TSTP Solution File: SCT097-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT097-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -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 : Fri Sep 1 22:00:46 EDT 2023
% Result : Unsatisfiable 17.55s 3.11s
% Output : Refutation 17.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2465
% Syntax : Number of formulae : 4083 (1355 unt; 0 def)
% Number of atoms : 10480 (1381 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 11202 (4805 ~;5097 |; 0 &)
% (1300 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 1385 (1383 usr;1301 prp; 0-6 aty)
% Number of functors : 109 ( 109 usr; 18 con; 0-7 aty)
% Number of variables : 8309 (;8309 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31915,plain,
$false,
inference(avatar_sat_refutation,[],[f1365,f1370,f1375,f1380,f1385,f1390,f1395,f1400,f1405,f1410,f1415,f1420,f1425,f1430,f1435,f1440,f1445,f1450,f1455,f1460,f1465,f1470,f1475,f1480,f1485,f1490,f1495,f1500,f1505,f1510,f1515,f1520,f1525,f1530,f1535,f1540,f1545,f1550,f1555,f1560,f1565,f1570,f1575,f1580,f1585,f1590,f1595,f1600,f1605,f1610,f1615,f1620,f1624,f1628,f1632,f1636,f1640,f1644,f1648,f1652,f1656,f1660,f1664,f1668,f1672,f1676,f1680,f1684,f1688,f1692,f1696,f1700,f1704,f1708,f1712,f1716,f1720,f1724,f1728,f1732,f1737,f1741,f1745,f1749,f1753,f1757,f1761,f1765,f1769,f1773,f1777,f1781,f1785,f1789,f1793,f1797,f1801,f1805,f1809,f1813,f1817,f1821,f1825,f1829,f1833,f1837,f1841,f1845,f1849,f1853,f1857,f1861,f1865,f1875,f1882,f1887,f1891,f1895,f1899,f1903,f1907,f1911,f1915,f1919,f1923,f1927,f1931,f1935,f1939,f1943,f1947,f1951,f1955,f1959,f1963,f1967,f1971,f1975,f1979,f1983,f1987,f1991,f1995,f1999,f2003,f2007,f2011,f2015,f2019,f2023,f2027,f2031,f2035,f2039,f2043,f2047,f2051,f2055,f2059,f2063,f2104,f2156,f2160,f2164,f2168,f2172,f2176,f2180,f2184,f2188,f2192,f2196,f2200,f2204,f2208,f2212,f2216,f2220,f2224,f2228,f2232,f2236,f2240,f2244,f2248,f2252,f2256,f2260,f2272,f2288,f2306,f2310,f2314,f2318,f2322,f2326,f2330,f2334,f2338,f2342,f2347,f2351,f2355,f2359,f2363,f2367,f2371,f2375,f2379,f2383,f2387,f2399,f2403,f2407,f2411,f2415,f2419,f2423,f2427,f2431,f2435,f2439,f2443,f2447,f2451,f2455,f2459,f2463,f2467,f2471,f2475,f2479,f2484,f2488,f2492,f2496,f2500,f2504,f2508,f2512,f2516,f2520,f2528,f2532,f2536,f2540,f2544,f2548,f2552,f2666,f2708,f2724,f2728,f2732,f2736,f2740,f2744,f2749,f2753,f2757,f2761,f2765,f2769,f2773,f2777,f2781,f2785,f2789,f2793,f2797,f2801,f2805,f2809,f2813,f2817,f2821,f2827,f2831,f2835,f2839,f2843,f2863,f3108,f3123,f3143,f3147,f3151,f3155,f3159,f3163,f3167,f3171,f3175,f3179,f3183,f3188,f3192,f3196,f3200,f3204,f3208,f3212,f3216,f3220,f3224,f3228,f3232,f3236,f3240,f3244,f3248,f3252,f3256,f3260,f3264,f3268,f3272,f3276,f3280,f3284,f3288,f3292,f3296,f3300,f3304,f3308,f3312,f3316,f3320,f3324,f3328,f3332,f3336,f3340,f3364,f3404,f3581,f3750,f3791,f3830,f3834,f3838,f3842,f3846,f3850,f3856,f3860,f3864,f3868,f3872,f3876,f3880,f3884,f3888,f3892,f3908,f3912,f3916,f3920,f3924,f3928,f3932,f3936,f3940,f3944,f3959,f3963,f3967,f3971,f3975,f3979,f3983,f3987,f3991,f3995,f4011,f4015,f4019,f4023,f4027,f4031,f4035,f4039,f4043,f4047,f4064,f4068,f4072,f4076,f4080,f4084,f4088,f4092,f4096,f4100