,X5,X0] :
( hBOOL(hAPP(hAPP(c_in(X0),X5),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X5),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f800,axiom,
! [X0,X6,X5] :
( hBOOL(hAPP(hAPP(c_in(X0),X5),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X5),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
fof(f6371,plain,
spl0_468,
inference(avatar_split_clause,[],[f792,f6369]) ).
fof(f6369,plain,
( spl0_468
<=> ! [X5,X0,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X5),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f792,axiom,
! [X0,X6,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X5),X7))
| hBOOL(hAPP(hAPP(c_in(X0),X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
fof(f6367,plain,
spl0_467,
inference(avatar_split_clause,[],[f791,f6365]) ).
fof(f6365,plain,
( spl0_467
<=> ! [X5,X0,X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X5),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f791,axiom,
! [X0,X6,X7,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X5),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
fof(f6362,plain,
spl0_466,
inference(avatar_split_clause,[],[f621,f6360]) ).
fof(f621,axiom,
! [X0,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__gt__0__iff_2) ).
fof(f6358,plain,
spl0_465,
inference(avatar_split_clause,[],[f600,f6356]) ).
fof(f6356,plain,
( spl0_465
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f600,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__add_0) ).
fof(f6354,plain,
spl0_464,
inference(avatar_split_clause,[],[f364,f6352]) ).
fof(f6352,plain,
( spl0_464
<=> ! [X2,X0,X14] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X2,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f364,axiom,
! [X2,X0,X14] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X2,X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
fof(f6350,plain,
spl0_463,
inference(avatar_split_clause,[],[f169,f6348]) ).
fof(f6348,plain,
( spl0_463
<=> ! [X6,X0,X15] :
( ~ c_Wellfounded_Owf(X15,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X6,c_Relation_OImage(X15,X6,X0,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f169,axiom,
! [X0,X6,X15] :
( ~ c_Wellfounded_Owf(X15,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X6,c_Relation_OImage(X15,X6,X0,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
fof(f6345,plain,
spl0_462,
inference(avatar_split_clause,[],[f142,f6343]) ).
fof(f142,axiom,
! [X0] :
( ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV__card__ge__0_0) ).
fof(f6341,plain,
spl0_461,
inference(avatar_split_clause,[],[f123,f6339]) ).
fof(f6339,plain,
( spl0_461
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f123,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
fof(f6337,plain,
spl0_460,
inference(avatar_split_clause,[],[f56,f6335]) ).
fof(f6335,plain,
( spl0_460
<=> ! [X0,X21,X2,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,X7,X0),X21,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f56,axiom,
! [X2,X21,X0,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,X7,X0),X21,tc_fun(X0,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X7,X21,tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
fof(f6333,plain,
spl0_459,
inference(avatar_split_clause,[],[f55,f6331]) ).
fof(f6331,plain,
( spl0_459
<=> ! [X0,X6,X2,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Set_Oinsert(X2,X7,X0),tc_fun(X0,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f55,axiom,
! [X2,X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Set_Oinsert(X2,X7,X0),tc_fun(X0,tc_bool)) = c_Set_Oinsert(X2,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
fof(f6329,plain,
spl0_458,
inference(avatar_split_clause,[],[f34,f6327]) ).
fof(f6327,plain,
( spl0_458
<=> ! [X17,X0,X18,X2] : hBOOL(hAPP(hAPP(c_in(X17),X2),c_Set_Ovimage(X18,c_Set_Oinsert(hAPP(X18,X2),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X17,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f34,axiom,
! [X2,X0,X18,X17] : hBOOL(hAPP(hAPP(c_in(X17),X2),c_Set_Ovimage(X18,c_Set_Oinsert(hAPP(X18,X2),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X17,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
fof(f6174,plain,
( spl0_457
| ~ spl0_397
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f5321,f4960,f4956,f6172]) ).
fof(f6172,plain,
( spl0_457
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| ~ c_Nitpick_Orefl_H(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f5321,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| ~ c_Nitpick_Orefl_H(X0,X1) )
| ~ spl0_397
| ~ spl0_398 ),
inference(resolution,[],[f4961,f4957]) ).
fof(f6126,plain,
spl0_456,
inference(avatar_split_clause,[],[f1202,f6124]) ).
fof(f6124,plain,
( spl0_456
<=> ! [X2,X1] :
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f1202,axiom,
! [X2,X1] :
( X1 = X2
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_1) ).
fof(f6122,plain,
spl0_455,
inference(avatar_split_clause,[],[f1186,f6120]) ).
fof(f6120,plain,
( spl0_455
<=> ! [X4,X0,X6,X3] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_OId__on(X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f1186,axiom,
! [X3,X0,X6,X4] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X4,X0,X0)),c_Relation_OId__on(X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
fof(f6118,plain,
spl0_454,
inference(avatar_split_clause,[],[f698,f6116]) ).
fof(f6116,plain,
( spl0_454
<=> ! [X44,X0,X21,X2] :
( ~ c_lessequals(X21,X44,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X2,X21,X0),c_Set_Oinsert(X2,X44,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f698,axiom,
! [X2,X21,X0,X44] :
( ~ c_lessequals(X21,X44,tc_fun(X0,tc_bool))
| c_lessequals(c_Set_Oinsert(X2,X21,X0),c_Set_Oinsert(X2,X44,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
fof(f6114,plain,
spl0_453,
inference(avatar_split_clause,[],[f602,f6112]) ).
fof(f6112,plain,
( spl0_453
<=> ! [X6,X0,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f602,axiom,
! [X0,X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
fof(f6110,plain,
spl0_452,
inference(avatar_split_clause,[],[f601,f6108]) ).
fof(f6108,plain,
( spl0_452
<=> ! [X50,X0,X49] :
( ~ c_lessequals(X50,X49,tc_fun(tc_prod(X0,X0),tc_bool))
| c_lessequals(c_Wellfounded_Oacc(X49,X0),c_Wellfounded_Oacc(X50,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f601,axiom,
! [X50,X0,X49] :
( ~ c_lessequals(X50,X49,tc_fun(tc_prod(X0,X0),tc_bool))
| c_lessequals(c_Wellfounded_Oacc(X49,X0),c_Wellfounded_Oacc(X50,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__subset_0) ).
fof(f6106,plain,
( spl0_451
| ~ spl0_395
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f5310,f4956,f4947,f6104]) ).
fof(f6104,plain,
( spl0_451
<=> ! [X0,X1] :
( ~ c_Nitpick_Orefl_H(X0,X1)
| ~ c_Relation_Oirrefl(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f5310,plain,
( ! [X0,X1] :
( ~ c_Nitpick_Orefl_H(X0,X1)
| ~ c_Relation_Oirrefl(X0,X1) )
| ~ spl0_395
| ~ spl0_397 ),
inference(resolution,[],[f4957,f4948]) ).
fof(f6102,plain,
spl0_450,
inference(avatar_split_clause,[],[f567,f6100]) ).
fof(f6100,plain,
( spl0_450
<=> ! [X0,X6,X21,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X21,tc_fun(X0,tc_bool))
| c_lessequals(X6,X21,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f567,axiom,
! [X21,X0,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X21,tc_fun(X0,tc_bool))
| c_lessequals(X6,X21,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
fof(f6098,plain,
spl0_449,
inference(avatar_split_clause,[],[f518,f6096]) ).
fof(f6096,plain,
( spl0_449
<=> ! [X6,X0,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f518,axiom,
! [X0,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
fof(f6094,plain,
spl0_448,
inference(avatar_split_clause,[],[f439,f6092]) ).
fof(f6092,plain,
( spl0_448
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X5
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f439,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X5
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X5),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f6090,plain,
spl0_447,
inference(avatar_split_clause,[],[f438,f6088]) ).
fof(f6088,plain,
( spl0_447
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X5
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f438,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X5
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f6086,plain,
spl0_446,
inference(avatar_split_clause,[],[f437,f6084]) ).
fof(f6084,plain,
( spl0_446
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X1 = X5
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f437,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X1 = X5
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f6082,plain,
spl0_445,
inference(avatar_split_clause,[],[f405,f6080]) ).
fof(f6080,plain,
( spl0_445
<=> ! [X2,X0,X1] :
( X1 = X2
| c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f405,axiom,
! [X2,X0,X1] :
( X1 = X2
| c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) != c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
fof(f5849,plain,
( spl0_444
| ~ spl0_212
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f5494,f5491,f2440,f5847]) ).
fof(f5847,plain,
( spl0_444
<=> ! [X3,X0,X14] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f5491,plain,
( spl0_428
<=> ! [X3,X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X14,X0),X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f5494,plain,
( ! [X3,X0,X14] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X14,X0),X0) )
| ~ spl0_212
| ~ spl0_428 ),
inference(forward_demodulation,[],[f5492,f2442]) ).
fof(f5492,plain,
( ! [X3,X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X14,X0),X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14)) )
| ~ spl0_428 ),
inference(avatar_component_clause,[],[f5491]) ).
fof(f5598,plain,
( spl0_443
| ~ spl0_370
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f5320,f4960,f4558,f5596]) ).
fof(f5320,plain,
( ! [X0,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X0,X1),X1)
| ~ spl0_370
| ~ spl0_398 ),
inference(resolution,[],[f4961,f4559]) ).
fof(f5550,plain,
( spl0_442
| ~ spl0_370
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f5305,f4947,f4558,f5548]) ).
fof(f5305,plain,
( ! [X0,X1] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Ortrancl(X0,X1),X1)
| ~ spl0_370
| ~ spl0_395 ),
inference(resolution,[],[f4948,f4559]) ).
fof(f5546,plain,
spl0_441,
inference(avatar_split_clause,[],[f1355,f5544]) ).
fof(f5542,plain,
spl0_440,
inference(avatar_split_clause,[],[f1260,f5540]) ).
fof(f1260,axiom,
! [X65,X3,X37] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X37,X3,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X65),X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
fof(f5538,plain,
spl0_439,
inference(avatar_split_clause,[],[f1249,f5536]) ).
fof(f5536,plain,
( spl0_439
<=> ! [X16,X14] :
( X14 = X16
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X14),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f1249,axiom,
! [X16,X14] :
( X14 = X16
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),X14))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X14),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
fof(f5534,plain,
spl0_438,
inference(avatar_split_clause,[],[f1243,f5532]) ).
fof(f1243,axiom,
! [X65,X3,X4] : ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X3,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X65),X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).
fof(f5530,plain,
spl0_437,
inference(avatar_split_clause,[],[f1188,f5528]) ).
fof(f5528,plain,
( spl0_437
<=> ! [X2,X0,X1] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Relation_OId(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f1188,axiom,
! [X2,X0,X1] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),c_Relation_OId(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).
fof(f5526,plain,
spl0_436,
inference(avatar_split_clause,[],[f1139,f5524]) ).
fof(f5524,plain,
( spl0_436
<=> ! [X18,X0,X10,X15] : c_Relation_Oconverse(c_Relation_Oinv__image(X15,X18,X10,X0),X0,X0) = c_Relation_Oinv__image(c_Relation_Oconverse(X15,X10,X10),X18,X10,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f1139,axiom,
! [X10,X0,X18,X15] : c_Relation_Oconverse(c_Relation_Oinv__image(X15,X18,X10,X0),X0,X0) = c_Relation_Oinv__image(c_Relation_Oconverse(X15,X10,X10),X18,X10,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
fof(f5522,plain,
spl0_435,
inference(avatar_split_clause,[],[f975,f5520]) ).
fof(f5520,plain,
( spl0_435
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f975,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f5518,plain,
spl0_434,
inference(avatar_split_clause,[],[f835,f5516]) ).
fof(f5516,plain,
( spl0_434
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(X4,X3,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f835,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(X4,X3,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f5514,plain,
spl0_433,
inference(avatar_split_clause,[],[f785,f5512]) ).
fof(f5512,plain,
( spl0_433
<=> ! [X0,X6,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X2),c_Set_Oinsert(X1,X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f785,axiom,
! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| hBOOL(hAPP(hAPP(c_in(X0),X2),c_Set_Oinsert(X1,X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
fof(f5510,plain,
spl0_432,
inference(avatar_split_clause,[],[f692,f5508]) ).
fof(f5508,plain,
( spl0_432
<=> ! [X0,X6,X3,X7] :
( ~ hBOOL(hAPP(X6,X3))
| ~ hBOOL(hAPP(X7,X3))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f692,axiom,
! [X3,X0,X6,X7] :
( ~ hBOOL(hAPP(X6,X3))
| ~ hBOOL(hAPP(X7,X3))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
fof(f5506,plain,
spl0_431,
inference(avatar_split_clause,[],[f686,f5504]) ).
fof(f5504,plain,
( spl0_431
<=> ! [X6,X0] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f686,axiom,
! [X0,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
fof(f5502,plain,
spl0_430,
inference(avatar_split_clause,[],[f608,f5500]) ).
fof(f5500,plain,
( spl0_430
<=> ! [X6,X0,X7] :
( ~ c_Finite__Set_Ofinite(X7,X0)
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X7,X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f608,axiom,
! [X0,X6,X7] :
( ~ c_Finite__Set_Ofinite(X7,X0)
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(X7,X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__mono_0) ).
fof(f5498,plain,
spl0_429,
inference(avatar_split_clause,[],[f599,f5496]) ).
fof(f5496,plain,
( spl0_429
<=> ! [X6,X2,X0] : c_Set_Oinsert(X2,X6,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f599,axiom,
! [X2,X0,X6] : c_Set_Oinsert(X2,X6,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
fof(f5493,plain,
spl0_428,
inference(avatar_split_clause,[],[f557,f5491]) ).
fof(f557,axiom,
! [X3,X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X14,X0),X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_0) ).
fof(f5489,plain,
spl0_427,
inference(avatar_split_clause,[],[f556,f5487]) ).
fof(f5487,plain,
( spl0_427
<=> ! [X6,X0,X21,X7] :
( c_lessequals(X7,X21,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X21,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f556,axiom,
! [X21,X0,X6,X7] :
( c_lessequals(X7,X21,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X21,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
fof(f5485,plain,
spl0_426,
inference(avatar_split_clause,[],[f555,f5483]) ).
fof(f5483,plain,
( spl0_426
<=> ! [X0,X6,X21,X7] :
( c_lessequals(X6,X21,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X21,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f555,axiom,
! [X21,X0,X6,X7] :
( c_lessequals(X6,X21,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X21,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
fof(f5481,plain,
spl0_425,
inference(avatar_split_clause,[],[f482,f5479]) ).
fof(f5479,plain,
( spl0_425
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X3,X23,X0)
| c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f482,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X3,X23,X0)
| c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
fof(f5477,plain,
spl0_424,
inference(avatar_split_clause,[],[f462,f5475]) ).
fof(f5475,plain,
( spl0_424
<=> ! [X0,X6,X21,X7] :
( c_lessequals(X21,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X21,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f462,axiom,
! [X21,X0,X6,X7] :
( c_lessequals(X21,X6,tc_fun(X0,tc_bool))
| ~ c_lessequals(X21,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
fof(f5473,plain,
spl0_423,
inference(avatar_split_clause,[],[f461,f5471]) ).
fof(f5471,plain,
( spl0_423
<=> ! [X0,X6,X21,X7] :
( c_lessequals(X21,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X21,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f461,axiom,
! [X21,X0,X6,X7] :
( c_lessequals(X21,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X21,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
fof(f5469,plain,
spl0_422,
inference(avatar_split_clause,[],[f455,f5467]) ).
fof(f5467,plain,
( spl0_422
<=> ! [X6,X0,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f455,axiom,
! [X0,X6,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
fof(f5465,plain,
spl0_421,
inference(avatar_split_clause,[],[f454,f5463]) ).
fof(f5463,plain,
( spl0_421
<=> ! [X6,X0,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X7
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f454,axiom,
! [X0,X6,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X7
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
fof(f5461,plain,
spl0_420,
inference(avatar_split_clause,[],[f389,f5459]) ).
fof(f5459,plain,
( spl0_420
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X3,X23,X0)
| ~ c_lessequals(X4,X23,X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f389,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X3,X23,X0)
| ~ c_lessequals(X4,X23,X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X23,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
fof(f5457,plain,
spl0_419,
inference(avatar_split_clause,[],[f374,f5455]) ).
fof(f5455,plain,
( spl0_419
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X23,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f374,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X23,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
fof(f5453,plain,
spl0_418,
inference(avatar_split_clause,[],[f373,f5451]) ).
fof(f5451,plain,
( spl0_418
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X23,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f373,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X23,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
fof(f5449,plain,
spl0_417,
inference(avatar_split_clause,[],[f372,f5447]) ).
fof(f5447,plain,
( spl0_417
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X23,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f372,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X23,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
fof(f5445,plain,
spl0_416,
inference(avatar_split_clause,[],[f354,f5443]) ).
fof(f5443,plain,
( spl0_416
<=> ! [X6,X0] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f354,axiom,
! [X0,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_0) ).
fof(f5441,plain,
spl0_415,
inference(avatar_split_clause,[],[f271,f5439]) ).
fof(f5439,plain,
( spl0_415
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X23,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f271,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X23,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
fof(f5437,plain,
spl0_414,
inference(avatar_split_clause,[],[f139,f5435]) ).
fof(f5435,plain,
( spl0_414
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X23,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f139,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X23,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
fof(f5433,plain,
spl0_413,
inference(avatar_split_clause,[],[f138,f5431]) ).
fof(f5431,plain,
( spl0_413
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X3,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f138,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X3,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
fof(f5429,plain,
spl0_412,
inference(avatar_split_clause,[],[f137,f5427]) ).