,f4105,f4109,f4113,f4117,f4121,f4363,f4652,f4863,f4963,f4967,f4971,f4975,f4979,f4987,f4991,f4995,f4999,f5003,f5007,f5011,f5015,f5019,f5023,f5028,f5032,f5036,f5040,f5044,f5048,f5052,f5056,f5061,f5065,f5069,f5073,f5077,f5081,f5085,f5089,f5093,f5097,f5101,f5105,f5109,f5114,f5118,f5441,f5463,f5618,f5622,f5629,f5633,f5637,f5641,f5645,f5649,f5653,f5657,f5661,f5665,f5669,f5673,f5678,f5682,f5686,f5690,f5694,f5698,f5702,f5706,f5710,f5714,f5718,f5723,f5727,f5731,f5735,f5739,f5743,f5747,f5751,f5755,f5759,f5763,f5767,f5771,f5775,f5779,f5783,f5869,f6005,f6011,f6151,f6197,f6396,f6479,f6483,f6487,f6491,f6495,f6499,f6503,f6507,f6511,f6515,f6519,f6523,f6527,f6531,f6535,f6539,f6543,f6547,f6551,f6555,f6559,f6563,f6567,f6571,f6575,f6579,f6583,f6588,f6592,f6596,f6600,f6604,f6608,f6612,f6616,f6620,f6624,f6628,f6632,f6636,f6640,f6670,f7049,f7211,f7299,f7303,f7307,f7311,f7315,f7319,f7323,f7327,f7331,f7335,f7339,f7343,f7347,f7351,f7355,f7359,f7363,f7367,f7371,f7375,f7379,f7383,f7387,f7391,f7395,f7399,f7427,f7623,f7652,f7656,f7660,f7664,f7668,f7673,f7677,f7682,f7686,f7690,f7694,f7698,f7702,f7706,f7710,f7715,f7720,f7724,f7728,f7732,f7736,f7740,f7744,f7748,f7752,f7756,f7760,f7764,f7768,f7772,f7776,f7780,f7784,f7788,f7865,f7951,f8009,f8036,f8107,f8441,f8480,f8484,f8488,f8492,f8496,f8500,f8504,f8508,f8512,f8516,f8520,f8524,f8528,f8532,f8536,f8540,f8544,f8548,f8552,f8556,f8560,f8565,f8569,f8573,f8577,f8581,f8585,f8589,f8593,f8597,f8601,f8605,f8609,f8613,f8617,f8621,f8625,f8632,f8636,f8640,f8644,f8648,f8652,f8656,f8660,f8664,f8668,f8676,f8680,f8684,f8688,f8692,f8696,f8700,f8704,f8708,f8712,f8716,f8720,f8724,f8823,f9054,f9253,f9405,f9539,f9555,f9559,f9563,f9567,f9571,f9575,f9579,f9583,f9589,f9593,f9597,f9601,f9605,f9609,f9613,f9617,f9621,f9625,f9629,f9633,f9637,f9641,f9645,f9649,f9653,f9657,f9661,f9665,f9669,f9679,f9683,f9688,f10018,f10511,f10524,f10528,f10567,f10571,f10575,f10579,f10583,f10587,f10591,f10595,f10599,f10603,f10607,f10611,f10615,f10619,f10623,f10627,f10631,f10635,f10639,f10643,f10647,f10651,f10655,f10659,f10663,f10667,f10671,f10675,f10679,f10683,f10687,f10691,f10695,f10699,f10703,f10707,f10711,f10715,f10719,f10723,f10727,f10731,f10735,f10739,f10743,f10747,f10751,f10758,f10762,f10766,f10770,f11480,f11744,f11905,f11909,f11913,f11917,f11921,f11925,f11929,f11933,f11937,f11944,f11948,f11952,f11956,f11960,f11964,f11968,f11972,f11976,f11980,f11984,f11988,f11992,f11996,f12000,f12004,f12008,f12012,f12287,f12823,f13030,f13139,f13143,f13147,f13151,f13155,f13159,f13163,f13167,f13171,f13175,f13179,f13183,f13187,f13191,f13195,f13199,f13203,f13207,f13211,f13215,f13219,f13223,f13227,f13231,f13235,f13239,f13243,f13247,f13251,f13255,f13259,f13263,f13267,f13271,f13275,f13279,f13283,f13287,f13291,f13295,f13299,f13831,f14098,f14102,f14106,f14110,f14114,f14118,f14122,f14126,f14130,f14134,f14138,f14142,f14146,f14150,f14154,f14158,f14162,f14166,f14170,f14174,f14178,f14182,f14186,f14190,f14194,f14198,f14202,f14206,f14210,f14214,f14218,f14222,f14226,f14230,f14234,f14238,f14242,f14246,f14250,f14254,f14258,f14262,f14266,f14270,f14274,f14278,f14282,f14286,f14290,f14294,f14298,f14819,f15205,f15301,f15307,f15311,f15315,f15319,f15323,f15327,f15331,f15335,f15339,f15343,f