fof(f5427,plain,
( spl0_412
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X3,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f137,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X3,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
fof(f5425,plain,
( spl0_411
| ~ spl0_339
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f5319,f4960,f3806,f5423]) ).
fof(f5423,plain,
( spl0_411
<=> ! [X0] : ~ c_Wellfounded_Owf(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f5319,plain,
( ! [X0] : ~ c_Wellfounded_Owf(c_Relation_OId(X0),X0)
| ~ spl0_339
| ~ spl0_398 ),
inference(resolution,[],[f4961,f3807]) ).
fof(f5421,plain,
spl0_410,
inference(avatar_split_clause,[],[f136,f5419]) ).
fof(f5419,plain,
( spl0_410
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X23,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f136,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X23,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
fof(f5417,plain,
spl0_409,
inference(avatar_split_clause,[],[f134,f5415]) ).
fof(f5415,plain,
( spl0_409
<=> ! [X9,X0,X8,X10,X25] :
( ~ c_Relation_Osingle__valued(X8,X0,X10)
| ~ c_Relation_Osingle__valued(X9,X10,X25)
| c_Relation_Osingle__valued(c_Relation_Orel__comp(X8,X9,X0,X10,X25),X0,X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f134,axiom,
! [X10,X0,X8,X9,X25] :
( ~ c_Relation_Osingle__valued(X8,X0,X10)
| ~ c_Relation_Osingle__valued(X9,X10,X25)
| c_Relation_Osingle__valued(c_Relation_Orel__comp(X8,X9,X0,X10,X25),X0,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).
fof(f5413,plain,
spl0_408,
inference(avatar_split_clause,[],[f128,f5411]) ).
fof(f5411,plain,
( spl0_408
<=> ! [X0,X6,X3,X7] :
( hBOOL(hAPP(X7,X3))
| hBOOL(hAPP(X6,X3))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f128,axiom,
! [X3,X0,X6,X7] :
( hBOOL(hAPP(X7,X3))
| hBOOL(hAPP(X6,X3))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
fof(f5329,plain,
( spl0_407
| ~ spl0_339
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f5304,f4947,f3806,f5327]) ).
fof(f5327,plain,
( spl0_407
<=> ! [X0] : ~ c_Relation_Oirrefl(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f5304,plain,
( ! [X0] : ~ c_Relation_Oirrefl(c_Relation_OId(X0),X0)
| ~ spl0_339
| ~ spl0_395 ),
inference(resolution,[],[f4948,f3807]) ).
fof(f5199,plain,
( spl0_406
| ~ spl0_212
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f4929,f4926,f2440,f5197]) ).
fof(f5197,plain,
( spl0_406
<=> ! [X0,X14] :
( c_Orderings_Obot__class_Obot(tc_nat) = X14
| ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f4926,plain,
( spl0_390
<=> ! [X0,X14] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f4929,plain,
( ! [X0,X14] :
( c_Orderings_Obot__class_Obot(tc_nat) = X14
| ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0) )
| ~ spl0_212
| ~ spl0_390 ),
inference(forward_demodulation,[],[f4927,f2442]) ).
fof(f4927,plain,
( ! [X0,X14] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0) )
| ~ spl0_390 ),
inference(avatar_component_clause,[],[f4926]) ).
fof(f5092,plain,
( spl0_405
| ~ spl0_212
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f4898,f4895,f2440,f5090]) ).
fof(f5090,plain,
( spl0_405
<=> ! [X2,X0] :
( c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X2,c_Orderings_Obot__class_Obot(tc_nat),X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f4895,plain,
( spl0_383
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f4898,plain,
( ! [X2,X0] :
( c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X2,c_Orderings_Obot__class_Obot(tc_nat),X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0) )
| ~ spl0_212
| ~ spl0_383 ),
inference(forward_demodulation,[],[f4896,f2442]) ).
fof(f4896,plain,
( ! [X2,X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0) )
| ~ spl0_383 ),
inference(avatar_component_clause,[],[f4895]) ).
fof(f4987,plain,
spl0_404,
inference(avatar_split_clause,[],[f1354,f4985]) ).
fof(f4985,plain,
( spl0_404
<=> ! [X0,X8] : c_Relation_ORange(X8,X0,X0) = c_Relation_ORange(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f1354,plain,
! [X0,X8] : c_Relation_ORange(X8,X0,X0) = c_Relation_ORange(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0,X0),
inference(definition_unfolding,[],[f1126,f1163]) ).
fof(f1126,axiom,
! [X0,X8] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X8,X0),X0,X0) = c_Relation_ORange(X8,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).
fof(f4982,plain,
spl0_403,
inference(avatar_split_clause,[],[f1349,f4980]) ).
fof(f4980,plain,
( spl0_403
<=> ! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X15,X0),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X15,X0),X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f1349,plain,
! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X15,X0),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X15,X0),X0),X0,X0,X0),
inference(definition_unfolding,[],[f1135,f1163]) ).
fof(f1135,axiom,
! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X15,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
fof(f4978,plain,
spl0_402,
inference(avatar_split_clause,[],[f1341,f4976]) ).
fof(f4976,plain,
( spl0_402
<=> ! [X15,X47,X0,X10,X25,X32] : hAPP(c_COMBS(X32,X47,X10,X25,X0),X15) = hAPP(hAPP(X32,X15),hAPP(X47,X15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f1341,axiom,
! [X10,X0,X47,X15,X25,X32] : hAPP(c_COMBS(X32,X47,X10,X25,X0),X15) = hAPP(hAPP(X32,X15),hAPP(X47,X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
fof(f4974,plain,
spl0_401,
inference(avatar_split_clause,[],[f1235,f4972]) ).
fof(f4972,plain,
( spl0_401
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f1235,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f4970,plain,
spl0_400,
inference(avatar_split_clause,[],[f1234,f4968]) ).
fof(f4968,plain,
( spl0_400
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f1234,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f4966,plain,
spl0_399,
inference(avatar_split_clause,[],[f1232,f4964]) ).
fof(f4964,plain,
( spl0_399
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f1232,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f4962,plain,
spl0_398,
inference(avatar_split_clause,[],[f1190,f4960]) ).
fof(f1190,axiom,
! [X2,X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X2,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
fof(f4958,plain,
spl0_397,
inference(avatar_split_clause,[],[f1189,f4956]) ).
fof(f1189,axiom,
! [X3,X0,X8] :
( ~ c_Nitpick_Orefl_H(X8,X0)
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
fof(f4954,plain,
( spl0_396
| ~ spl0_212
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f4052,f4048,f2440,f4951]) ).
fof(f4951,plain,
( spl0_396
<=> c_Orderings_Obot__class_Obot(tc_nat) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f4048,plain,
( spl0_347
<=> c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f4052,plain,
( c_Orderings_Obot__class_Obot(tc_nat) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_Orderings_Obot__class_Obot(tc_nat))
| ~ spl0_212
| ~ spl0_347 ),
inference(forward_demodulation,[],[f4050,f2442]) ).
fof(f4050,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_347 ),
inference(avatar_component_clause,[],[f4048]) ).
fof(f4949,plain,
spl0_395,
inference(avatar_split_clause,[],[f1173,f4947]) ).
fof(f1173,axiom,
! [X3,X0,X8] :
( ~ c_Relation_Oirrefl(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
fof(f4945,plain,
spl0_394,
inference(avatar_split_clause,[],[f814,f4943]) ).
fof(f4943,plain,
( spl0_394
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ c_lessequals(X3,X4,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f814,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ c_lessequals(X3,X4,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
fof(f4941,plain,
spl0_393,
inference(avatar_split_clause,[],[f810,f4939]) ).
fof(f4939,plain,
( spl0_393
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| ~ c_lessequals(X3,X4,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f810,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| ~ c_lessequals(X3,X4,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f4937,plain,
spl0_392,
inference(avatar_split_clause,[],[f778,f4935]) ).
fof(f4935,plain,
( spl0_392
<=> ! [X18,X20,X0,X10,X3] :
( ~ class_HOL_Oord(X10)
| ~ c_lessequals(X18,X20,tc_fun(X0,X10))
| c_lessequals(hAPP(X18,X3),hAPP(X20,X3),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f778,axiom,
! [X3,X10,X0,X18,X20] :
( ~ class_HOL_Oord(X10)
| ~ c_lessequals(X18,X20,tc_fun(X0,X10))
| c_lessequals(hAPP(X18,X3),hAPP(X20,X3),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
fof(f4933,plain,
spl0_391,
inference(avatar_split_clause,[],[f677,f4931]) ).
fof(f4931,plain,
( spl0_391
<=> ! [X10,X0,X9,X8] :
( ~ c_Relation_Osingle__valued(X9,X0,X10)
| c_Relation_Osingle__valued(X8,X0,X10)
| ~ c_lessequals(X8,X9,tc_fun(tc_prod(X0,X10),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f677,axiom,
! [X10,X0,X8,X9] :
( ~ c_Relation_Osingle__valued(X9,X0,X10)
| c_Relation_Osingle__valued(X8,X0,X10)
| ~ c_lessequals(X8,X9,tc_fun(tc_prod(X0,X10),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).
fof(f4928,plain,
spl0_390,
inference(avatar_split_clause,[],[f478,f4926]) ).
fof(f478,axiom,
! [X0,X14] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X14
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
fof(f4924,plain,
spl0_389,
inference(avatar_split_clause,[],[f453,f4922]) ).
fof(f4922,plain,
( spl0_389
<=> ! [X4,X0,X14,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X3,X14,X0),c_Power_Opower__class_Opower(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f453,axiom,
! [X3,X0,X14,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X3,X14,X0),c_Power_Opower__class_Opower(X4,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
fof(f4920,plain,
spl0_388,
inference(avatar_split_clause,[],[f433,f4918]) ).
fof(f4918,plain,
( spl0_388
<=> ! [X0,X6,X3,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X7))
| ~ c_lessequals(c_Set_Oinsert(X3,X6,X0),X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f433,axiom,
! [X3,X0,X6,X7] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),X7))
| ~ c_lessequals(c_Set_Oinsert(X3,X6,X0),X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
fof(f4916,plain,
spl0_387,
inference(avatar_split_clause,[],[f415,f4914]) ).
fof(f4914,plain,
( spl0_387
<=> ! [X6,X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f415,axiom,
! [X0,X6] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition_0) ).
fof(f4912,plain,
spl0_386,
inference(avatar_split_clause,[],[f414,f4910]) ).
fof(f4910,plain,
( spl0_386
<=> ! [X6,X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f414,axiom,
! [X0,X6] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition2_0) ).
fof(f4906,plain,
spl0_385,
inference(avatar_split_clause,[],[f303,f4904]) ).
fof(f4904,plain,
( spl0_385
<=> ! [X6,X0,X7] :
( X6 = X7
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f303,axiom,
! [X0,X6,X7] :
( X6 = X7
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
fof(f4902,plain,
spl0_384,
inference(avatar_split_clause,[],[f258,f4900]) ).
fof(f4900,plain,
( spl0_384
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f258,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X4) = c_Lattices_Olower__semilattice__class_Oinf(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).
fof(f4897,plain,
spl0_383,
inference(avatar_split_clause,[],[f234,f4895]) ).
fof(f234,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
fof(f4893,plain,
spl0_382,
inference(avatar_split_clause,[],[f202,f4891]) ).
fof(f4891,plain,
( spl0_382
<=> ! [X2,X0,X1] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f202,axiom,
! [X2,X0,X1] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_in(X0),X1),c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
fof(f4889,plain,
spl0_381,
inference(avatar_split_clause,[],[f190,f4887]) ).
fof(f4887,plain,
( spl0_381
<=> ! [X0,X16,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X16,X14,tc_nat)
| c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X16),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f190,axiom,
! [X0,X16,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X16,X14,tc_nat)
| c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X16),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
fof(f4885,plain,
spl0_380,
inference(avatar_split_clause,[],[f189,f4883]) ).
fof(f4883,plain,
( spl0_380
<=> ! [X0,X16,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X16),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f189,axiom,
! [X0,X16,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X16),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
fof(f4881,plain,
spl0_379,
inference(avatar_split_clause,[],[f173,f4879]) ).
fof(f4879,plain,
( spl0_379
<=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f173,axiom,
! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).
fof(f4877,plain,
spl0_378,
inference(avatar_split_clause,[],[f172,f4875]) ).
fof(f4875,plain,
( spl0_378
<=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f172,axiom,
! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).
fof(f4873,plain,
spl0_377,
inference(avatar_split_clause,[],[f30,f4871]) ).
fof(f4871,plain,
( spl0_377
<=> ! [X0,X14,X16,X2] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_lessequals(X16,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X16,X0),c_Power_Opower__class_Opower(X2,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f30,axiom,
! [X2,X0,X16,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_lessequals(X16,X14,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X2,X16,X0),c_Power_Opower__class_Opower(X2,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__power__dvd_0) ).
fof(f4869,plain,
spl0_376,
inference(avatar_split_clause,[],[f16,f4867]) ).
fof(f4867,plain,
( spl0_376
<=> ! [X9,X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| ~ c_Relation_Osym(X9,X0)
| c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f16,axiom,
! [X0,X8,X9] :
( ~ c_Relation_Osym(X8,X0)
| ~ c_Relation_Osym(X9,X0)
| c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un_0) ).
fof(f4865,plain,
( spl0_375
| ~ spl0_285
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3923,f3649,f3159,f4863]) ).
fof(f4863,plain,
( spl0_375
<=> ! [X0] : c_Relation_Osym(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f3159,plain,
( spl0_285
<=> ! [X0,X8] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_Oconverse(X8,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f3649,plain,
( spl0_300
<=> ! [X0,X7] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f3923,plain,
( ! [X0] : c_Relation_Osym(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_285
| ~ spl0_300 ),
inference(superposition,[],[f3160,f3650]) ).
fof(f3650,plain,
( ! [X0,X7] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool))
| ~ spl0_300 ),
inference(avatar_component_clause,[],[f3649]) ).
fof(f3160,plain,
( ! [X0,X8] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_Oconverse(X8,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0)
| ~ spl0_285 ),
inference(avatar_component_clause,[],[f3159]) ).
fof(f4793,plain,
( spl0_374
| ~ spl0_212
| ~ spl0_363 ),
inference(avatar_split_clause,[],[f4532,f4529,f2440,f4791]) ).
fof(f4791,plain,
( spl0_374
<=> ! [X6,X0] :
( c_Finite__Set_Ocard(X6,X0) != c_Orderings_Obot__class_Obot(tc_nat)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f4529,plain,
( spl0_363
<=> ! [X6,X0] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Finite__Set_Ocard(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f4532,plain,
( ! [X0,X6] :
( c_Finite__Set_Ocard(X6,X0) != c_Orderings_Obot__class_Obot(tc_nat)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_212
| ~ spl0_363 ),
inference(forward_demodulation,[],[f4530,f2442]) ).
fof(f4530,plain,
( ! [X0,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Finite__Set_Ocard(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 )
| ~ spl0_363 ),
inference(avatar_component_clause,[],[f4529]) ).
fof(f4789,plain,
( spl0_373
| ~ spl0_212
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f3813,f3810,f2440,f4787]) ).
fof(f4787,plain,
( spl0_373
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f3810,plain,
( spl0_340
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f3813,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_212
| ~ spl0_340 ),
inference(forward_demodulation,[],[f3811,f2442]) ).
fof(f3811,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_340 ),
inference(avatar_component_clause,[],[f3810]) ).
fof(f4568,plain,
spl0_372,
inference(avatar_split_clause,[],[f1346,f4566]) ).
fof(f4566,plain,
( spl0_372
<=> ! [X0,X8,X10] : c_Relation_ORange(X8,X10,X0) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Oconverse(X8,X10,X0),X0,X10),X10,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f1346,plain,
! [X10,X0,X8] : c_Relation_ORange(X8,X10,X0) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Oconverse(X8,X10,X0),X0,X10),X10,X0),
inference(definition_unfolding,[],[f1164,f1146]) ).
fof(f1164,axiom,
! [X10,X0,X8] : c_Relation_ORange(X8,X10,X0) = c_Relation_ODomain(c_Relation_Oconverse(X8,X10,X0),X0,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def_0) ).
fof(f4564,plain,
spl0_371,
inference(avatar_split_clause,[],[f1268,f4562]) ).
fof(f4562,plain,
( spl0_371
<=> ! [X32,X0,X10,X25,X15,X47] : hAPP(hAPP(c_COMBC(X32,X10,X25,X0),X47),X15) = hAPP(hAPP(X32,X15),X47) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f1268,axiom,
! [X10,X0,X47,X15,X25,X32] : hAPP(hAPP(c_COMBC(X32,X10,X25,X0),X47),X15) = hAPP(hAPP(X32,X15),X47),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
fof(f4560,plain,
spl0_370,
inference(avatar_split_clause,[],[f1180,f4558]) ).
fof(f1180,axiom,
! [X2,X0,X8] : hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X2,X0,X0)),c_Transitive__Closure_Ortrancl(X8,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
fof(f4556,plain,
spl0_369,
inference(avatar_split_clause,[],[f1153,f4554]) ).
fof(f4554,plain,
( spl0_369
<=> ! [X6,X0,X8] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| c_Relation_Orel__comp(c_Relation_Oconverse(X8,X0,X0),X8,X0,X0,X0) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f1153,axiom,
! [X0,X8,X6] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| c_Relation_Orel__comp(c_Relation_Oconverse(X8,X0,X0),X8,X0,X0,X0) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).