15347,f15351,f15355,f15359,f15363,f15367,f15371,f15375,f15379,f15383,f15396,f15400,f15404,f15408,f15412,f15416,f15420,f15424,f15428,f15432,f15469,f15473,f15477,f15481,f15485,f15489,f15493,f15497,f15501,f15505,f15509,f15513,f15517,f15554,f16385,f16389,f16393,f16397,f16451,f16455,f16459,f16463,f16467,f16471,f16475,f16479,f16483,f16487,f16491,f16495,f16499,f16503,f16507,f16511,f16515,f17226,f17230,f17234,f17238,f17298,f17302,f17306,f17310,f17314,f17318,f17322,f17326,f17330,f17334,f17402,f17406,f17410,f17414,f17418,f17422,f17426,f17430,f17434,f17438,f17548,f17552,f17556,f17560,f17564,f17568,f17572,f19391,f19395,f19429,f19433,f19437,f19441,f19445,f19449,f19454,f19458,f19462,f19466,f19474,f19478,f19482,f19486,f19490,f19494,f19959,f20283,f20426,f20430,f20434,f20438,f20442,f20446,f20450,f20454,f20458,f20462,f20466,f20470,f20474,f20478,f20482,f20486,f20490,f20494,f20498,f20502,f20506,f20820,f20903,f20907,f20911,f20915,f20919,f20923,f20927,f20931,f20935,f20939,f20943,f20947,f20951,f20955,f20959,f20963,f20967,f20972,f20976,f20980,f20984,f20988,f20992,f20996,f21000,f21602,f21606,f21610,f21614,f21619,f21623,f21629,f21633,f21637,f21641,f21645,f21649,f21653,f21657,f21661,f21665,f21833,f21848,f21861,f22167,f22355,f22359,f22363,f22367,f22371,f22404,f22408,f22412,f22416,f22420,f22424,f22428,f22432,f22436,f22440,f22444,f22448,f22452,f22456,f22460,f22464,f22468,f22472,f22476,f22480,f22484,f22517,f22521,f22525,f22736,f23334,f23357,f23361,f23365,f23369,f23373,f23377,f23381,f23385,f23389,f23417,f23421,f23425,f23429,f23433,f23437,f23441,f23445,f23449,f23453,f23457,f23461,f23465,f23469,f23473,f23477,f23481,f23485,f23489,f23493,f23497,f23523,f23938,f24824,f24846,f24850,f24854,f24858,f24862,f24866,f24871,f24875,f24879,f24905,f24909,f24913,f25201,f25207,f25501,f25505,f25509,f25513,f25541,f25545,f25549,f25553,f25557,f25561,f25565,f25569,f25573,f25577,f25581,f25585,f25589,f25593,f25597,f25757,f26005,f26097,f26101,f26105,f26109,f26113,f26117,f26121,f26125,f26129,f26133,f26433,f26437,f26441,f26445,f26449,f26453,f26457,f26461,f26806,f26810,f26962,f26966,f26970,f26974,f26978,f26982,f26986,f26990,f26994,f27341,f27345,f27388,f27459,f27463,f27557,f27561,f27608,f27612,f27616,f27620,f27624,f27628,f27632,f27636,f27640,f27644,f27652,f27656,f28204,f28208,f28212,f28216,f28220,f28224,f28228,f28232,f28236,f28240,f28244,f28248,f28252,f28256,f28260,f28347,f28805,f28976,f28980,f28984,f28988,f28992,f28996,f29000,f29004,f29008,f29013,f29017,f29472,f29560,f29564,f29568,f29718,f29722,f29723,f29727,f29731,f29735,f29739,f29743,f29747,f29847,f30017,f30021,f30025,f30029,f30033,f30080,f30283,f30287,f30344,f30348,f30352,f30356,f30479,f30483,f30487,f30491,f30495,f30540,f30682,f30749,f30753,f30757,f30761,f30767,f30771,f31142,f31146,f31150,f31228,f31295,f31299,f31326,f31330,f31648,f31652,f31668,f31738,f31747,f31752,f31809,f31813,f31832,f31879,f31894,f31905,f31914]) ).
fof(f31914,plain,
( ~ spl0_53
| spl0_1300 ),
inference(avatar_contradiction_clause,[],[f31906]) ).
fof(f31906,plain,
( $false
| ~ spl0_53
| spl0_1300 ),
inference(resolution,[],[f31904,f1623]) ).
fof(f1623,plain,
( ! [X14] : c_lessequals(X14,X14,tc_nat)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f1622]) ).