fof(f4552,plain,
spl0_368,
inference(avatar_split_clause,[],[f1151,f4550]) ).
fof(f4550,plain,
( spl0_368
<=> ! [X18,X10,X0,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_Finite__Set_Ofinite(X6,X10)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),X18),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f1151,axiom,
! [X10,X0,X18,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_Finite__Set_Ofinite(X6,X10)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),X18),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__def_1) ).
fof(f4548,plain,
spl0_367,
inference(avatar_split_clause,[],[f961,f4546]) ).
fof(f961,axiom,
! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(X15,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).
fof(f4544,plain,
spl0_366,
inference(avatar_split_clause,[],[f960,f4542]) ).
fof(f4542,plain,
( spl0_366
<=> ! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X15,X0),c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f960,axiom,
! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(X15,X0),c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).
fof(f4540,plain,
spl0_365,
inference(avatar_split_clause,[],[f926,f4538]) ).
fof(f4538,plain,
( spl0_365
<=> ! [X18,X0,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),X18),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f926,axiom,
! [X10,X0,X18] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),X18),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__empty_0) ).
fof(f4536,plain,
spl0_364,
inference(avatar_split_clause,[],[f921,f4534]) ).
fof(f4534,plain,
( spl0_364
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Oone__class_Oone(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f921,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Oone__class_Oone(X0)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f4531,plain,
spl0_363,
inference(avatar_split_clause,[],[f679,f4529]) ).
fof(f679,axiom,
! [X0,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Finite__Set_Ocard(X6,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__0__iff_0) ).
fof(f4527,plain,
spl0_362,
inference(avatar_split_clause,[],[f513,f4525]) ).
fof(f4525,plain,
( spl0_362
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f513,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
fof(f4523,plain,
spl0_361,
inference(avatar_split_clause,[],[f512,f4521]) ).
fof(f4521,plain,
( spl0_361
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f512,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
fof(f4519,plain,
spl0_360,
inference(avatar_split_clause,[],[f511,f4517]) ).
fof(f4517,plain,
( spl0_360
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f511,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
fof(f4515,plain,
spl0_359,
inference(avatar_split_clause,[],[f510,f4513]) ).
fof(f4513,plain,
( spl0_359
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X5,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f510,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X5,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
fof(f4511,plain,
spl0_358,
inference(avatar_split_clause,[],[f356,f4509]) ).
fof(f4509,plain,
( spl0_358
<=> ! [X6,X0] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f356,axiom,
! [X0,X6] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = X6
| ~ c_lessequals(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
fof(f4494,plain,
spl0_357,
inference(avatar_split_clause,[],[f308,f4492]) ).
fof(f4492,plain,
( spl0_357
<=> ! [X6,X0,X7] :
( X6 = X7
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f308,axiom,
! [X0,X6,X7] :
( X6 = X7
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
fof(f4490,plain,
spl0_356,
inference(avatar_split_clause,[],[f238,f4488]) ).
fof(f4488,plain,
( spl0_356
<=> ! [X4,X0,X6,X3] : c_Set_Oinsert(X3,c_Set_Oinsert(X4,X6,X0),X0) = c_Set_Oinsert(X4,c_Set_Oinsert(X3,X6,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f238,axiom,
! [X3,X0,X6,X4] : c_Set_Oinsert(X3,c_Set_Oinsert(X4,X6,X0),X0) = c_Set_Oinsert(X4,c_Set_Oinsert(X3,X6,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
fof(f4486,plain,
spl0_355,
inference(avatar_split_clause,[],[f211,f4484]) ).
fof(f4484,plain,
( spl0_355
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f211,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f4482,plain,
spl0_354,
inference(avatar_split_clause,[],[f196,f4480]) ).
fof(f4480,plain,
( spl0_354
<=> ! [X6,X0,X7,X3] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X3,X6,X0),X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f196,axiom,
! [X3,X0,X6,X7] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X3,X6,X0),X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
fof(f4478,plain,
spl0_353,
inference(avatar_split_clause,[],[f195,f4476]) ).
fof(f4476,plain,
( spl0_353
<=> ! [X0,X6,X1,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(X6,c_Set_Oinsert(X1,X7,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f195,axiom,
! [X0,X1,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_lessequals(X6,c_Set_Oinsert(X1,X7,X0),tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
fof(f4474,plain,
spl0_352,
inference(avatar_split_clause,[],[f156,f4472]) ).
fof(f4472,plain,
( spl0_352
<=> ! [X0,X8] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f156,axiom,
! [X0,X8] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__reflcl_0) ).
fof(f4470,plain,
spl0_351,
inference(avatar_split_clause,[],[f71,f4468]) ).
fof(f4468,plain,
( spl0_351
<=> ! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f71,axiom,
! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X2,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
fof(f4466,plain,
spl0_350,
inference(avatar_split_clause,[],[f53,f4464]) ).
fof(f4464,plain,
( spl0_350
<=> ! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X2,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X2,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f53,axiom,
! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X2,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X2,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
fof(f4462,plain,
spl0_349,
inference(avatar_split_clause,[],[f6,f4460]) ).
fof(f4460,plain,
( spl0_349
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f4458,plain,
spl0_348,
inference(avatar_split_clause,[],[f5,f4456]) ).
fof(f4456,plain,
( spl0_348
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f5,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
fof(f4051,plain,
( spl0_347
| ~ spl0_23
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f2289,f2238,f1534,f4048]) ).
fof(f1534,plain,
( spl0_23
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f2238,plain,
( spl0_170
<=> ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f2289,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_23
| ~ spl0_170 ),
inference(resolution,[],[f2239,f1536]) ).
fof(f1536,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f1534]) ).
fof(f2239,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f2238]) ).
fof(f3928,plain,
( spl0_346
| ~ spl0_45
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f2278,f2210,f1644,f3925]) ).
fof(f3925,plain,
( spl0_346
<=> c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f2210,plain,
( spl0_163
<=> ! [X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f2278,plain,
( c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))
| ~ spl0_45
| ~ spl0_163 ),
inference(resolution,[],[f2211,f1646]) ).
fof(f2211,plain,
( ! [X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0)) )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f2210]) ).
fof(f3833,plain,
spl0_345,
inference(avatar_split_clause,[],[f1352,f3831]) ).
fof(f3831,plain,
( spl0_345
<=> ! [X0,X15] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ORange(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X15,X0),X0,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f1352,plain,
! [X0,X15] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ORange(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X15,X0),X0,X0),X0,X0),
inference(definition_unfolding,[],[f959,f1146]) ).
fof(f959,axiom,
! [X0,X15] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X15,X0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__rtrancl_0) ).
fof(f3829,plain,
spl0_344,
inference(avatar_split_clause,[],[f1350,f3827]) ).
fof(f3827,plain,
( spl0_344
<=> ! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Transitive__Closure_Ortrancl(c_Relation_Orel__comp(X15,c_Transitive__Closure_Ortrancl(X15,X0),X0,X0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f1350,plain,
! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Transitive__Closure_Ortrancl(c_Relation_Orel__comp(X15,c_Transitive__Closure_Ortrancl(X15,X0),X0,X0,X0),X0),
inference(definition_unfolding,[],[f1170,f1163]) ).
fof(f1170,axiom,
! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X15,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
fof(f3825,plain,
spl0_343,
inference(avatar_split_clause,[],[f1267,f3823]) ).
fof(f3823,plain,
( spl0_343
<=> ! [X15,X32,X0,X10,X25,X47] : hAPP(c_COMBB(X32,X47,X10,X0,X25),X15) = hAPP(X32,hAPP(X47,X15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f1267,axiom,
! [X10,X0,X47,X15,X25,X32] : hAPP(c_COMBB(X32,X47,X10,X0,X25),X15) = hAPP(X32,hAPP(X47,X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
fof(f3821,plain,
spl0_342,
inference(avatar_split_clause,[],[f1239,f3819]) ).
fof(f3819,plain,
( spl0_342
<=> ! [X1,X0,X10,X67,X2,X66] :
( X2 = X66
| c_Pair(X2,X1,X0,X10) != c_Pair(X66,X67,X0,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f1239,axiom,
! [X2,X10,X0,X1,X66,X67] :
( X2 = X66
| c_Pair(X2,X1,X0,X10) != c_Pair(X66,X67,X0,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
fof(f3817,plain,
spl0_341,
inference(avatar_split_clause,[],[f1238,f3815]) ).
fof(f3815,plain,
( spl0_341
<=> ! [X2,X0,X10,X67,X1,X66] :
( X1 = X67
| c_Pair(X2,X1,X0,X10) != c_Pair(X66,X67,X0,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f1238,axiom,
! [X2,X10,X0,X1,X66,X67] :
( X1 = X67
| c_Pair(X2,X1,X0,X10) != c_Pair(X66,X67,X0,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
fof(f3812,plain,
( spl0_340
| ~ spl0_39
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2276,f2202,f1614,f3810]) ).
fof(f1614,plain,
( spl0_39
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f2202,plain,
( spl0_161
<=> ! [X2,X0] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f2276,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_39
| ~ spl0_161 ),
inference(resolution,[],[f2203,f1616]) ).
fof(f1616,plain,
( class_Power_Opower(tc_nat)
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f1614]) ).
fof(f2203,plain,
( ! [X2,X0] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0) )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f2202]) ).
fof(f3808,plain,
spl0_339,
inference(avatar_split_clause,[],[f1199,f3806]) ).
fof(f1199,axiom,
! [X2,X0] : hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X2,X0,X0)),c_Relation_OId(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdI_0) ).
fof(f3804,plain,
spl0_338,
inference(avatar_split_clause,[],[f1168,f3802]) ).
fof(f3802,plain,
( spl0_338
<=> ! [X18,X10,X0,X6,X3] :
( ~ hBOOL(hAPP(X6,hAPP(X18,X3)))
| hBOOL(hAPP(c_Set_Ovimage(X18,X6,X0,X10),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f1168,axiom,
! [X3,X10,X0,X18,X6] :
( ~ hBOOL(hAPP(X6,hAPP(X18,X3)))
| hBOOL(hAPP(c_Set_Ovimage(X18,X6,X0,X10),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
fof(f3800,plain,
spl0_337,
inference(avatar_split_clause,[],[f1167,f3798]) ).
fof(f3798,plain,
( spl0_337
<=> ! [X18,X10,X0,X6,X3] :
( hBOOL(hAPP(X6,hAPP(X18,X3)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X18,X6,X0,X10),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f1167,axiom,
! [X3,X10,X0,X18,X6] :
( hBOOL(hAPP(X6,hAPP(X18,X3)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X18,X6,X0,X10),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
fof(f3796,plain,
spl0_336,
inference(avatar_split_clause,[],[f1154,f3794]) ).
fof(f3794,plain,
( spl0_336
<=> ! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X15,X0),c_Transitive__Closure_Ortrancl(X15,X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f1154,axiom,
! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X15,X0),c_Transitive__Closure_Ortrancl(X15,X0),X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
fof(f3792,plain,
spl0_335,
inference(avatar_split_clause,[],[f1141,f3790]) ).
fof(f3790,plain,
( spl0_335
<=> ! [X0,X16,X14] :
( ~ class_Nat_Osemiring__char__0(X0)
| X14 = X16
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X16) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f1141,axiom,
! [X0,X16,X14] :
( ~ class_Nat_Osemiring__char__0(X0)
| X14 = X16
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X16) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
fof(f3788,plain,
spl0_334,
inference(avatar_split_clause,[],[f1024,f3786]) ).
fof(f3786,plain,
( spl0_334
<=> ! [X0,X8] :
( c_Wellfounded_Owf(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X8,X0)),c_Wellfounded_Oacc(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f1024,axiom,
! [X0,X8] :
( c_Wellfounded_Owf(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X8,X0)),c_Wellfounded_Oacc(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
fof(f3784,plain,
spl0_333,
inference(avatar_split_clause,[],[f1023,f3782]) ).
fof(f3782,plain,
( spl0_333
<=> ! [X0,X8] :
( c_Wellfounded_Owf(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X8,X0)),c_Wellfounded_Oacc(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f1023,axiom,
! [X0,X8] :
( c_Wellfounded_Owf(X8,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X8,X0)),c_Wellfounded_Oacc(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).
fof(f3780,plain,
spl0_332,
inference(avatar_split_clause,[],[f971,f3778]) ).
fof(f3778,plain,
( spl0_332
<=> ! [X0,X8] :
( ~ c_Relation_Oantisym(X8,X0)
| c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f971,axiom,
! [X0,X8] :
( ~ c_Relation_Oantisym(X8,X0)
| c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).
fof(f3776,plain,
spl0_331,
inference(avatar_split_clause,[],[f970,f3774]) ).
fof(f3774,plain,
( spl0_331
<=> ! [X0,X8] :
( c_Relation_Oantisym(X8,X0)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f970,axiom,
! [X0,X8] :
( c_Relation_Oantisym(X8,X0)
| ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_OId(X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).
fof(f3772,plain,
spl0_330,
inference(avatar_split_clause,[],[f969,f3770]) ).
fof(f3770,plain,
( spl0_330
<=> ! [X6,X0,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Relation_OImage(c_Relation_OId__on(X6,X0),X7,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f969,axiom,
! [X0,X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = c_Relation_OImage(c_Relation_OId__on(X6,X0),X7,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
fof(f3768,plain,
( spl0_329
| ~ spl0_45
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f2274,f2198,f1644,f3765]) ).
fof(f3765,plain,
( spl0_329
<=> c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f2198,plain,
( spl0_160
<=> ! [X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f2274,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))
| ~ spl0_45
| ~ spl0_160 ),
inference(resolution,[],[f2199,f1646]) ).
fof(f2199,plain,
( ! [X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0)) )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f2198]) ).
fof(f3763,plain,
spl0_328,
inference(avatar_split_clause,[],[f856,f3761]) ).
fof(f3761,plain,
( spl0_328
<=> ! [X16,X14] :
( X14 = X16
| ~ c_lessequals(X16,X14,tc_nat)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f856,axiom,
! [X16,X14] :
( X14 = X16
| ~ c_lessequals(X16,X14,tc_nat)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
fof(f3759,plain,
spl0_327,
inference(avatar_split_clause,[],[f675,f3757]) ).
fof(f3757,plain,
( spl0_327
<=> ! [X9,X0,X8] :
( ~ c_Wellfounded_Oacyclic(X9,X0)
| c_Wellfounded_Oacyclic(X8,X0)
| ~ c_lessequals(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f675,axiom,
! [X0,X8,X9] :
( ~ c_Wellfounded_Oacyclic(X9,X0)
| c_Wellfounded_Oacyclic(X8,X0)
| ~ c_lessequals(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).
fof(f3755,plain,
spl0_326,
inference(avatar_split_clause,[],[f672,f3753]) ).
fof(f3753,plain,
( spl0_326
<=> ! [X9,X0,X8] :
( ~ c_Relation_Oantisym(X9,X0)
| c_Relation_Oantisym(X8,X0)
| ~ c_lessequals(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f672,axiom,
! [X0,X8,X9] :
( ~ c_Relation_Oantisym(X9,X0)
| c_Relation_Oantisym(X8,X0)
| ~ c_lessequals(X8,X9,tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).
fof(f3751,plain,
spl0_325,
inference(avatar_split_clause,[],[f613,f3749]) ).
fof(f3749,plain,
( spl0_325
<=> ! [X32,X0,X8,X2] :
( ~ c_Wellfounded_Owf(X8,X0)
| hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X32,X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f613,axiom,
! [X2,X0,X8,X32] :
( ~ c_Wellfounded_Owf(X8,X0)
| hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1(X32,X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).
fof(f3747,plain,
spl0_324,
inference(avatar_split_clause,[],[f604,f3745]) ).
fof(f3745,plain,
( spl0_324
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f604,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
fof(f3743,plain,
spl0_323,
inference(avatar_split_clause,[],[f603,f3741]) ).
fof(f3741,plain,
( spl0_323
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f603,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
fof(f3739,plain,
spl0_322,
inference(avatar_split_clause,[],[f569,f3737]) ).
fof(f3737,plain,
( spl0_322
<=> ! [X48,X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Owf(X48,X0)
| ~ c_lessequals(X48,X8,tc_fun(tc_prod(X0,X0),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f569,axiom,
! [X48,X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Owf(X48,X0)
| ~ c_lessequals(X48,X8,tc_fun(tc_prod(X0,X0),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).
fof(f3735,plain,
spl0_321,
inference(avatar_split_clause,[],[f568,f3733]) ).
fof(f3733,plain,
( spl0_321
<=> ! [X47,X0,X3,X32] :
( ~ hBOOL(hAPP(X32,X3))
| hBOOL(hAPP(X47,X3))
| ~ c_lessequals(X32,X47,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f568,axiom,
! [X3,X0,X47,X32] :
( ~ hBOOL(hAPP(X32,X3))
| hBOOL(hAPP(X47,X3))
| ~ c_lessequals(X32,X47,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
fof(f3731,plain,
spl0_320,
inference(avatar_split_clause,[],[f561,f3729]) ).
fof(f3729,plain,
( spl0_320
<=> ! [X4,X0,X23,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X23,X0)
| c_lessequals(X3,X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f561,axiom,
! [X3,X0,X4,X23] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X23,X0)
| c_lessequals(X3,X23,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f3727,plain,
spl0_319,
inference(avatar_split_clause,[],[f558,f3725]) ).