fof(f1622,plain,
( spl0_53
<=> ! [X14] : c_lessequals(X14,X14,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f31904,plain,
( ~ c_lessequals(v_n____,v_n____,tc_nat)
| spl0_1300 ),
inference(avatar_component_clause,[],[f31902]) ).
fof(f31902,plain,
( spl0_1300
<=> c_lessequals(v_n____,v_n____,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f31905,plain,
( ~ spl0_1300
| ~ spl0_1296
| spl0_1299 ),
inference(avatar_split_clause,[],[f31895,f31891,f31830,f31902]) ).
fof(f31830,plain,
( spl0_1296
<=> ! [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_1296])]) ).
fof(f31891,plain,
( spl0_1299
<=> 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_1299])]) ).
fof(f31895,plain,
( ~ c_lessequals(v_n____,v_n____,tc_nat)
| ~ spl0_1296
| spl0_1299 ),
inference(resolution,[],[f31893,f31831]) ).
fof(f31831,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_1296 ),
inference(avatar_component_clause,[],[f31830]) ).
fof(f31893,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_1299 ),
inference(avatar_component_clause,[],[f31891]) ).
fof(f31894,plain,
( spl0_1291
| ~ spl0_1299 ),
inference(avatar_split_clause,[],[f1273,f31891,f31735]) ).
fof(f31735,plain,
( spl0_1291
<=> 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_1291])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_CHAINED_1) ).
fof(f31879,plain,
( ~ spl0_1297
| spl0_1298 ),
inference(avatar_split_clause,[],[f1240,f31876,f31872]) ).
fof(f31872,plain,
( spl0_1297
<=> 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_1297])]) ).
fof(f31876,plain,
( spl0_1298
<=> 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_1298])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_PW_1) ).
fof(f31832,plain,
spl0_1296,
inference(avatar_split_clause,[],[f1272,f31830]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_CHAINED_0) ).
fof(f31813,plain,
( spl0_1295
| ~ spl0_45
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2858,f2738,f1582,f31811]) ).
fof(f31811,plain,
( spl0_1295
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X0),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f1582,plain,
( spl0_45
<=> class_Lattices_Oboolean__algebra(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f2738,plain,
( spl0_256
<=> ! [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_256])]) ).
fof(f2858,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X0),tc_bool)
| ~ spl0_45
| ~ spl0_256 ),
inference(resolution,[],[f2739,f1584]) ).
fof(f1584,plain,
( class_Lattices_Oboolean__algebra(tc_bool)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f1582]) ).
fof(f2739,plain,
( ! [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) )
| ~ spl0_256 ),
inference(avatar_component_clause,[],[f2738]) ).
fof(f31809,plain,
spl0_1294,
inference(avatar_split_clause,[],[f867,f31807]) ).
fof(f31807,plain,
( spl0_1294
<=> ! [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_1294])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__cases_0) ).
fof(f31752,plain,
spl0_1293,
inference(avatar_split_clause,[],[f997,f31750]) ).
fof(f31750,plain,
( spl0_1293
<=> ! [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_1293])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_single__valued__confluent_0) ).
fof(f31747,plain,
spl0_1292,
inference(avatar_split_clause,[],[f1007,f31745]) ).
fof(f31745,plain,
( spl0_1292
<=> ! [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_1292])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__commute_0) ).
fof(f31738,plain,
~ spl0_1291,
inference(avatar_split_clause,[],[f1275,f31735]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_conjecture_0) ).
fof(f31668,plain,
spl0_1290,
inference(avatar_split_clause,[],[f1066,f31666]) ).
fof(f31666,plain,
( spl0_1290
<=> ! [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_1290])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__if_2) ).
fof(f31652,plain,
( spl0_1289
| ~ spl0_45
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2856,f2734,f1582,f31650]) ).
fof(f31650,plain,
( spl0_1289
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X0),X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f2734,plain,
( spl0_255
<=> ! [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_255])]) ).
fof(f2856,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X0),X0,tc_bool)
| ~ spl0_45
| ~ spl0_255 ),
inference(resolution,[],[f2735,f1584]) ).
fof(f2735,plain,
( ! [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) )
| ~ spl0_255 ),
inference(avatar_component_clause,[],[f2734]) ).
fof(f31648,plain,
spl0_1288,
inference(avatar_split_clause,[],[f1069,f31646]) ).
fof(f31646,plain,
( spl0_1288
<=> ! [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_1288])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__restrict__set_0) ).
fof(f31330,plain,
spl0_1287,
inference(avatar_split_clause,[],[f1068,f31328]) ).
fof(f31328,plain,
( spl0_1287
<=> ! [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_1287])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__if_3) ).
fof(f31326,plain,
spl0_1286,
inference(avatar_split_clause,[],[f1067,f31324]) ).
fof(f31324,plain,
( spl0_1286
<=> ! [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_1286])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__if_0) ).
fof(f31299,plain,
spl0_1285,
inference(avatar_split_clause,[],[f332,f31297]) ).
fof(f31297,plain,
( spl0_1285
<=> ! [X18,X10,X0,X6,X7] :
( ~ class_OrderedGroup_Oab__group__add(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X7,X0)
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool))) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),X6)),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),X7))),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f332,axiom,
! [X10,X0,X18,X6,X7] :
( ~ class_OrderedGroup_Oab__group__add(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| ~ c_Finite__Set_Ofinite(X7,X0)
| hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_fun(X0,tc_bool))) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X10),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),X6)),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),X7))),hAPP(hAPP(c_Finite__Set_Osetsum(X0,X10),X18),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_fun(X0,tc_bool)))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__Un_0) ).
fof(f31295,plain,
spl0_1284,
inference(avatar_split_clause,[],[f52,f31293]) ).
fof(f31293,plain,
( spl0_1284
<=> ! [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_1284])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__Un__Int_0) ).
fof(f31228,plain,
( spl0_1283
| ~ spl0_14
| ~ spl0_201
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2855,f2730,f2344,f1427,f31226]) ).
fof(f31226,plain,
( spl0_1283
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f1427,plain,
( spl0_14
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f2344,plain,
( spl0_201
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f2730,plain,
( spl0_254
<=> ! [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_254])]) ).
fof(f2855,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat))
| ~ spl0_14
| ~ spl0_201
| ~ spl0_254 ),
inference(forward_demodulation,[],[f2854,f2346]) ).
fof(f2346,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f2344]) ).
fof(f2854,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_14
| ~ spl0_254 ),
inference(resolution,[],[f2731,f1429]) ).
fof(f1429,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f1427]) ).
fof(f2731,plain,
( ! [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)) )
| ~ spl0_254 ),
inference(avatar_component_clause,[],[f2730]) ).
fof(f31150,plain,
spl0_1282,
inference(avatar_split_clause,[],[f1207,f31148]) ).
fof(f31148,plain,
( spl0_1282
<=> ! [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_1282])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__if_1) ).
fof(f31146,plain,
spl0_1281,
inference(avatar_split_clause,[],[f1204,f31144]) ).
fof(f31144,plain,
( spl0_1281
<=> ! [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_1281])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__delta_0) ).
fof(f31142,plain,
spl0_1280,
inference(avatar_split_clause,[],[f1065,f31140]) ).
fof(f31140,plain,
( spl0_1280
<=> ! [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_1280])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__gen__delta_1) ).
fof(f30771,plain,
( spl0_1279
| ~ spl0_298
| ~ spl0_315
| ~ spl0_956
| ~ spl0_969
| ~ spl0_1277 ),
inference(avatar_split_clause,[],[f30763,f30759,f17424,f17308,f3262,f3194,f30769]) ).
fof(f30769,plain,
( spl0_1279
<=> ! [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_1279])]) ).
fof(f3194,plain,
( spl0_298
<=> ! [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_298])]) ).
fof(f3262,plain,
( spl0_315
<=> ! [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_315])]) ).
fof(f17308,plain,
( spl0_956
<=> ! [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_956])]) ).
fof(f17424,plain,
( spl0_969
<=> ! [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_969])]) ).
fof(f30759,plain,
( spl0_1277
<=> ! [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_1277])]) ).
fof(f30763,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_298
| ~ spl0_315
| ~ spl0_956
| ~ spl0_969
| ~ spl0_1277 ),
inference(forward_demodulation,[],[f30762,f18049]) ).
fof(f18049,plain,
( ! [X3,X6,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X6,X3,tc_fun(X5,tc_bool)),X4,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X6,X4,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ spl0_298
| ~ spl0_956 ),
inference(superposition,[],[f17309,f3195]) ).
fof(f3195,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_298 ),
inference(avatar_component_clause,[],[f3194]) ).
fof(f17309,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_956 ),
inference(avatar_component_clause,[],[f17308]) ).
fof(f30762,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_315
| ~ spl0_969
| ~ spl0_1277 ),
inference(forward_demodulation,[],[f30760,f18701]) ).
fof(f18701,plain,
( ! [X3,X6,X4,X5] : c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X6,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X3,tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X3,X6,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ spl0_315
| ~ spl0_969 ),
inference(superposition,[],[f17425,f3263]) ).
fof(f3263,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_315 ),
inference(avatar_component_clause,[],[f3262]) ).
fof(f17425,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_969 ),
inference(avatar_component_clause,[],[f17424]) ).
fof(f30760,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_1277 ),
inference(avatar_component_clause,[],[f30759]) ).