fof(f3725,plain,
( spl0_319
<=> ! [X4,X0,X23,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ c_lessequals(X23,X4,X0)
| c_lessequals(X23,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f558,axiom,
! [X3,X0,X4,X23] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ c_lessequals(X23,X4,X0)
| c_lessequals(X23,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f3723,plain,
( spl0_318
| ~ spl0_28
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f2273,f2194,f1559,f3721]) ).
fof(f3721,plain,
( spl0_318
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f2194,plain,
( spl0_159
<=> ! [X0,X14] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f2273,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ spl0_28
| ~ spl0_159 ),
inference(resolution,[],[f2195,f1561]) ).
fof(f2195,plain,
( ! [X0,X14] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X14,X0) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f2194]) ).
fof(f3719,plain,
spl0_317,
inference(avatar_split_clause,[],[f517,f3717]) ).
fof(f3717,plain,
( spl0_317
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f517,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
fof(f3715,plain,
spl0_316,
inference(avatar_split_clause,[],[f516,f3713]) ).
fof(f3713,plain,
( spl0_316
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f516,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
fof(f3711,plain,
spl0_315,
inference(avatar_split_clause,[],[f515,f3709]) ).
fof(f3709,plain,
( spl0_315
<=> ! [X0] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f515,axiom,
! [X0] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).
fof(f3707,plain,
spl0_314,
inference(avatar_split_clause,[],[f377,f3705]) ).
fof(f3705,plain,
( spl0_314
<=> ! [X6,X0,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f377,axiom,
! [X0,X6,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
fof(f3703,plain,
spl0_313,
inference(avatar_split_clause,[],[f376,f3701]) ).
fof(f3701,plain,
( spl0_313
<=> ! [X6,X0,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f376,axiom,
! [X0,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
fof(f3699,plain,
spl0_312,
inference(avatar_split_clause,[],[f327,f3697]) ).
fof(f3697,plain,
( spl0_312
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X5,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f327,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X5,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
fof(f3695,plain,
spl0_311,
inference(avatar_split_clause,[],[f324,f3693]) ).
fof(f3693,plain,
( spl0_311
<=> ! [X6,X0,X7] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) != X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f324,axiom,
! [X0,X6,X7] :
( c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) != X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
fof(f3691,plain,
spl0_310,
inference(avatar_split_clause,[],[f323,f3689]) ).
fof(f3689,plain,
( spl0_310
<=> ! [X6,X0,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f323,axiom,
! [X0,X6,X7] :
( ~ c_lessequals(X7,X6,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
fof(f3687,plain,
spl0_309,
inference(avatar_split_clause,[],[f322,f3685]) ).
fof(f3685,plain,
( spl0_309
<=> ! [X6,X0,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f322,axiom,
! [X0,X6,X7] :
( ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool))
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
fof(f3683,plain,
spl0_308,
inference(avatar_split_clause,[],[f301,f3681]) ).
fof(f3681,plain,
( spl0_308
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oboolean__algebra(X0)
| X3 = X4
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3) != hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f301,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oboolean__algebra(X0)
| X3 = X4
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3) != hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
fof(f3679,plain,
( spl0_307
| ~ spl0_44
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f2271,f2190,f1639,f3677]) ).
fof(f3677,plain,
( spl0_307
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f1639,plain,
( spl0_44
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f2190,plain,
( spl0_158
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Orderings_Otop__class_Otop(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f2271,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| ~ spl0_44
| ~ spl0_158 ),
inference(resolution,[],[f2191,f1641]) ).
fof(f1641,plain,
( class_Lattices_Obounded__lattice(tc_bool)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f1639]) ).
fof(f2191,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Orderings_Otop__class_Otop(X0),X0) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f2190]) ).
fof(f3675,plain,
spl0_306,
inference(avatar_split_clause,[],[f293,f3673]) ).
fof(f3673,plain,
( spl0_306
<=> ! [X40,X0,X32,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| hBOOL(hAPP(X32,X40))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X32,X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f293,axiom,
! [X40,X0,X8,X32] :
( ~ c_Wellfounded_Owf(X8,X0)
| hBOOL(hAPP(X32,X40))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1(X32,X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_1) ).
fof(f3671,plain,
spl0_305,
inference(avatar_split_clause,[],[f279,f3669]) ).
fof(f3669,plain,
( spl0_305
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f279,axiom,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).
fof(f3667,plain,
spl0_304,
inference(avatar_split_clause,[],[f233,f3665]) ).
fof(f3665,plain,
( spl0_304
<=> ! [X15,X35,X0,X32] :
( ~ c_Wellfounded_Owf(X15,X0)
| hBOOL(hAPP(X32,X35))
| ~ hBOOL(hAPP(X32,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X32,X15,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f233,axiom,
! [X0,X15,X35,X32] :
( ~ c_Wellfounded_Owf(X15,X0)
| hBOOL(hAPP(X32,X35))
| ~ hBOOL(hAPP(X32,c_List_Osko__Recdef__Xtfl__wf__induct__1__1(X32,X15,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).
fof(f3663,plain,
spl0_303,
inference(avatar_split_clause,[],[f186,f3661]) ).
fof(f3661,plain,
( spl0_303
<=> ! [X32,X0,X8,X2] :
( ~ c_Wellfounded_Owf(X8,X0)
| hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X32,X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f186,axiom,
! [X2,X0,X8,X32] :
( ~ c_Wellfounded_Owf(X8,X0)
| hBOOL(hAPP(X32,X2))
| ~ hBOOL(hAPP(X32,c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1(X32,X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_1) ).
fof(f3659,plain,
spl0_302,
inference(avatar_split_clause,[],[f115,f3657]) ).
fof(f3657,plain,
( spl0_302
<=> ! [X6,X0,X3] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(c_Set_Oinsert(X3,X6,X0),X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f115,axiom,
! [X3,X0,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_lessequals(c_Finite__Set_Ocard(X6,X0),c_Finite__Set_Ocard(c_Set_Oinsert(X3,X6,X0),X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__le_0) ).
fof(f3655,plain,
spl0_301,
inference(avatar_split_clause,[],[f96,f3653]) ).
fof(f3653,plain,
( spl0_301
<=> ! [X0,X24,X19] :
( ~ c_Finite__Set_Ofinite(X19,X0)
| ~ c_Finite__Set_Ofinite(X24,X0)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X19,X24,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f96,axiom,
! [X0,X19,X24] :
( ~ c_Finite__Set_Ofinite(X19,X0)
| ~ c_Finite__Set_Ofinite(X24,X0)
| c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X19,X24,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).
fof(f3651,plain,
spl0_300,
inference(avatar_split_clause,[],[f37,f3649]) ).
fof(f37,axiom,
! [X0,X7] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
fof(f3647,plain,
spl0_299,
inference(avatar_split_clause,[],[f36,f3645]) ).
fof(f3645,plain,
( spl0_299
<=> ! [X6,X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f36,axiom,
! [X0,X6] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
fof(f3643,plain,
spl0_298,
inference(avatar_split_clause,[],[f19,f3641]) ).
fof(f3641,plain,
( spl0_298
<=> ! [X4,X0,X6,X3] :
( X3 = X4
| hBOOL(hAPP(X6,X3))
| ~ hBOOL(hAPP(c_Set_Oinsert(X4,X6,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f19,axiom,
! [X3,X0,X6,X4] :
( X3 = X4
| hBOOL(hAPP(X6,X3))
| ~ hBOOL(hAPP(c_Set_Oinsert(X4,X6,X0),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
fof(f3639,plain,
spl0_297,
inference(avatar_split_clause,[],[f9,f3637]) ).
fof(f3637,plain,
( spl0_297
<=> ! [X0,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f9,axiom,
! [X0,X7] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
fof(f3635,plain,
( spl0_296
| ~ spl0_44
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f2269,f2186,f1639,f3633]) ).
fof(f3633,plain,
( spl0_296
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f2186,plain,
( spl0_157
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f2269,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),X0,tc_bool)
| ~ spl0_44
| ~ spl0_157 ),
inference(resolution,[],[f2187,f1641]) ).
fof(f2187,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X0),X3,X0) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f2186]) ).
fof(f3631,plain,
spl0_295,
inference(avatar_split_clause,[],[f8,f3629]) ).
fof(f3629,plain,
( spl0_295
<=> ! [X6,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f8,axiom,
! [X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
fof(f3589,plain,
( spl0_294
| ~ spl0_44
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2263,f2182,f1639,f3587]) ).
fof(f3587,plain,
( spl0_294
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f2182,plain,
( spl0_156
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Orderings_Obot__class_Obot(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f2263,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| ~ spl0_44
| ~ spl0_156 ),
inference(resolution,[],[f2183,f1641]) ).
fof(f2183,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Orderings_Obot__class_Obot(X0),X0) )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f2182]) ).
fof(f3511,plain,
( spl0_293
| ~ spl0_44
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f2261,f2178,f1639,f3509]) ).
fof(f3509,plain,
( spl0_293
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f2178,plain,
( spl0_155
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f2261,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool)
| ~ spl0_44
| ~ spl0_155 ),
inference(resolution,[],[f2179,f1641]) ).
fof(f2179,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X3,X0) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f2178]) ).
fof(f3209,plain,
( spl0_292
| ~ spl0_212
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f3053,f3050,f2440,f3207]) ).
fof(f3050,plain,
( spl0_259
<=> ! [X6,X0] :
( c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(X6,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f3053,plain,
( ! [X0,X6] :
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),c_Finite__Set_Ocard(X6,X0)))
| c_Finite__Set_Ofinite(X6,X0) )
| ~ spl0_212
| ~ spl0_259 ),
inference(forward_demodulation,[],[f3051,f2442]) ).
fof(f3051,plain,
( ! [X0,X6] :
( c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(X6,X0))) )
| ~ spl0_259 ),
inference(avatar_component_clause,[],[f3050]) ).
fof(f3185,plain,
spl0_291,
inference(avatar_split_clause,[],[f1366,f3183]) ).
fof(f3183,plain,
( spl0_291
<=> ! [X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f1366,plain,
! [X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0) ),
inference(definition_unfolding,[],[f1137,f1163]) ).
fof(f1137,axiom,
! [X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
fof(f3181,plain,
( ~ spl0_42
| spl0_290
| ~ spl0_135
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2665,f2352,f2022,f3179,f1629]) ).
fof(f3179,plain,
( spl0_290
<=> ! [X0] : c_lessequals(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f2022,plain,
( spl0_135
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f2352,plain,
( spl0_190
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f2665,plain,
( ! [X0] :
( c_lessequals(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| ~ class_Lattices_Olower__semilattice(tc_bool) )
| ~ spl0_135
| ~ spl0_190 ),
inference(superposition,[],[f2023,f2353]) ).
fof(f2353,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = X0
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f2352]) ).
fof(f2023,plain,
( ! [X3,X0,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X4,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f2022]) ).
fof(f3177,plain,
spl0_289,
inference(avatar_split_clause,[],[f1365,f3175]) ).
fof(f3175,plain,
( spl0_289
<=> ! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f1365,plain,
! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0),X0) ),
inference(definition_unfolding,[],[f1103,f1163]) ).
fof(f1103,axiom,
! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
fof(f3173,plain,
spl0_288,
inference(avatar_split_clause,[],[f1159,f3171]) ).
fof(f3169,plain,
spl0_287,
inference(avatar_split_clause,[],[f1127,f3167]) ).
fof(f3167,plain,
( spl0_287
<=> ! [X18,X10,X0,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Finite__Set_Ofinite(X6,X10)
| c_HOL_Oone__class_Oone(X0) = c_Finite__Set_Osetprod(X18,X6,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f1127,axiom,
! [X10,X0,X18,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Finite__Set_Ofinite(X6,X10)
| c_HOL_Oone__class_Oone(X0) = c_Finite__Set_Osetprod(X18,X6,X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__def_1) ).
fof(f3165,plain,
spl0_286,
inference(avatar_split_clause,[],[f1110,f3163]) ).
fof(f3163,plain,
( spl0_286
<=> ! [X0,X16] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X16)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f1110,axiom,
! [X0,X16] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X16)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
fof(f3161,plain,
spl0_285,
inference(avatar_split_clause,[],[f965,f3159]) ).
fof(f965,axiom,
! [X0,X8] : c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(X8,c_Relation_Oconverse(X8,X0,X0),tc_fun(tc_prod(X0,X0),tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).
fof(f3157,plain,
spl0_284,
inference(avatar_split_clause,[],[f944,f3155]) ).
fof(f3155,plain,
( spl0_284
<=> ! [X18,X0,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Finite__Set_Osetprod(X18,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f944,axiom,
! [X10,X0,X18] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Finite__Set_Osetprod(X18,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__empty_0) ).
fof(f3153,plain,
spl0_283,
inference(avatar_split_clause,[],[f845,f3151]) ).
fof(f3151,plain,
( spl0_283
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f845,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f3149,plain,
spl0_282,
inference(avatar_split_clause,[],[f843,f3147]) ).
fof(f3147,plain,
( spl0_282
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f843,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f3145,plain,
spl0_281,
inference(avatar_split_clause,[],[f838,f3143]) ).
fof(f3143,plain,
( spl0_281
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X3,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f838,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X3,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f3141,plain,
spl0_280,
inference(avatar_split_clause,[],[f831,f3139]) ).
fof(f3139,plain,
( spl0_280
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X3,X4,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f831,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X3,X4,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f3133,plain,
spl0_279,
inference(avatar_split_clause,[],[f830,f3131]) ).
fof(f3131,plain,
( spl0_279
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,X4,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f830,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,X4,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f3129,plain,
spl0_278,
inference(avatar_split_clause,[],[f809,f3127]) ).
fof(f3127,plain,
( spl0_278
<=> ! [X6,X2,X0] :
( c_Set_Oinsert(X2,X6,X0) = X6
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f809,axiom,
! [X2,X0,X6] :
( c_Set_Oinsert(X2,X6,X0) = X6
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f3125,plain,
spl0_277,
inference(avatar_split_clause,[],[f714,f3123]) ).
fof(f3123,plain,
( spl0_277
<=> ! [X18,X0,X10] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X18,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X0,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f714,axiom,
! [X10,X0,X18] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X18,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X0,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
fof(f3121,plain,
spl0_276,
inference(avatar_split_clause,[],[f665,f3119]) ).
fof(f3119,plain,
( spl0_276
<=> ! [X6,X0] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f665,axiom,
! [X0,X6] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X6)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).
fof(f3117,plain,
spl0_275,
inference(avatar_split_clause,[],[f628,f3115]) ).
fof(f3115,plain,
( spl0_275
<=> ! [X0,X6,X3,X7] :
( hBOOL(hAPP(X6,X3))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f628,axiom,
! [X3,X0,X6,X7] :
( hBOOL(hAPP(X6,X3))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
fof(f3113,plain,
spl0_274,
inference(avatar_split_clause,[],[f627,f3111]) ).
fof(f3111,plain,
( spl0_274
<=> ! [X6,X0,X7,X3] :
( hBOOL(hAPP(X7,X3))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f627,axiom,
! [X3,X0,X6,X7] :
( hBOOL(hAPP(X7,X3))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
fof(f3109,plain,
spl0_273,
inference(avatar_split_clause,[],[f584,f3107]) ).
fof(f3105,plain,
spl0_272,
inference(avatar_split_clause,[],[f553,f3103]) ).
fof(f3103,plain,
( spl0_272
<=> ! [X2,X0,X1,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f553,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
fof(f3101,plain,
spl0_271,
inference(avatar_split_clause,[],[f552,f3099]) ).
fof(f3099,plain,
( spl0_271
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X3,X2,X0)
| c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f552,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X3,X2,X0)
| c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
fof(f3097,plain,
spl0_270,
inference(avatar_split_clause,[],[f551,f3095]) ).
fof(f3095,plain,
( spl0_270
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f551,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
fof(f3093,plain,
( ~ spl0_48
| spl0_269
| ~ spl0_130
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2610,f2226,f2002,f3091,f1659]) ).
fof(f3091,plain,
( spl0_269
<=> ! [X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f2002,plain,
( spl0_130
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f2226,plain,
( spl0_167
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f2610,plain,
( ! [X0] :
( c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_130
| ~ spl0_167 ),
inference(superposition,[],[f2003,f2227]) ).
fof(f2227,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f2226]) ).
fof(f2003,plain,
( ! [X3,X0,X4] :
( c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f2002]) ).
fof(f3089,plain,
spl0_268,
inference(avatar_split_clause,[],[f550,f3087]) ).
fof(f3087,plain,
( spl0_268
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X3,X23,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f550,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X3,X23,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X23,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
fof(f3085,plain,
spl0_267,
inference(avatar_split_clause,[],[f467,f3083]) ).
fof(f3083,plain,
( spl0_267
<=> ! [X4,X0,X23,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X4,X0)
| ~ c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f467,axiom,
! [X3,X0,X4,X23] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X4,X0)
| ~ c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
fof(f3081,plain,
spl0_266,
inference(avatar_split_clause,[],[f466,f3079]) ).
fof(f3079,plain,
( spl0_266
<=> ! [X2,X0,X1,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f466,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
fof(f3077,plain,
spl0_265,
inference(avatar_split_clause,[],[f465,f3075]) ).
fof(f3075,plain,
( spl0_265
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f465,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
fof(f3073,plain,
spl0_264,
inference(avatar_split_clause,[],[f464,f3071]) ).
fof(f3071,plain,
( spl0_264
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f464,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(X3,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
fof(f3069,plain,
spl0_263,
inference(avatar_split_clause,[],[f457,f3067]) ).
fof(f3067,plain,
( spl0_263
<=> ! [X6,X0,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X7
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f457,axiom,
! [X0,X6,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X7
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
fof(f3065,plain,
spl0_262,
inference(avatar_split_clause,[],[f456,f3063]) ).
fof(f3063,plain,
( spl0_262
<=> ! [X6,X0,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X6
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f456,axiom,
! [X0,X6,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = X6
| c_Orderings_Obot__class_Obot(X0) != c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
fof(f3061,plain,
spl0_261,
inference(avatar_split_clause,[],[f392,f3059]) ).
fof(f3057,plain,
spl0_260,
inference(avatar_split_clause,[],[f313,f3055]) ).
fof(f3055,plain,
( spl0_260
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ c_lessequals(X4,X3,X0)
| ~ c_lessequals(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f313,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ c_lessequals(X4,X3,X0)
| ~ c_lessequals(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
fof(f3052,plain,
spl0_259,
inference(avatar_split_clause,[],[f253,f3050]) ).
fof(f253,axiom,
! [X0,X6] :
( c_Finite__Set_Ofinite(X6,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(X6,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__gt__0__iff_1) ).
fof(f3047,plain,
spl0_258,
inference(avatar_split_clause,[],[f159,f3045]) ).
fof(f3045,plain,
( spl0_258
<=> ! [X6,X0,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X6
| c_Orderings_Otop__class_Otop(X0) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f159,axiom,
! [X0,X6,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X6
| c_Orderings_Otop__class_Otop(X0) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
fof(f3043,plain,
spl0_257,
inference(avatar_split_clause,[],[f158,f3041]) ).
fof(f3041,plain,
( spl0_257
<=> ! [X6,X0,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X7
| c_Orderings_Otop__class_Otop(X0) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f158,axiom,
! [X0,X6,X7] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = X7
| c_Orderings_Otop__class_Otop(X0) != c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
fof(f3039,plain,
spl0_256,
inference(avatar_split_clause,[],[f130,f3037]) ).
fof(f3037,plain,
( spl0_256
<=> ! [X0,X6,X3,X7] :
( ~ hBOOL(hAPP(X6,X3))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f130,axiom,
! [X3,X0,X6,X7] :
( ~ hBOOL(hAPP(X6,X3))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
fof(f3035,plain,
spl0_255,
inference(avatar_split_clause,[],[f129,f3033]) ).
fof(f3033,plain,
( spl0_255
<=> ! [X6,X0,X7,X3] :
( ~ hBOOL(hAPP(X7,X3))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f129,axiom,
! [X3,X0,X6,X7] :
( ~ hBOOL(hAPP(X7,X3))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
fof(f3031,plain,
spl0_254,
inference(avatar_split_clause,[],[f40,f3029]) ).
fof(f3029,plain,
( spl0_254
<=> ! [X18,X0,X10] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X18,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_bool)),X0,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f40,axiom,
! [X10,X0,X18] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Set_Ovimage(X18,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_bool)),X0,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
fof(f3027,plain,
spl0_253,
inference(avatar_split_clause,[],[f29,f3025]) ).
fof(f3025,plain,
( spl0_253
<=> ! [X15,X0,X10] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Relation_OImage(X15,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f29,axiom,
! [X10,X0,X15] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Relation_OImage(X15,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).
fof(f3016,plain,
( spl0_252
| ~ spl0_212
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f2764,f2760,f2440,f3014]) ).
fof(f2760,plain,
( spl0_249
<=> ! [X14] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f2764,plain,
( ! [X14] :
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X14))
| c_Orderings_Obot__class_Obot(tc_nat) = X14 )
| ~ spl0_212
| ~ spl0_249 ),
inference(forward_demodulation,[],[f2763,f2442]) ).
fof(f2763,plain,
( ! [X14] :
( c_Orderings_Obot__class_Obot(tc_nat) = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14)) )
| ~ spl0_212
| ~ spl0_249 ),
inference(forward_demodulation,[],[f2761,f2442]) ).
fof(f2761,plain,
( ! [X14] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14)) )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2760]) ).
fof(f2987,plain,
( ~ spl0_14
| spl0_251
| ~ spl0_83
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2491,f2440,f1805,f2985,f1489]) ).
fof(f2985,plain,
( spl0_251
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f1805,plain,
( spl0_83
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f2491,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat) )
| ~ spl0_83
| ~ spl0_212 ),
inference(superposition,[],[f1806,f2442]) ).
fof(f1806,plain,
( ! [X2,X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f1805]) ).
fof(f2768,plain,
spl0_250,
inference(avatar_split_clause,[],[f1102,f2766]) ).
fof(f1102,axiom,
! [X3,X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| hBOOL(hAPP(hAPP(c_in(X0),X3),c_Wellfounded_Oacc(X8,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
fof(f2762,plain,
spl0_249,
inference(avatar_split_clause,[],[f858,f2760]) ).
fof(f858,axiom,
! [X14] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X14
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f2758,plain,
spl0_248,
inference(avatar_split_clause,[],[f673,f2756]) ).
fof(f2756,plain,
( spl0_248
<=> ! [X6,X0,X7] :
( ~ c_Finite__Set_Ofinite(X7,X0)
| c_Finite__Set_Ofinite(X6,X0)
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f673,axiom,
! [X0,X6,X7] :
( ~ c_Finite__Set_Ofinite(X7,X0)
| c_Finite__Set_Ofinite(X6,X0)
| ~ c_lessequals(X6,X7,tc_fun(X0,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).
fof(f2754,plain,
spl0_247,
inference(avatar_split_clause,[],[f563,f2752]) ).
fof(f563,axiom,
! [X31,X46,X45] :
( ~ c_lessequals(X45,X46,tc_nat)
| ~ c_lessequals(X46,X31,tc_nat)
| c_lessequals(X45,X31,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
fof(f2750,plain,
( ~ spl0_20
| ~ spl0_246
| ~ spl0_90
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2490,f2440,f1833,f2747,f1519]) ).
fof(f1519,plain,
( spl0_20
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f2747,plain,
( spl0_246
<=> c_HOL_Oone__class_Oone(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f1833,plain,
( spl0_90
<=> ! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f2490,plain,
( c_HOL_Oone__class_Oone(tc_nat) != c_Orderings_Obot__class_Obot(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(tc_nat)
| ~ spl0_90
| ~ spl0_212 ),
inference(superposition,[],[f1834,f2442]) ).
fof(f1834,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1833]) ).
fof(f2745,plain,
spl0_245,
inference(avatar_split_clause,[],[f417,f2743]) ).
fof(f2743,plain,
( spl0_245
<=> ! [X0,X3] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f417,axiom,
! [X3,X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).
fof(f2741,plain,
spl0_244,
inference(avatar_split_clause,[],[f416,f2739]) ).
fof(f2739,plain,
( spl0_244
<=> ! [X0,X3] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f416,axiom,
! [X3,X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).
fof(f2737,plain,
spl0_243,
inference(avatar_split_clause,[],[f380,f2735]) ).
fof(f2735,plain,
( spl0_243
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X4,X3,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f380,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X4,X3,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
fof(f2733,plain,
spl0_242,
inference(avatar_split_clause,[],[f379,f2731]) ).
fof(f2731,plain,
( spl0_242
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X4,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f379,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X3,X4,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
fof(f2729,plain,
spl0_241,
inference(avatar_split_clause,[],[f378,f2727]) ).
fof(f2727,plain,
( spl0_241
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X3,X4,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f378,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X3,X4,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
fof(f2725,plain,
spl0_240,
inference(avatar_split_clause,[],[f321,f2723]) ).
fof(f321,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X3,X4,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
fof(f2721,plain,
spl0_239,
inference(avatar_split_clause,[],[f320,f2719]) ).
fof(f2719,plain,
( spl0_239
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X3,X4,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f320,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X3,X4,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
fof(f2717,plain,
spl0_238,
inference(avatar_split_clause,[],[f319,f2715]) ).
fof(f319,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X4,X3,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
fof(f2713,plain,
spl0_237,
inference(avatar_split_clause,[],[f275,f2711]) ).
fof(f2711,plain,
( spl0_237
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f275,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f2709,plain,
spl0_236,
inference(avatar_split_clause,[],[f274,f2707]) ).
fof(f2707,plain,
( spl0_236
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f274,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f2701,plain,
spl0_235,
inference(avatar_split_clause,[],[f175,f2699]) ).
fof(f2699,plain,
( spl0_235
<=> ! [X0,X3] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f175,axiom,
! [X3,X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
fof(f2697,plain,
spl0_234,
inference(avatar_split_clause,[],[f174,f2695]) ).
fof(f2695,plain,
( spl0_234
<=> ! [X0,X3] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f174,axiom,
! [X3,X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
fof(f2693,plain,
spl0_233,
inference(avatar_split_clause,[],[f171,f2691]) ).
fof(f2691,plain,
( spl0_233
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f171,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f2689,plain,
spl0_232,
inference(avatar_split_clause,[],[f170,f2687]) ).
fof(f2687,plain,
( spl0_232
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f170,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f2685,plain,
spl0_231,
inference(avatar_split_clause,[],[f27,f2683]) ).
fof(f2683,plain,
( spl0_231
<=> ! [X6,X0,X3] : c_Set_Oinsert(X3,X6,X0) = c_Set_Oinsert(X3,c_Set_Oinsert(X3,X6,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f27,axiom,
! [X3,X0,X6] : c_Set_Oinsert(X3,X6,X0) = c_Set_Oinsert(X3,c_Set_Oinsert(X3,X6,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
fof(f2538,plain,
( spl0_230
| ~ spl0_57
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2486,f2440,f1700,f2536]) ).
fof(f2536,plain,
( spl0_230
<=> ! [X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f2486,plain,
( ! [X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat)
| ~ spl0_57
| ~ spl0_212 ),
inference(superposition,[],[f1701,f2442]) ).
fof(f2519,plain,
spl0_229,
inference(avatar_split_clause,[],[f1348,f2517]) ).
fof(f2517,plain,
( spl0_229
<=> ! [X6,X0] : c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(X6,X0),X0,X0),X0,X0) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f1348,plain,
! [X0,X6] : c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(X6,X0),X0,X0),X0,X0) = X6,
inference(definition_unfolding,[],[f1123,f1146]) ).
fof(f1123,axiom,
! [X0,X6] : c_Relation_ODomain(c_Relation_OId__on(X6,X0),X0,X0) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
fof(f2515,plain,
spl0_228,
inference(avatar_split_clause,[],[f1266,f2513]) ).
fof(f1266,axiom,
! [X3,X0,X22] :
( hBOOL(hAPP(X22,X3))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f2511,plain,
spl0_227,
inference(avatar_split_clause,[],[f1265,f2509]) ).
fof(f2509,plain,
( spl0_227
<=> ! [X22,X0,X3] :
( ~ hBOOL(hAPP(X22,X3))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f1265,axiom,
! [X3,X0,X22] :
( ~ hBOOL(hAPP(X22,X3))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f2507,plain,
spl0_226,
inference(avatar_split_clause,[],[f1166,f2505]) ).
fof(f2505,plain,
( spl0_226
<=> ! [X6,X0,X8] :
( ~ c_Relation_Ototal__on(X6,X8,X0)
| c_Relation_Ototal__on(X6,c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1166,axiom,
! [X0,X8,X6] :
( ~ c_Relation_Ototal__on(X6,X8,X0)
| c_Relation_Ototal__on(X6,c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
fof(f2503,plain,
spl0_225,
inference(avatar_split_clause,[],[f1165,f2501]) ).
fof(f2501,plain,
( spl0_225
<=> ! [X6,X0,X8] :
( c_Relation_Ototal__on(X6,X8,X0)
| ~ c_Relation_Ototal__on(X6,c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1165,axiom,
! [X0,X8,X6] :
( c_Relation_Ototal__on(X6,X8,X0)
| ~ c_Relation_Ototal__on(X6,c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
fof(f2499,plain,
spl0_224,
inference(avatar_split_clause,[],[f1158,f2497]) ).
fof(f2497,plain,
( spl0_224
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Oone__class_Oone(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1158,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Oone__class_Oone(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f2495,plain,
spl0_223,
inference(avatar_split_clause,[],[f1148,f2493]) ).
fof(f2493,plain,
( spl0_223
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f1148,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f2483,plain,
spl0_222,
inference(avatar_split_clause,[],[f1120,f2481]) ).
fof(f2481,plain,
( spl0_222
<=> ! [X0,X15] :
( c_Wellfounded_Owf(X15,X0)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X15,X15,X0,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f1120,axiom,
! [X0,X15] :
( c_Wellfounded_Owf(X15,X0)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X15,X15,X0,X0,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
fof(f2479,plain,
spl0_221,
inference(avatar_split_clause,[],[f1119,f2477]) ).
fof(f2477,plain,
( spl0_221
<=> ! [X0,X15] :
( ~ c_Wellfounded_Owf(X15,X0)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X15,X15,X0,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f1119,axiom,
! [X0,X15] :
( ~ c_Wellfounded_Owf(X15,X0)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X15,X15,X0,X0,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
fof(f2475,plain,
spl0_220,
inference(avatar_split_clause,[],[f1117,f2473]) ).
fof(f2473,plain,
( spl0_220
<=> ! [X6,X0,X8] :
( ~ c_Relation_Orefl__on(X6,X8,X0)
| c_Relation_Orefl__on(X6,c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f1117,axiom,
! [X0,X8,X6] :
( ~ c_Relation_Orefl__on(X6,X8,X0)
| c_Relation_Orefl__on(X6,c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
fof(f2471,plain,
spl0_219,
inference(avatar_split_clause,[],[f1116,f2469]) ).
fof(f2469,plain,
( spl0_219
<=> ! [X6,X0,X8] :
( c_Relation_Orefl__on(X6,X8,X0)
| ~ c_Relation_Orefl__on(X6,c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f1116,axiom,
! [X0,X8,X6] :
( c_Relation_Orefl__on(X6,X8,X0)
| ~ c_Relation_Orefl__on(X6,c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
fof(f2467,plain,
spl0_218,
inference(avatar_split_clause,[],[f963,f2465]) ).
fof(f2465,plain,
( spl0_218
<=> ! [X0,X15] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X15,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f963,axiom,
! [X0,X15] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X15,X0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__rtrancl_0) ).
fof(f2463,plain,
spl0_217,
inference(avatar_split_clause,[],[f859,f2461]) ).
fof(f2461,plain,
( spl0_217
<=> ! [X16,X14] :
( c_lessequals(X16,X14,tc_nat)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f859,axiom,
! [X16,X14] :
( c_lessequals(X16,X14,tc_nat)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
fof(f2459,plain,
spl0_216,
inference(avatar_split_clause,[],[f777,f2457]) ).
fof(f2457,plain,
( spl0_216
<=> ! [X0,X24,X19] :
( ~ c_Finite__Set_Ofinite(X19,X0)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X19,X24,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f777,axiom,
! [X0,X19,X24] :
( ~ c_Finite__Set_Ofinite(X19,X0)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X19,X24,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
fof(f2455,plain,
spl0_215,
inference(avatar_split_clause,[],[f776,f2453]) ).
fof(f776,axiom,
! [X0,X19,X24] :
( ~ c_Finite__Set_Ofinite(X24,X0)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X19,X24,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
fof(f2451,plain,
spl0_214,
inference(avatar_split_clause,[],[f667,f2449]) ).
fof(f667,axiom,
! [X3,X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
fof(f2447,plain,
spl0_213,
inference(avatar_split_clause,[],[f643,f2445]) ).
fof(f2445,plain,
( spl0_213
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f643,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f2443,plain,
( ~ spl0_38
| spl0_212
| ~ spl0_82
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f2111,f1978,f1801,f2440,f1609]) ).
fof(f1609,plain,
( spl0_38
<=> class_Orderings_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1801,plain,
( spl0_82
<=> ! [X0,X3] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f1978,plain,
( spl0_124
<=> ! [X14] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X14
| ~ c_lessequals(X14,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f2111,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ class_Orderings_Obot(tc_nat)
| ~ spl0_82
| ~ spl0_124 ),
inference(resolution,[],[f1979,f1802]) ).
fof(f1802,plain,
( ! [X3,X0] :
( c_lessequals(c_Orderings_Obot__class_Obot(X0),X3,X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f1801]) ).
fof(f1979,plain,
( ! [X14] :
( ~ c_lessequals(X14,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X14 )
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1978]) ).
fof(f2438,plain,
spl0_211,
inference(avatar_split_clause,[],[f642,f2436]) ).
fof(f2436,plain,
( spl0_211
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f642,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f2434,plain,
spl0_210,
inference(avatar_split_clause,[],[f641,f2432]) ).
fof(f2432,plain,
( spl0_210
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f641,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f2430,plain,
spl0_209,
inference(avatar_split_clause,[],[f640,f2428]) ).
fof(f2428,plain,
( spl0_209
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f640,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f2426,plain,
spl0_208,
inference(avatar_split_clause,[],[f639,f2424]) ).
fof(f639,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f2422,plain,
spl0_207,
inference(avatar_split_clause,[],[f637,f2420]) ).
fof(f637,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f2418,plain,
spl0_206,
inference(avatar_split_clause,[],[f586,f2416]) ).
fof(f2416,plain,
( spl0_206
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f586,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
fof(f2414,plain,
spl0_205,
inference(avatar_split_clause,[],[f585,f2412]) ).
fof(f585,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
fof(f2410,plain,
spl0_204,
inference(avatar_split_clause,[],[f488,f2408]) ).
fof(f2408,plain,
( spl0_204
<=> ! [X6,X0,X7] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f488,axiom,
! [X0,X6,X7] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
fof(f2406,plain,
spl0_203,
inference(avatar_split_clause,[],[f487,f2404]) ).