fof(f30767,plain,
( spl0_1278
| ~ spl0_14
| ~ spl0_201
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2853,f2726,f2344,f1427,f30765]) ).
fof(f30765,plain,
( spl0_1278
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f2726,plain,
( spl0_253
<=> ! [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_253])]) ).
fof(f2853,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0)
| ~ spl0_14
| ~ spl0_201
| ~ spl0_253 ),
inference(forward_demodulation,[],[f2852,f2346]) ).
fof(f2852,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X0)
| ~ spl0_14
| ~ spl0_253 ),
inference(resolution,[],[f2727,f1429]) ).
fof(f2727,plain,
( ! [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) )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f2726]) ).
fof(f30761,plain,
spl0_1277,
inference(avatar_split_clause,[],[f1352,f30759]) ).
fof(f1352,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__Int__crazy_0) ).
fof(f30757,plain,
spl0_1276,
inference(avatar_split_clause,[],[f1206,f30755]) ).
fof(f30755,plain,
( spl0_1276
<=> ! [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_1276])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__delta_1) ).
fof(f30753,plain,
spl0_1275,
inference(avatar_split_clause,[],[f629,f30751]) ).
fof(f30751,plain,
( spl0_1275
<=> ! [X3,X4,X0,X23,X26] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X23
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X26),X23)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X26),X4))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f629,axiom,
! [X3,X0,X26,X4,X23] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X23
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X26),X23)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X26),X4))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X23)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_diff__frac__eq_0) ).
fof(f30749,plain,
spl0_1274,
inference(avatar_split_clause,[],[f163,f30747]) ).
fof(f30747,plain,
( spl0_1274
<=> ! [X3,X4,X0,X23,X26] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X23
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X26),X23)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X26),X4))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f163,axiom,
! [X3,X0,X26,X4,X23] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X23
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X26),X23)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X26),X4))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X23)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__frac__eq_0) ).
fof(f30682,plain,
spl0_1273,
inference(avatar_split_clause,[],[f1205,f30680]) ).
fof(f30680,plain,
( spl0_1273
<=> ! [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_1273])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__delta_0) ).
fof(f30540,plain,
( spl0_1272
| ~ spl0_64
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2290,f2246,f1666,f30538]) ).
fof(f30538,plain,
( spl0_1272
<=> ! [X0,X3,X2,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Oinv__image(X0,X2,X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f1666,plain,
( spl0_64
<=> ! [X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Oacyclic(X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f2246,plain,
( spl0_185
<=> ! [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_185])]) ).
fof(f2290,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Relation_Oinv__image(X0,X2,X1,X3),X3) )
| ~ spl0_64
| ~ spl0_185 ),
inference(resolution,[],[f2247,f1667]) ).
fof(f1667,plain,
( ! [X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Oacyclic(X8,X0) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1666]) ).
fof(f2247,plain,
( ! [X10,X0,X18,X8] :
( c_Wellfounded_Owf(c_Relation_Oinv__image(X8,X18,X0,X10),X10)
| ~ c_Wellfounded_Owf(X8,X0) )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f2246]) ).
fof(f30495,plain,
spl0_1271,
inference(avatar_split_clause,[],[f1203,f30493]) ).
fof(f30493,plain,
( spl0_1271
<=> ! [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_1271])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__delta_1) ).
fof(f30491,plain,
spl0_1270,
inference(avatar_split_clause,[],[f120,f30489]) ).
fof(f30489,plain,
( spl0_1270
<=> ! [X2,X11,X0,X12,X5,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X11)),X5)),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f120,axiom,
! [X2,X0,X11,X1,X5,X12] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X11)),X5)),X12))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__add__iff1_0) ).
fof(f30487,plain,
spl0_1269,
inference(avatar_split_clause,[],[f119,f30485]) ).
fof(f30485,plain,
( spl0_1269
<=> ! [X2,X11,X0,X12,X5,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X11)),X5)),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f119,axiom,
! [X2,X0,X11,X1,X5,X12] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X11)),X5)),X12))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__add__iff1_1) ).
fof(f30483,plain,
spl0_1268,
inference(avatar_split_clause,[],[f118,f30481]) ).
fof(f30481,plain,
( spl0_1268
<=> ! [X5,X11,X0,X12,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X1),X2)),X11)),X12)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f118,axiom,
! [X2,X0,X11,X1,X5,X12] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X1),X2)),X11)),X12)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__add__iff2_0) ).
fof(f30479,plain,
spl0_1267,
inference(avatar_split_clause,[],[f117,f30477]) ).
fof(f30477,plain,
( spl0_1267
<=> ! [X5,X11,X0,X12,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X1),X2)),X11)),X12)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f117,axiom,
! [X2,X0,X11,X1,X5,X12] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X1),X2)),X11)),X12)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__add__iff2_1) ).