fof(f2404,plain,
( spl0_203
<=> ! [X6,X0,X7] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f487,axiom,
! [X0,X6,X7] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
fof(f2402,plain,
spl0_202,
inference(avatar_split_clause,[],[f435,f2400]) ).
fof(f2400,plain,
( spl0_202
<=> ! [X6,X4,X0,X3] :
( ~ hBOOL(hAPP(X6,X3))
| hBOOL(hAPP(c_Set_Oinsert(X4,X6,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f435,axiom,
! [X3,X0,X6,X4] :
( ~ hBOOL(hAPP(X6,X3))
| hBOOL(hAPP(c_Set_Oinsert(X4,X6,X0),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
fof(f2398,plain,
( spl0_201
| ~ spl0_44
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f2105,f1970,f1639,f2396]) ).
fof(f2396,plain,
( spl0_201
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1970,plain,
( spl0_122
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X0),X3,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f2105,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),X0,tc_bool) = X0
| ~ spl0_44
| ~ spl0_122 ),
inference(resolution,[],[f1971,f1641]) ).
fof(f1971,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X0),X3,X0) = X3 )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1970]) ).
fof(f2394,plain,
spl0_200,
inference(avatar_split_clause,[],[f407,f2392]) ).
fof(f2392,plain,
( spl0_200
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f407,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
fof(f2390,plain,
spl0_199,
inference(avatar_split_clause,[],[f394,f2388]) ).
fof(f2388,plain,
( spl0_199
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f394,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f2386,plain,
spl0_198,
inference(avatar_split_clause,[],[f393,f2384]) ).
fof(f393,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f2382,plain,
spl0_197,
inference(avatar_split_clause,[],[f383,f2380]) ).
fof(f2380,plain,
( spl0_197
<=> ! [X6,X0,X7] : c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f383,axiom,
! [X0,X6,X7] : c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
fof(f2378,plain,
spl0_196,
inference(avatar_split_clause,[],[f382,f2376]) ).
fof(f2376,plain,
( spl0_196
<=> ! [X6,X0,X7] : c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f382,axiom,
! [X0,X6,X7] : c_lessequals(X7,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
fof(f2374,plain,
spl0_195,
inference(avatar_split_clause,[],[f318,f2372]) ).
fof(f318,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
fof(f2370,plain,
spl0_194,
inference(avatar_split_clause,[],[f309,f2368]) ).
fof(f2368,plain,
( spl0_194
<=> ! [X16,X14] :
( X14 = X16
| ~ c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(X14,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f309,axiom,
! [X16,X14] :
( X14 = X16
| ~ c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(X14,X16,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f2366,plain,
spl0_193,
inference(avatar_split_clause,[],[f292,f2364]) ).
fof(f292,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
fof(f2362,plain,
spl0_192,
inference(avatar_split_clause,[],[f288,f2360]) ).
fof(f288,axiom,
! [X0,X6] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
fof(f2358,plain,
spl0_191,
inference(avatar_split_clause,[],[f287,f2356]) ).
fof(f2356,plain,
( spl0_191
<=> ! [X0,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f287,axiom,
! [X0,X7] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
fof(f2354,plain,
( spl0_190
| ~ spl0_44
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f2103,f1966,f1639,f2352]) ).
fof(f1966,plain,
( spl0_121
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Orderings_Otop__class_Otop(X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f2103,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = X0
| ~ spl0_44
| ~ spl0_121 ),
inference(resolution,[],[f1967,f1641]) ).
fof(f1967,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Orderings_Otop__class_Otop(X0),X0) = X3 )
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1966]) ).
fof(f2350,plain,
spl0_189,
inference(avatar_split_clause,[],[f185,f2348]) ).
fof(f2348,plain,
( spl0_189
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f185,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
fof(f2346,plain,
spl0_188,
inference(avatar_split_clause,[],[f184,f2344]) ).
fof(f2344,plain,
( spl0_188
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f184,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
fof(f2342,plain,
spl0_187,
inference(avatar_split_clause,[],[f183,f2340]) ).
fof(f183,axiom,
! [X31,X0,X1] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X31),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).
fof(f2338,plain,
spl0_186,
inference(avatar_split_clause,[],[f180,f2336]) ).
fof(f2336,plain,
( spl0_186
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oone__class_Oone(X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f180,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oone__class_Oone(X0)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(f2334,plain,
spl0_185,
inference(avatar_split_clause,[],[f179,f2332]) ).
fof(f179,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Oone__class_Oone(X0)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
fof(f2330,plain,
spl0_184,
inference(avatar_split_clause,[],[f178,f2328]) ).
fof(f2328,plain,
( spl0_184
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f178,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
fof(f2326,plain,
spl0_183,
inference(avatar_split_clause,[],[f177,f2324]) ).
fof(f2324,plain,
( spl0_183
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f177,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
fof(f2322,plain,
spl0_182,
inference(avatar_split_clause,[],[f176,f2320]) ).
fof(f176,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Oone__class_Oone(X0)),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
fof(f2318,plain,
spl0_181,
inference(avatar_split_clause,[],[f153,f2316]) ).
fof(f2316,plain,
( spl0_181
<=> ! [X6,X0] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f153,axiom,
! [X0,X6] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
fof(f2314,plain,
spl0_180,
inference(avatar_split_clause,[],[f152,f2312]) ).
fof(f2312,plain,
( spl0_180
<=> ! [X0,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f152,axiom,
! [X0,X7] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X7,tc_fun(X0,tc_bool)) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
fof(f2309,plain,
spl0_179,
inference(avatar_split_clause,[],[f149,f2307]) ).
fof(f2307,plain,
( spl0_179
<=> ! [X0,X24,X19] :
( c_Finite__Set_Ofinite(X24,X0)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X19,X24,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f149,axiom,
! [X0,X19,X24] :
( c_Finite__Set_Ofinite(X24,X0)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X19,X24,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
fof(f2305,plain,
spl0_178,
inference(avatar_split_clause,[],[f148,f2303]) ).
fof(f2303,plain,
( spl0_178
<=> ! [X0,X24,X19] :
( c_Finite__Set_Ofinite(X19,X0)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X19,X24,tc_fun(X0,tc_bool)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f148,axiom,
! [X0,X19,X24] :
( c_Finite__Set_Ofinite(X19,X0)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(X19,X24,tc_fun(X0,tc_bool)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
fof(f2288,plain,
( spl0_177
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2284,f2214,f2286]) ).
fof(f2286,plain,
( spl0_177
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f2214,plain,
( spl0_164
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X4,X0)
| c_lessequals(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f2284,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_164 ),
inference(factoring,[],[f2215]) ).
fof(f2215,plain,
( ! [X3,X0,X4] :
( c_lessequals(X4,X3,X0)
| c_lessequals(X3,X4,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f2214]) ).
fof(f2268,plain,
( spl0_176
| ~ spl0_44
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f2101,f1958,f1639,f2266]) ).
fof(f2266,plain,
( spl0_176
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1958,plain,
( spl0_119
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X3,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f2101,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0
| ~ spl0_44
| ~ spl0_119 ),
inference(resolution,[],[f1959,f1641]) ).
fof(f1959,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X3,X0) = X3 )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1958]) ).
fof(f2260,plain,
spl0_175,
inference(avatar_split_clause,[],[f1345,f2258]) ).
fof(f2258,plain,
( spl0_175
<=> ! [X70,X0,X71] :
( X70 = X71
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X70),X71)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1345,axiom,
! [X70,X0,X71] :
( X70 = X71
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X70),X71)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f2256,plain,
spl0_174,
inference(avatar_split_clause,[],[f1142,f2254]) ).
fof(f2254,plain,
( spl0_174
<=> ! [X6,X0] : c_Relation_OId__on(X6,X0) = c_Relation_Oconverse(c_Relation_OId__on(X6,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1142,axiom,
! [X0,X6] : c_Relation_OId__on(X6,X0) = c_Relation_Oconverse(c_Relation_OId__on(X6,X0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
fof(f2252,plain,
spl0_173,
inference(avatar_split_clause,[],[f1134,f2250]) ).
fof(f2250,plain,
( spl0_173
<=> ! [X18,X0,X10,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Relation_Oinv__image(X8,X18,X0,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1134,axiom,
! [X10,X0,X18,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Relation_Oinv__image(X8,X18,X0,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
fof(f2248,plain,
spl0_172,
inference(avatar_split_clause,[],[f1132,f2246]) ).
fof(f2246,plain,
( spl0_172
<=> ! [X18,X0,X10,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Owf(c_Relation_Oinv__image(X8,X18,X0,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1132,axiom,
! [X10,X0,X18,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Owf(c_Relation_Oinv__image(X8,X18,X0,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
fof(f2244,plain,
spl0_171,
inference(avatar_split_clause,[],[f967,f2242]) ).
fof(f967,axiom,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ORange(c_Relation_OId(X0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id_0) ).
fof(f2240,plain,
spl0_170,
inference(avatar_split_clause,[],[f931,f2238]) ).
fof(f931,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
fof(f2236,plain,
spl0_169,
inference(avatar_split_clause,[],[f929,f2234]) ).
fof(f2234,plain,
( spl0_169
<=> ! [X0,X16] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X16),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f929,axiom,
! [X0,X16] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),X16),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
fof(f2232,plain,
spl0_168,
inference(avatar_split_clause,[],[f804,f2230]) ).
fof(f2230,plain,
( spl0_168
<=> ! [X0,X7,X3] : hBOOL(hAPP(hAPP(c_in(X0),X3),c_Set_Oinsert(X3,X7,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f804,axiom,
! [X3,X0,X7] : hBOOL(hAPP(hAPP(c_in(X0),X3),c_Set_Oinsert(X3,X7,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
fof(f2228,plain,
( spl0_167
| ~ spl0_44
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f2099,f1954,f1639,f2226]) ).
fof(f1954,plain,
( spl0_118
<=> ! [X0,X3] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Orderings_Obot__class_Obot(X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f2099,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
| ~ spl0_44
| ~ spl0_118 ),
inference(resolution,[],[f1955,f1641]) ).
fof(f1955,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Orderings_Obot__class_Obot(X0),X0) = X3 )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1954]) ).
fof(f2224,plain,
spl0_166,
inference(avatar_split_clause,[],[f799,f2222]) ).
fof(f799,axiom,
! [X3,X0] : hBOOL(hAPP(hAPP(c_in(X0),X3),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
fof(f2220,plain,
spl0_165,
inference(avatar_split_clause,[],[f795,f2218]) ).
fof(f795,axiom,
! [X0,X5] : ~ hBOOL(hAPP(hAPP(c_in(X0),X5),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
fof(f2216,plain,
spl0_164,
inference(avatar_split_clause,[],[f731,f2214]) ).
fof(f731,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X4,X0)
| c_lessequals(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f2212,plain,
spl0_163,
inference(avatar_split_clause,[],[f514,f2210]) ).
fof(f514,axiom,
! [X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Otop__class_Otop(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
fof(f2208,plain,
spl0_162,
inference(avatar_split_clause,[],[f473,f2206]) ).
fof(f2206,plain,
( spl0_162
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X3,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f473,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X3,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
fof(f2204,plain,
spl0_161,
inference(avatar_split_clause,[],[f472,f2202]) ).
fof(f472,axiom,
! [X2,X0] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
fof(f2200,plain,
spl0_160,
inference(avatar_split_clause,[],[f278,f2198]) ).
fof(f278,axiom,
! [X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| c_Orderings_Obot__class_Obot(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).
fof(f2196,plain,
spl0_159,
inference(avatar_split_clause,[],[f239,f2194]) ).
fof(f239,axiom,
! [X0,X14] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f2192,plain,
spl0_158,
inference(avatar_split_clause,[],[f39,f2190]) ).
fof(f39,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Orderings_Otop__class_Otop(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
fof(f2188,plain,
spl0_157,
inference(avatar_split_clause,[],[f38,f2186]) ).
fof(f38,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Otop__class_Otop(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
fof(f2184,plain,
spl0_156,
inference(avatar_split_clause,[],[f11,f2182]) ).
fof(f11,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Orderings_Obot__class_Obot(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
fof(f2180,plain,
spl0_155,
inference(avatar_split_clause,[],[f10,f2178]) ).
fof(f10,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Orderings_Obot__class_Obot(X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
fof(f2159,plain,
( ~ spl0_41
| spl0_154
| ~ spl0_112
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f2120,f1994,f1930,f2157,f1624]) ).
fof(f2157,plain,
( spl0_154
<=> ! [X0] : c_lessequals(X0,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1930,plain,
( spl0_112
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1994,plain,
( spl0_128
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f2120,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_112
| ~ spl0_128 ),
inference(superposition,[],[f1995,f1931]) ).
fof(f1931,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1930]) ).
fof(f1995,plain,
( ! [X3,X0,X4] :
( c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1994]) ).
fof(f2096,plain,
spl0_153,
inference(avatar_split_clause,[],[f1255,f2094]) ).
fof(f2094,plain,
( spl0_153
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1255,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f2092,plain,
spl0_152,
inference(avatar_split_clause,[],[f1254,f2090]) ).
fof(f2090,plain,
( spl0_152
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1254,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f2088,plain,
spl0_151,
inference(avatar_split_clause,[],[f1253,f2086]) ).
fof(f2086,plain,
( spl0_151
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1253,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f2084,plain,
spl0_150,
inference(avatar_split_clause,[],[f1171,f2082]) ).
fof(f2082,plain,
( spl0_150
<=> ! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X8,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1171,axiom,
! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X8,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
fof(f2080,plain,
spl0_149,
inference(avatar_split_clause,[],[f1156,f2078]) ).
fof(f2078,plain,
( spl0_149
<=> ! [X0,X8] :
( ~ c_Relation_Oantisym(X8,X0)
| c_Relation_Oantisym(c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1156,axiom,
! [X0,X8] :
( ~ c_Relation_Oantisym(X8,X0)
| c_Relation_Oantisym(c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
fof(f2076,plain,
spl0_148,
inference(avatar_split_clause,[],[f1155,f2074]) ).
fof(f2074,plain,
( spl0_148
<=> ! [X0,X8] :
( c_Relation_Oantisym(X8,X0)
| ~ c_Relation_Oantisym(c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1155,axiom,
! [X0,X8] :
( c_Relation_Oantisym(X8,X0)
| ~ c_Relation_Oantisym(c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
fof(f2072,plain,
spl0_147,
inference(avatar_split_clause,[],[f1149,f2070]) ).
fof(f2070,plain,
( spl0_147
<=> ! [X0,X8,X10] : c_Relation_Oconverse(c_Relation_Oconverse(X8,X0,X10),X10,X0) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1149,axiom,
! [X10,X0,X8] : c_Relation_Oconverse(c_Relation_Oconverse(X8,X0,X10),X10,X0) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).
fof(f2068,plain,
spl0_146,
inference(avatar_split_clause,[],[f1145,f2066]) ).
fof(f1145,axiom,
! [X0,X18,X15] :
( ~ c_Wellfounded_Owf(X15,X0)
| c_Wellfounded_Owf(c_Wellfounded_Omlex__prod(X18,X15,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__mlex_0) ).
fof(f2064,plain,
spl0_145,
inference(avatar_split_clause,[],[f1125,f2062]) ).
fof(f2062,plain,
( spl0_145
<=> ! [X0,X8] :
( c_Relation_Osym(X8,X0)
| c_Relation_Oconverse(X8,X0,X0) != X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1125,axiom,
! [X0,X8] :
( c_Relation_Osym(X8,X0)
| c_Relation_Oconverse(X8,X0,X0) != X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
fof(f2060,plain,
spl0_144,
inference(avatar_split_clause,[],[f1124,f2058]) ).
fof(f2058,plain,
( spl0_144
<=> ! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Oconverse(X8,X0,X0) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1124,axiom,
! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Oconverse(X8,X0,X0) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
fof(f2056,plain,
spl0_143,
inference(avatar_split_clause,[],[f1113,f2054]) ).
fof(f1113,axiom,
! [X10,X0,X15] : c_Relation_Orel__comp(X15,c_Relation_OId(X10),X0,X10,X10) = X15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
fof(f2052,plain,
spl0_142,
inference(avatar_split_clause,[],[f1112,f2050]) ).
fof(f2050,plain,
( spl0_142
<=> ! [X10,X0,X15] : c_Relation_Orel__comp(c_Relation_OId(X0),X15,X0,X0,X10) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1112,axiom,
! [X10,X0,X15] : c_Relation_Orel__comp(c_Relation_OId(X0),X15,X0,X0,X10) = X15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
fof(f2048,plain,
spl0_141,
inference(avatar_split_clause,[],[f1106,f2046]) ).
fof(f2046,plain,
( spl0_141
<=> ! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1106,axiom,
! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).
fof(f2044,plain,
spl0_140,
inference(avatar_split_clause,[],[f1105,f2042]) ).
fof(f2042,plain,
( spl0_140
<=> ! [X0,X8] :
( c_Relation_Osym(X8,X0)
| ~ c_Relation_Osym(c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1105,axiom,
! [X0,X8] :
( c_Relation_Osym(X8,X0)
| ~ c_Relation_Osym(c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).
fof(f2040,plain,
spl0_139,
inference(avatar_split_clause,[],[f962,f2038]) ).
fof(f2038,plain,
( spl0_139
<=> ! [X0,X8] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Transitive__Closure_Ortrancl(X8,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f962,axiom,
! [X0,X8] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Transitive__Closure_Ortrancl(X8,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__rtrancl_0) ).
fof(f2036,plain,
spl0_138,
inference(avatar_split_clause,[],[f619,f2034]) ).
fof(f2034,plain,
( spl0_138
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f619,axiom,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__empty_0) ).
fof(f2032,plain,
spl0_137,
inference(avatar_split_clause,[],[f491,f2030]) ).
fof(f2030,plain,
( spl0_137
<=> ! [X6,X0] : c_lessequals(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f491,axiom,
! [X0,X6] : c_lessequals(X6,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
fof(f2028,plain,
spl0_136,
inference(avatar_split_clause,[],[f486,f2026]) ).
fof(f2026,plain,
( spl0_136
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f486,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
fof(f2024,plain,
spl0_135,
inference(avatar_split_clause,[],[f485,f2022]) ).
fof(f485,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
fof(f2020,plain,
( spl0_134
| ~ spl0_42
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1920,f1857,f1629,f2018]) ).
fof(f2018,plain,
( spl0_134
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1857,plain,
( spl0_96
<=> ! [X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X3,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1920,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0
| ~ spl0_42
| ~ spl0_96 ),
inference(resolution,[],[f1858,f1631]) ).
fof(f1858,plain,
( ! [X3,X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X3,X0) = X3 )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1857]) ).
fof(f2016,plain,
spl0_133,
inference(avatar_split_clause,[],[f481,f2014]) ).
fof(f2014,plain,
( spl0_133
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f481,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
fof(f2012,plain,
spl0_132,
inference(avatar_split_clause,[],[f480,f2010]) ).
fof(f2010,plain,
( spl0_132
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f480,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
fof(f2008,plain,
spl0_131,
inference(avatar_split_clause,[],[f391,f2006]) ).
fof(f2006,plain,
( spl0_131
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f391,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
fof(f2004,plain,
spl0_130,
inference(avatar_split_clause,[],[f390,f2002]) ).
fof(f390,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
fof(f2000,plain,
spl0_129,
inference(avatar_split_clause,[],[f387,f1998]) ).
fof(f1998,plain,
( spl0_129
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f387,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
fof(f1996,plain,
spl0_128,
inference(avatar_split_clause,[],[f386,f1994]) ).
fof(f386,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
fof(f1992,plain,
spl0_127,
inference(avatar_split_clause,[],[f307,f1990]) ).
fof(f1990,plain,
( spl0_127
<=> ! [X0,X8] :
( ~ c_Wellfounded_Oacyclic(X8,X0)
| c_Wellfounded_Oacyclic(c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f307,axiom,
! [X0,X8] :
( ~ c_Wellfounded_Oacyclic(X8,X0)
| c_Wellfounded_Oacyclic(c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).
fof(f1988,plain,
spl0_126,
inference(avatar_split_clause,[],[f306,f1986]) ).
fof(f1986,plain,
( spl0_126
<=> ! [X0,X8] :
( c_Wellfounded_Oacyclic(X8,X0)
| ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f306,axiom,
! [X0,X8] :
( c_Wellfounded_Oacyclic(X8,X0)
| ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).
fof(f1984,plain,
spl0_125,
inference(avatar_split_clause,[],[f300,f1982]) ).
fof(f1982,plain,
( spl0_125
<=> ! [X6,X0] :
( c_Finite__Set_Ofinite(X6,X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f300,axiom,
! [X0,X6] :
( c_Finite__Set_Ofinite(X6,X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Finite__Set_Ocard(X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__0__iff_2) ).
fof(f1980,plain,
spl0_124,
inference(avatar_split_clause,[],[f298,f1978]) ).
fof(f298,axiom,
! [X14] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X14
| ~ c_lessequals(X14,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
fof(f1976,plain,
( spl0_123
| ~ spl0_22
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1919,f1857,f1529,f1974]) ).
fof(f1974,plain,
( spl0_123
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1919,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0
| ~ spl0_22
| ~ spl0_96 ),
inference(resolution,[],[f1858,f1531]) ).
fof(f1972,plain,
spl0_122,
inference(avatar_split_clause,[],[f286,f1970]) ).
fof(f286,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X0),X3,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
fof(f1968,plain,
spl0_121,
inference(avatar_split_clause,[],[f285,f1966]) ).
fof(f285,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Orderings_Otop__class_Otop(X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
fof(f1964,plain,
spl0_120,
inference(avatar_split_clause,[],[f283,f1962]) ).
fof(f1962,plain,
( spl0_120
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f283,axiom,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
fof(f1960,plain,
spl0_119,
inference(avatar_split_clause,[],[f151,f1958]) ).
fof(f151,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X3,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
fof(f1956,plain,
spl0_118,
inference(avatar_split_clause,[],[f150,f1954]) ).
fof(f150,axiom,
! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Orderings_Obot__class_Obot(X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
fof(f1952,plain,
spl0_117,
inference(avatar_split_clause,[],[f76,f1950]) ).
fof(f1950,plain,
( spl0_117
<=> ! [X6,X2,X0] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f76,axiom,
! [X2,X0,X6] :
( ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X2,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
fof(f1948,plain,
spl0_116,
inference(avatar_split_clause,[],[f75,f1946]) ).
fof(f1946,plain,
( spl0_116
<=> ! [X6,X2,X0] :
( c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f75,axiom,
! [X2,X0,X6] :
( c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X2,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
fof(f1944,plain,
spl0_115,
inference(avatar_split_clause,[],[f72,f1942]) ).
fof(f1942,plain,
( spl0_115
<=> ! [X2,X0,X7] : c_lessequals(X7,c_Set_Oinsert(X2,X7,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f72,axiom,
! [X2,X0,X7] : c_lessequals(X7,c_Set_Oinsert(X2,X7,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
fof(f1940,plain,
spl0_114,
inference(avatar_split_clause,[],[f42,f1938]) ).
fof(f1938,plain,
( spl0_114
<=> ! [X6,X0] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f42,axiom,
! [X0,X6] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
fof(f1936,plain,
spl0_113,
inference(avatar_split_clause,[],[f35,f1934]) ).
fof(f1934,plain,
( spl0_113
<=> ! [X6,X2,X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X2,X6,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f35,axiom,
! [X2,X0,X6] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X2,X6,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
fof(f1932,plain,
( spl0_112
| ~ spl0_41
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1917,f1853,f1624,f1930]) ).
fof(f1853,plain,
( spl0_95
<=> ! [X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X3,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1917,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
| ~ spl0_41
| ~ spl0_95 ),
inference(resolution,[],[f1854,f1626]) ).
fof(f1854,plain,
( ! [X3,X0] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X3,X0) = X3 )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1853]) ).
fof(f1926,plain,
( spl0_111
| ~ spl0_21
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1916,f1853,f1524,f1924]) ).
fof(f1924,plain,
( spl0_111
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1916,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0
| ~ spl0_21
| ~ spl0_95 ),
inference(resolution,[],[f1854,f1526]) ).
fof(f1915,plain,
spl0_110,
inference(avatar_split_clause,[],[f1282,f1913]) ).
fof(f1913,plain,
( spl0_110
<=> ! [X69,X68] :
( ~ class_Finite__Set_Ofinite_Ofinite(X68)
| ~ class_Finite__Set_Ofinite_Ofinite(X69)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X68,X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1282,axiom,
! [X68,X69] :
( ~ class_Finite__Set_Ofinite_Ofinite(X68)
| ~ class_Finite__Set_Ofinite_Ofinite(X69)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X68,X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(f1911,plain,
spl0_109,
inference(avatar_split_clause,[],[f1276,f1909]) ).
fof(f1909,plain,
( spl0_109
<=> ! [X69,X68] :
( ~ class_Finite__Set_Ofinite_Ofinite(X68)
| ~ class_Finite__Set_Ofinite_Ofinite(X69)
| class_Finite__Set_Ofinite_Ofinite(tc_prod(X68,X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1276,axiom,
! [X68,X69] :
( ~ class_Finite__Set_Ofinite_Ofinite(X68)
| ~ class_Finite__Set_Ofinite_Ofinite(X69)
| class_Finite__Set_Ofinite_Ofinite(tc_prod(X68,X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod__Finite__Set_Ofinite_Ofinite) ).
fof(f1907,plain,
spl0_108,
inference(avatar_split_clause,[],[f1157,f1905]) ).
fof(f1905,plain,
( spl0_108
<=> ! [X6,X0,X8] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| c_Relation_Orefl__on(X6,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1157,axiom,
! [X0,X8,X6] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| c_Relation_Orefl__on(X6,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).
fof(f1903,plain,
spl0_107,
inference(avatar_split_clause,[],[f1147,f1901]) ).
fof(f1901,plain,
( spl0_107
<=> ! [X6,X0] : c_Relation_ORange(c_Relation_OId__on(X6,X0),X0,X0) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1147,axiom,
! [X0,X6] : c_Relation_ORange(c_Relation_OId__on(X6,X0),X0,X0) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
fof(f1899,plain,
spl0_106,
inference(avatar_split_clause,[],[f1136,f1897]) ).
fof(f1136,axiom,
! [X0] : c_Relation_OId(X0) = c_Relation_Oconverse(c_Relation_OId(X0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).
fof(f1895,plain,
spl0_105,
inference(avatar_split_clause,[],[f1121,f1893]) ).
fof(f1893,plain,
( spl0_105
<=> ! [X6,X0] : c_Relation_OImage(c_Relation_OId(X0),X6,X0,X0) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1121,axiom,
! [X0,X6] : c_Relation_OImage(c_Relation_OId(X0),X6,X0,X0) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).
fof(f1891,plain,
spl0_104,
inference(avatar_split_clause,[],[f1118,f1889]) ).
fof(f1889,plain,
( spl0_104
<=> ! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Transitive__Closure_Ortrancl(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1118,axiom,
! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Transitive__Closure_Ortrancl(X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
fof(f1887,plain,
spl0_103,
inference(avatar_split_clause,[],[f968,f1885]) ).
fof(f1885,plain,
( spl0_103
<=> ! [X0] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f968,axiom,
! [X0] : c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Relation_OId(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__Id_0) ).
fof(f1883,plain,
spl0_102,
inference(avatar_split_clause,[],[f964,f1881]) ).
fof(f1881,plain,
( spl0_102
<=> ! [X0,X8] :
( ~ c_Wellfounded_Oacyclic(X8,X0)
| c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f964,axiom,
! [X0,X8] :
( ~ c_Wellfounded_Oacyclic(X8,X0)
| c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).
fof(f1879,plain,
spl0_101,
inference(avatar_split_clause,[],[f918,f1877]) ).
fof(f918,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f1875,plain,
spl0_100,
inference(avatar_split_clause,[],[f917,f1873]) ).
fof(f1873,plain,
( spl0_100
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f917,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f1871,plain,
spl0_99,
inference(avatar_split_clause,[],[f861,f1869]) ).
fof(f861,axiom,
! [X16] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X16),c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
fof(f1867,plain,
spl0_98,
inference(avatar_split_clause,[],[f730,f1865]) ).
fof(f1865,plain,
( spl0_98
<=> ! [X16,X14] :
( c_lessequals(X16,X14,tc_nat)
| c_lessequals(X14,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f730,axiom,
! [X16,X14] :
( c_lessequals(X16,X14,tc_nat)
| c_lessequals(X14,X16,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f1863,plain,
spl0_97,
inference(avatar_split_clause,[],[f542,f1861]) ).
fof(f1861,plain,
( spl0_97
<=> ! [X6,X0] : c_Lattices_Olower__semilattice__class_Oinf(X6,X6,tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f542,axiom,
! [X0,X6] : c_Lattices_Olower__semilattice__class_Oinf(X6,X6,tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
fof(f1859,plain,
spl0_96,
inference(avatar_split_clause,[],[f541,f1857]) ).
fof(f541,axiom,
! [X3,X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X3,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f1855,plain,
spl0_95,
inference(avatar_split_clause,[],[f218,f1853]) ).
fof(f218,axiom,
! [X3,X0] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X3,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
fof(f1851,plain,
spl0_94,
inference(avatar_split_clause,[],[f217,f1849]) ).
fof(f1849,plain,
( spl0_94
<=> ! [X6,X0] : c_Lattices_Oupper__semilattice__class_Osup(X6,X6,tc_fun(X0,tc_bool)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f217,axiom,
! [X0,X6] : c_Lattices_Oupper__semilattice__class_Osup(X6,X6,tc_fun(X0,tc_bool)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
fof(f1847,plain,
spl0_93,
inference(avatar_split_clause,[],[f1344,f1845]) ).
fof(f1845,plain,
( spl0_93
<=> ! [X0,X3] : hBOOL(hAPP(hAPP(c_fequal(X0),X3),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1344,axiom,
! [X3,X0] : hBOOL(hAPP(hAPP(c_fequal(X0),X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f1843,plain,
spl0_92,
inference(avatar_split_clause,[],[f1256,f1841]) ).
fof(f1841,plain,
( spl0_92
<=> ! [X14] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X14),X14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1256,axiom,
! [X14] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X14),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
fof(f1839,plain,
spl0_91,
inference(avatar_split_clause,[],[f1160,f1837]) ).
fof(f1837,plain,
( spl0_91
<=> ! [X6,X0,X8] :
( c_Relation_Osym(X8,X0)
| ~ c_Equiv__Relations_Oequiv(X6,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1160,axiom,
! [X0,X8,X6] :
( c_Relation_Osym(X8,X0)
| ~ c_Equiv__Relations_Oequiv(X6,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
fof(f1835,plain,
spl0_90,
inference(avatar_split_clause,[],[f1122,f1833]) ).
fof(f1122,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f1831,plain,
spl0_89,
inference(avatar_split_clause,[],[f508,f1829]) ).
fof(f1829,plain,
( spl0_89
<=> ! [X6,X0,X3] : hBOOL(hAPP(c_Set_Oinsert(X3,X6,X0),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f508,axiom,
! [X3,X0,X6] : hBOOL(hAPP(c_Set_Oinsert(X3,X6,X0),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
fof(f1827,plain,
spl0_88,
inference(avatar_split_clause,[],[f492,f1825]) ).
fof(f1825,plain,
( spl0_88
<=> ! [X0,X3] :
( ~ class_Orderings_Otop(X0)
| c_lessequals(X3,c_Orderings_Otop__class_Otop(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f492,axiom,
! [X3,X0] :
( ~ class_Orderings_Otop(X0)
| c_lessequals(X3,c_Orderings_Otop__class_Otop(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
fof(f1823,plain,
spl0_87,
inference(avatar_split_clause,[],[f474,f1821]) ).
fof(f1821,plain,
( spl0_87
<=> ! [X0,X8] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f474,axiom,
! [X0,X8] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X8,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
fof(f1819,plain,
spl0_86,
inference(avatar_split_clause,[],[f369,f1817]) ).
fof(f1817,plain,
( spl0_86
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f369,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).
fof(f1815,plain,
spl0_85,
inference(avatar_split_clause,[],[f299,f1813]) ).
fof(f1813,plain,
( spl0_85
<=> ! [X0,X3] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f299,axiom,
! [X3,X0] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
fof(f1811,plain,
spl0_84,
inference(avatar_split_clause,[],[f282,f1809]) ).
fof(f1809,plain,
( spl0_84
<=> ! [X0,X3] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f282,axiom,
! [X3,X0] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f1807,plain,
spl0_83,
inference(avatar_split_clause,[],[f160,f1805]) ).
fof(f160,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
fof(f1803,plain,
spl0_82,
inference(avatar_split_clause,[],[f41,f1801]) ).
fof(f41,axiom,
! [X3,X0] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f1799,plain,
( spl0_81
| ~ spl0_61
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f1795,f1728,f1716,f1797]) ).
fof(f1797,plain,
( spl0_81
<=> ! [X0,X1] : c_Wellfounded_Oacyclic(c_Wellfounded_Omeasure(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1795,plain,
( ! [X0,X1] : c_Wellfounded_Oacyclic(c_Wellfounded_Omeasure(X0,X1),X1)
| ~ spl0_61
| ~ spl0_64 ),
inference(resolution,[],[f1729,f1717]) ).
fof(f1794,plain,
spl0_80,
inference(avatar_split_clause,[],[f1288,f1792]) ).
fof(f1792,plain,
( spl0_80
<=> ! [X69,X68] :
( ~ class_HOL_Oord(X69)
| class_HOL_Oord(tc_fun(X68,X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1288,axiom,
! [X68,X69] :
( ~ class_HOL_Oord(X69)
| class_HOL_Oord(tc_fun(X68,X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
fof(f1790,plain,
spl0_79,
inference(avatar_split_clause,[],[f1287,f1788]) ).
fof(f1788,plain,
( spl0_79
<=> ! [X69,X68] :
( ~ class_Orderings_Obot(X69)
| class_Orderings_Obot(tc_fun(X68,X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1287,axiom,
! [X68,X69] :
( ~ class_Orderings_Obot(X69)
| class_Orderings_Obot(tc_fun(X68,X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f1786,plain,
spl0_78,
inference(avatar_split_clause,[],[f1286,f1784]) ).
fof(f1784,plain,
( spl0_78
<=> ! [X69,X68] :
( ~ class_Orderings_Otop(X69)
| class_Orderings_Otop(tc_fun(X68,X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1286,axiom,
! [X68,X69] :
( ~ class_Orderings_Otop(X69)
| class_Orderings_Otop(tc_fun(X68,X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
fof(f1782,plain,
spl0_77,
inference(avatar_split_clause,[],[f1285,f1780]) ).