fof(f30356,plain,
spl0_1266,
inference(avatar_split_clause,[],[f1075,f30354]) ).
fof(f30354,plain,
( spl0_1266
<=> ! [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_1266])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__delta_H_0) ).
fof(f30352,plain,
( spl0_1265
| ~ spl0_102
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f2152,f2049,f1819,f30350]) ).
fof(f30350,plain,
( spl0_1265
<=> ! [X6,X7] :
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X6,X7),X7)
| ~ c_Wellfounded_Oacyclic(c_Transitive__Closure_Ortrancl(X6,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f1819,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(f2049,plain,
( spl0_157
<=> ! [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_157])]) ).
fof(f2152,plain,
( ! [X6,X7] :
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X6,X7),X7)
| ~ c_Wellfounded_Oacyclic(c_Transitive__Closure_Ortrancl(X6,X7),X7) )
| ~ spl0_102
| ~ spl0_157 ),
inference(superposition,[],[f1820,f2050]) ).
fof(f2050,plain,
( ! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X8,X0),X0)
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f2049]) ).
fof(f1820,plain,
( ! [X0,X8] :
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X8,X0),X0)
| ~ c_Wellfounded_Oacyclic(X8,X0) )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1819]) ).
fof(f30348,plain,
spl0_1264,
inference(avatar_split_clause,[],[f742,f30346]) ).
fof(f30346,plain,
( spl0_1264
<=> ! [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_1264])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_subset__equiv__class_0) ).
fof(f30344,plain,
spl0_1263,
inference(avatar_split_clause,[],[f121,f30342]) ).
fof(f30342,plain,
( spl0_1263
<=> ! [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_1263])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__Un__disjoint_0) ).
fof(f30287,plain,
spl0_1262,
inference(avatar_split_clause,[],[f1076,f30285]) ).
fof(f30285,plain,
( spl0_1262
<=> ! [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_1262])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__delta_H_1) ).
fof(f30283,plain,
spl0_1261,
inference(avatar_split_clause,[],[f741,f30281]) ).
fof(f30281,plain,
( spl0_1261
<=> ! [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_1261])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_equiv__class__nondisjoint_0) ).
fof(f30080,plain,
( spl0_1260
| ~ spl0_102
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2146,f2045,f1819,f30078]) ).
fof(f30078,plain,
( spl0_1260
<=> ! [X6,X7] :
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X6,X7),X7)
| ~ c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X6,X7),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f2045,plain,
( spl0_156
<=> ! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X15,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f2146,plain,
( ! [X6,X7] :
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X6,X7),X7)
| ~ c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X6,X7),X7) )
| ~ spl0_102
| ~ spl0_156 ),
inference(superposition,[],[f1820,f2046]) ).
fof(f2046,plain,
( ! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X15,X0),X0)
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f2045]) ).
fof(f30033,plain,
spl0_1259,
inference(avatar_split_clause,[],[f1077,f30031]) ).
fof(f30031,plain,
( spl0_1259
<=> ! [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_1259])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__delta_H_0) ).
fof(f30029,plain,
spl0_1258,
inference(avatar_split_clause,[],[f618,f30027]) ).
fof(f30027,plain,
( spl0_1258
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f618,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__eq_8) ).
fof(f30025,plain,
spl0_1257,
inference(avatar_split_clause,[],[f617,f30023]) ).
fof(f30023,plain,
( spl0_1257
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Otimes__class_Otimes(X0),X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f617,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Otimes__class_Otimes(X0),X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__eq_9) ).
fof(f30021,plain,
spl0_1256,
inference(avatar_split_clause,[],[f616,f30019]) ).
fof(f30019,plain,
( spl0_1256
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f616,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__divide__eq_8) ).
fof(f30017,plain,
spl0_1255,
inference(avatar_split_clause,[],[f615,f30015]) ).
fof(f30015,plain,
( spl0_1255
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f615,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__divide__eq_9) ).
fof(f29847,plain,
( spl0_1254
| ~ spl0_105
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2145,f2045,f1831,f29845]) ).
fof(f29845,plain,
( spl0_1254
<=> ! [X4,X5] :
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X4,X5),X5)
| ~ c_Relation_Osym(c_Transitive__Closure_Otrancl(X4,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f1831,plain,
( spl0_105
<=> ! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Transitive__Closure_Ortrancl(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f2145,plain,
( ! [X4,X5] :
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X4,X5),X5)
| ~ c_Relation_Osym(c_Transitive__Closure_Otrancl(X4,X5),X5) )
| ~ spl0_105
| ~ spl0_156 ),
inference(superposition,[],[f1832,f2046]) ).
fof(f1832,plain,
( ! [X0,X8] :
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(X8,X0),X0)
| ~ c_Relation_Osym(X8,X0) )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1831]) ).