fof(f1780,plain,
( spl0_77
<=> ! [X69,X68] :
( ~ class_Orderings_Oorder(X69)
| class_Orderings_Oorder(tc_fun(X68,X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1285,axiom,
! [X68,X69] :
( ~ class_Orderings_Oorder(X69)
| class_Orderings_Oorder(tc_fun(X68,X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f1778,plain,
spl0_76,
inference(avatar_split_clause,[],[f1284,f1776]) ).
fof(f1776,plain,
( spl0_76
<=> ! [X69,X68] :
( ~ class_Lattices_Olattice(X69)
| class_Lattices_Olattice(tc_fun(X68,X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1284,axiom,
! [X68,X69] :
( ~ class_Lattices_Olattice(X69)
| class_Lattices_Olattice(tc_fun(X68,X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
fof(f1774,plain,
spl0_75,
inference(avatar_split_clause,[],[f1283,f1772]) ).
fof(f1772,plain,
( spl0_75
<=> ! [X69,X68] :
( ~ class_Orderings_Opreorder(X69)
| class_Orderings_Opreorder(tc_fun(X68,X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1283,axiom,
! [X68,X69] :
( ~ class_Orderings_Opreorder(X69)
| class_Orderings_Opreorder(tc_fun(X68,X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f1770,plain,
spl0_74,
inference(avatar_split_clause,[],[f1281,f1768]) ).
fof(f1768,plain,
( spl0_74
<=> ! [X69,X68] :
( ~ class_Lattices_Oboolean__algebra(X69)
| class_Lattices_Oboolean__algebra(tc_fun(X68,X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1281,axiom,
! [X68,X69] :
( ~ class_Lattices_Oboolean__algebra(X69)
| class_Lattices_Oboolean__algebra(tc_fun(X68,X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
fof(f1766,plain,
spl0_73,
inference(avatar_split_clause,[],[f1280,f1764]) ).
fof(f1764,plain,
( spl0_73
<=> ! [X69,X68] :
( ~ class_Lattices_Obounded__lattice(X69)
| class_Lattices_Obounded__lattice(tc_fun(X68,X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1280,axiom,
! [X68,X69] :
( ~ class_Lattices_Obounded__lattice(X69)
| class_Lattices_Obounded__lattice(tc_fun(X68,X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f1762,plain,
spl0_72,
inference(avatar_split_clause,[],[f1279,f1760]) ).
fof(f1760,plain,
( spl0_72
<=> ! [X69,X68] :
( ~ class_Lattices_Odistrib__lattice(X69)
| class_Lattices_Odistrib__lattice(tc_fun(X68,X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1279,axiom,
! [X68,X69] :
( ~ class_Lattices_Odistrib__lattice(X69)
| class_Lattices_Odistrib__lattice(tc_fun(X68,X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(f1758,plain,
spl0_71,
inference(avatar_split_clause,[],[f1278,f1756]) ).
fof(f1756,plain,
( spl0_71
<=> ! [X69,X68] :
( ~ class_Lattices_Olattice(X69)
| class_Lattices_Olower__semilattice(tc_fun(X68,X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1278,axiom,
! [X68,X69] :
( ~ class_Lattices_Olattice(X69)
| class_Lattices_Olower__semilattice(tc_fun(X68,X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f1754,plain,
spl0_70,
inference(avatar_split_clause,[],[f1277,f1752]) ).
fof(f1752,plain,
( spl0_70
<=> ! [X69,X68] :
( ~ class_Lattices_Olattice(X69)
| class_Lattices_Oupper__semilattice(tc_fun(X68,X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1277,axiom,
! [X68,X69] :
( ~ class_Lattices_Olattice(X69)
| class_Lattices_Oupper__semilattice(tc_fun(X68,X69)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(f1750,plain,
spl0_69,
inference(avatar_split_clause,[],[f1131,f1748]) ).
fof(f1748,plain,
( spl0_69
<=> ! [X6,X0] : c_Relation_Orefl__on(X6,c_Relation_OId__on(X6,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1131,axiom,
! [X0,X6] : c_Relation_Orefl__on(X6,c_Relation_OId__on(X6,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).
fof(f1746,plain,
spl0_68,
inference(avatar_split_clause,[],[f661,f1744]) ).
fof(f1744,plain,
( spl0_68
<=> ! [X6,X0] : c_Relation_Osingle__valued(c_Relation_OId__on(X6,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f661,axiom,
! [X0,X6] : c_Relation_Osingle__valued(c_Relation_OId__on(X6,X0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).
fof(f1742,plain,
spl0_67,
inference(avatar_split_clause,[],[f571,f1740]) ).
fof(f1740,plain,
( spl0_67
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f571,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1738,plain,
spl0_66,
inference(avatar_split_clause,[],[f570,f1736]) ).
fof(f1736,plain,
( spl0_66
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f570,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1734,plain,
spl0_65,
inference(avatar_split_clause,[],[f566,f1732]) ).
fof(f1732,plain,
( spl0_65
<=> ! [X6,X0] : c_lessequals(X6,X6,tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f566,axiom,
! [X0,X6] : c_lessequals(X6,X6,tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
fof(f1730,plain,
spl0_64,
inference(avatar_split_clause,[],[f395,f1728]) ).
fof(f395,axiom,
! [X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Oacyclic(X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).
fof(f1726,plain,
spl0_63,
inference(avatar_split_clause,[],[f328,f1724]) ).
fof(f1724,plain,
( spl0_63
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f328,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
fof(f1722,plain,
spl0_62,
inference(avatar_split_clause,[],[f77,f1720]) ).
fof(f1720,plain,
( spl0_62
<=> ! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f77,axiom,
! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
fof(f1718,plain,
spl0_61,
inference(avatar_split_clause,[],[f1169,f1716]) ).
fof(f1169,axiom,
! [X0,X18] : c_Wellfounded_Owf(c_Wellfounded_Omeasure(X18,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__measure_0) ).
fof(f1714,plain,
spl0_60,
inference(avatar_split_clause,[],[f1130,f1712]) ).
fof(f1712,plain,
( spl0_60
<=> ! [X6,X0] : c_Relation_Osym(c_Relation_OId__on(X6,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1130,axiom,
! [X0,X6] : c_Relation_Osym(c_Relation_OId__on(X6,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
fof(f1710,plain,
spl0_59,
inference(avatar_split_clause,[],[f1114,f1708]) ).
fof(f1708,plain,
( spl0_59
<=> ! [X6,X0] : c_Relation_Oantisym(c_Relation_OId__on(X6,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1114,axiom,
! [X0,X6] : c_Relation_Oantisym(c_Relation_OId__on(X6,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).
fof(f1706,plain,
spl0_58,
inference(avatar_split_clause,[],[f1104,f1704]) ).
fof(f1704,plain,
( spl0_58
<=> ! [X6,X0] :
( ~ class_Finite__Set_Ofinite_Ofinite(X0)
| c_Finite__Set_Ofinite(X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1104,axiom,
! [X0,X6] :
( ~ class_Finite__Set_Ofinite_Ofinite(X0)
| c_Finite__Set_Ofinite(X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
fof(f1702,plain,
spl0_57,
inference(avatar_split_clause,[],[f422,f1700]) ).
fof(f422,axiom,
! [X14] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).
fof(f1698,plain,
spl0_56,
inference(avatar_split_clause,[],[f240,f1696]) ).
fof(f1696,plain,
( spl0_56
<=> ! [X0] : c_Relation_Osingle__valued(c_Relation_OId(X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f240,axiom,
! [X0] : c_Relation_Osingle__valued(c_Relation_OId(X0),X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).
fof(f1694,plain,
spl0_55,
inference(avatar_split_clause,[],[f1144,f1692]) ).
fof(f1692,plain,
( spl0_55
<=> ! [X0] : c_Relation_Oantisym(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1144,axiom,
! [X0] : c_Relation_Oantisym(c_Relation_OId(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
fof(f1690,plain,
spl0_54,
inference(avatar_split_clause,[],[f1111,f1688]) ).
fof(f1688,plain,
( spl0_54
<=> ! [X0] : c_Relation_Osym(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1111,axiom,
! [X0] : c_Relation_Osym(c_Relation_OId(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).
fof(f1686,plain,
spl0_53,
inference(avatar_split_clause,[],[f562,f1684]) ).
fof(f562,axiom,
! [X14] : c_lessequals(X14,X14,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
fof(f1682,plain,
spl0_52,
inference(avatar_split_clause,[],[f1340,f1679]) ).
fof(f1679,plain,
( spl0_52
<=> class_HOL_Oord(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1340,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
fof(f1677,plain,
spl0_51,
inference(avatar_split_clause,[],[f1339,f1674]) ).
fof(f1674,plain,
( spl0_51
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1339,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f1672,plain,
spl0_50,
inference(avatar_split_clause,[],[f1338,f1669]) ).
fof(f1669,plain,
( spl0_50
<=> class_Orderings_Otop(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1338,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
fof(f1667,plain,
spl0_49,
inference(avatar_split_clause,[],[f1337,f1664]) ).
fof(f1664,plain,
( spl0_49
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f1337,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f1662,plain,
spl0_48,
inference(avatar_split_clause,[],[f1336,f1659]) ).
fof(f1336,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
fof(f1657,plain,
spl0_47,
inference(avatar_split_clause,[],[f1335,f1654]) ).
fof(f1654,plain,
( spl0_47
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1335,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f1652,plain,
spl0_46,
inference(avatar_split_clause,[],[f1334,f1649]) ).
fof(f1649,plain,
( spl0_46
<=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f1334,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
fof(f1647,plain,
spl0_45,
inference(avatar_split_clause,[],[f1333,f1644]) ).
fof(f1333,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
fof(f1642,plain,
spl0_44,
inference(avatar_split_clause,[],[f1332,f1639]) ).
fof(f1332,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f1637,plain,
spl0_43,
inference(avatar_split_clause,[],[f1331,f1634]) ).
fof(f1634,plain,
( spl0_43
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1331,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(f1632,plain,
spl0_42,
inference(avatar_split_clause,[],[f1330,f1629]) ).
fof(f1330,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f1627,plain,
spl0_41,
inference(avatar_split_clause,[],[f1329,f1624]) ).
fof(f1329,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(f1622,plain,
spl0_40,
inference(avatar_split_clause,[],[f1328,f1619]) ).
fof(f1619,plain,
( spl0_40
<=> class_HOL_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1328,axiom,
class_HOL_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
fof(f1617,plain,
spl0_39,
inference(avatar_split_clause,[],[f1327,f1614]) ).
fof(f1327,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f1612,plain,
spl0_38,
inference(avatar_split_clause,[],[f1326,f1609]) ).
fof(f1326,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
fof(f1607,plain,
spl0_37,
inference(avatar_split_clause,[],[f1325,f1604]) ).
fof(f1604,plain,
( spl0_37
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1325,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1602,plain,
spl0_36,
inference(avatar_split_clause,[],[f1324,f1599]) ).
fof(f1324,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
fof(f1597,plain,
spl0_35,
inference(avatar_split_clause,[],[f1323,f1594]) ).
fof(f1594,plain,
( spl0_35
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1323,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1592,plain,
spl0_34,
inference(avatar_split_clause,[],[f1322,f1589]) ).
fof(f1589,plain,
( spl0_34
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1322,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1587,plain,
spl0_33,
inference(avatar_split_clause,[],[f1321,f1584]) ).
fof(f1321,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
fof(f1582,plain,
spl0_32,
inference(avatar_split_clause,[],[f1320,f1579]) ).
fof(f1579,plain,
( spl0_32
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1320,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f1577,plain,
spl0_31,
inference(avatar_split_clause,[],[f1319,f1574]) ).
fof(f1574,plain,
( spl0_31
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1319,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f1572,plain,
spl0_30,
inference(avatar_split_clause,[],[f1318,f1569]) ).
fof(f1569,plain,
( spl0_30
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1318,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f1567,plain,
spl0_29,
inference(avatar_split_clause,[],[f1317,f1564]) ).
fof(f1564,plain,
( spl0_29
<=> class_Lattices_Odistrib__lattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f1317,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
fof(f1562,plain,
spl0_28,
inference(avatar_split_clause,[],[f1316,f1559]) ).
fof(f1316,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f1557,plain,
spl0_27,
inference(avatar_split_clause,[],[f1315,f1554]) ).
fof(f1554,plain,
( spl0_27
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1315,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f1552,plain,
spl0_26,
inference(avatar_split_clause,[],[f1314,f1549]) ).
fof(f1549,plain,
( spl0_26
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1314,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f1547,plain,
spl0_25,
inference(avatar_split_clause,[],[f1313,f1544]) ).
fof(f1544,plain,
( spl0_25
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f1313,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f1542,plain,
spl0_24,
inference(avatar_split_clause,[],[f1312,f1539]) ).
fof(f1539,plain,
( spl0_24
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1312,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f1537,plain,
spl0_23,
inference(avatar_split_clause,[],[f1311,f1534]) ).
fof(f1311,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f1532,plain,
spl0_22,
inference(avatar_split_clause,[],[f1310,f1529]) ).
fof(f1310,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
fof(f1527,plain,
spl0_21,
inference(avatar_split_clause,[],[f1309,f1524]) ).
fof(f1309,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
fof(f1522,plain,
spl0_20,
inference(avatar_split_clause,[],[f1308,f1519]) ).
fof(f1308,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f1517,plain,
spl0_19,
inference(avatar_split_clause,[],[f1307,f1514]) ).
fof(f1307,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1512,plain,
spl0_18,
inference(avatar_split_clause,[],[f1306,f1509]) ).
fof(f1509,plain,
( spl0_18
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1306,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f1507,plain,
spl0_17,
inference(avatar_split_clause,[],[f1305,f1504]) ).
fof(f1504,plain,
( spl0_17
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1305,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1502,plain,
spl0_16,
inference(avatar_split_clause,[],[f1304,f1499]) ).
fof(f1499,plain,
( spl0_16
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1304,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1497,plain,
spl0_15,
inference(avatar_split_clause,[],[f1303,f1494]) ).
fof(f1494,plain,
( spl0_15
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1303,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f1492,plain,
spl0_14,
inference(avatar_split_clause,[],[f1302,f1489]) ).
fof(f1302,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1487,plain,
spl0_13,
inference(avatar_split_clause,[],[f1301,f1484]) ).
fof(f1301,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f1482,plain,
spl0_12,
inference(avatar_split_clause,[],[f1300,f1479]) ).
fof(f1479,plain,
( spl0_12
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1300,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f1477,plain,
spl0_11,
inference(avatar_split_clause,[],[f1299,f1474]) ).
fof(f1474,plain,
( spl0_11
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1299,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f1472,plain,
spl0_10,
inference(avatar_split_clause,[],[f1298,f1469]) ).
fof(f1469,plain,
( spl0_10
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1298,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f1467,plain,
spl0_9,
inference(avatar_split_clause,[],[f1297,f1464]) ).
fof(f1464,plain,
( spl0_9
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1297,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1462,plain,
spl0_8,
inference(avatar_split_clause,[],[f1296,f1459]) ).
fof(f1459,plain,
( spl0_8
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1296,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1457,plain,
spl0_7,
inference(avatar_split_clause,[],[f1295,f1454]) ).
fof(f1454,plain,
( spl0_7
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1295,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1452,plain,
spl0_6,
inference(avatar_split_clause,[],[f1294,f1449]) ).
fof(f1449,plain,
( spl0_6
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1294,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1447,plain,
spl0_5,
inference(avatar_split_clause,[],[f1293,f1444]) ).
fof(f1444,plain,
( spl0_5
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1293,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1442,plain,
spl0_4,
inference(avatar_split_clause,[],[f1292,f1439]) ).
fof(f1439,plain,
( spl0_4
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1292,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1437,plain,
spl0_3,
inference(avatar_split_clause,[],[f1291,f1434]) ).
fof(f1434,plain,
( spl0_3
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1291,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1432,plain,
spl0_2,
inference(avatar_split_clause,[],[f1290,f1429]) ).
fof(f1429,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1290,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1427,plain,
spl0_1,
inference(avatar_split_clause,[],[f1289,f1424]) ).
fof(f1424,plain,
( spl0_1
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1289,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SCT097-1 : TPTP v8.2.0. Released v4.1.0.
% 0.08/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n013.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 23:50:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (18066)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.46 % (18069)WARNING: value z3 for option sas not known
% 0.22/0.47 % (18067)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.47 % (18069)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)
% 0.22/0.47 % (18070)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.47 % (18068)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.47 % (18071)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)
% 0.22/0.47 % (18072)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)
% 0.22/0.47 % (18073)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)
% 1.89/0.70 TRYING [1]
% 1.89/0.73 TRYING [2]
% 6.60/1.36 TRYING [1]
% 6.60/1.38 TRYING [3]
% 7.39/1.48 TRYING [2]
% 8.83/1.69 % (18071)First to succeed.
% 8.83/1.72 % (18071)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18066"
% 8.83/1.72 % (18071)Refutation found. Thanks to Tanya!
% 8.83/1.72 % SZS status Unsatisfiable for theBenchmark
% 8.83/1.72 % SZS output start Proof for theBenchmark
% See solution above
% 8.83/1.74 % (18071)------------------------------
% 8.83/1.74 % (18071)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 8.83/1.74 % (18071)Termination reason: Refutation
% 8.83/1.74
% 8.83/1.74 % (18071)Memory used [KB]: 17058
% 8.83/1.74 % (18071)Time elapsed: 1.256 s
% 8.83/1.74 % (18071)Instructions burned: 3519 (million)
% 8.83/1.74 % (18066)Success in time 1.349 s
%------------------------------------------------------------------------------