fof(f29747,plain,
spl0_1253,
inference(avatar_split_clause,[],[f1224,f29745]) ).
fof(f29745,plain,
( spl0_1253
<=> ! [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_1253])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_total__on__def_0) ).
fof(f29743,plain,
spl0_1252,
inference(avatar_split_clause,[],[f1074,f29741]) ).
fof(f29741,plain,
( spl0_1252
<=> ! [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_1252])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__delta_H_1) ).
fof(f29739,plain,
spl0_1251,
inference(avatar_split_clause,[],[f1014,f29737]) ).
fof(f29737,plain,
( spl0_1251
<=> ! [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_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))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_tranclE_0) ).
fof(f29735,plain,
spl0_1250,
inference(avatar_split_clause,[],[f1009,f29733]) ).
fof(f29733,plain,
( spl0_1250
<=> ! [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_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))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__tranclE_1) ).
fof(f29731,plain,
spl0_1249,
inference(avatar_split_clause,[],[f863,f29729]) ).
fof(f29729,plain,
( spl0_1249
<=> ! [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_1249])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_eq__equiv__class_0) ).
fof(f29727,plain,
spl0_1248,
inference(avatar_split_clause,[],[f353,f29725]) ).
fof(f29725,plain,
( spl0_1248
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ 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),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X2)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f353,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ 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),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X2)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X1))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__strict__left__mono_0) ).
fof(f29723,plain,
( spl0_1231
| ~ spl0_22
| ~ spl0_127
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2113,f1985,f1929,f1467,f28803]) ).
fof(f28803,plain,
( spl0_1231
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f1467,plain,
( spl0_22
<=> class_Lattices_Olower__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1929,plain,
( spl0_127
<=> ! [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_127])]) ).
fof(f1985,plain,
( spl0_141
<=> ! [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_141])]) ).
fof(f2113,plain,
( ! [X0] :
( ~ class_Lattices_Olower__semilattice(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
| ~ spl0_127
| ~ spl0_141 ),
inference(resolution,[],[f1986,f1930]) ).
fof(f1930,plain,
( ! [X14] :
( ~ c_lessequals(X14,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X14 )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1929]) ).
fof(f1986,plain,
( ! [X3,X0,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X3,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1985]) ).
fof(f29722,plain,
spl0_1247,
inference(avatar_split_clause,[],[f352,f29720]) ).
fof(f29720,plain,
( spl0_1247
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ 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)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X2)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f352,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ 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)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X2)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X1))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__strict__left__mono__neg_0) ).
fof(f29718,plain,
spl0_1246,
inference(avatar_split_clause,[],[f314,f29716]) ).
fof(f29716,plain,
( spl0_1246
<=> ! [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_1246])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__Un__Int_0) ).
fof(f29568,plain,
spl0_1245,
inference(avatar_split_clause,[],[f1011,f29566]) ).
fof(f29566,plain,
( spl0_1245
<=> ! [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_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))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_trancl_Ocases_0) ).
fof(f29564,plain,
spl0_1244,
inference(avatar_split_clause,[],[f187,f29562]) ).
fof(f29562,plain,
( spl0_1244
<=> ! [X4,X0,X23,X3,X26] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X26),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X26))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X23)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X4),X26))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f187,axiom,
! [X3,X0,X26,X4,X23] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X26),X23))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X26))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X23)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X4),X26))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_frac__less2_0) ).
fof(f29560,plain,
spl0_1243,
inference(avatar_split_clause,[],[f54,f29558]) ).
fof(f29558,plain,
( spl0_1243
<=> ! [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_1243])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__strict__mono_0) ).
fof(f29472,plain,
( spl0_1240
| ~ spl0_22
| ~ spl0_127
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f2109,f1981,f1929,f1467,f29006]) ).
fof(f29006,plain,
( spl0_1240
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f1981,plain,
( spl0_140
<=> ! [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_140])]) ).
fof(f2109,plain,
( ! [X0] :
( ~ class_Lattices_Olower__semilattice(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_127
| ~ spl0_140 ),
inference(resolution,[],[f1982,f1930]) ).
fof(f1982,plain,
( ! [X3,X0,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X4,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1981]) ).
fof(f29017,plain,
spl0_1242,
inference(avatar_split_clause,[],[f1197,f29015]) ).
fof(f29015,plain,
( spl0_1242
<=> ! [X0,X8,X5,X2,X1] :
( ~ 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))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_trancl__trans_0) ).
fof(f29013,plain,
spl0_1241,
inference(avatar_split_clause,[],[f1179,f29011]) ).
fof(f29011,plain,
( spl0_1241
<=> ! [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_1241])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__trans_0) ).
fof(f29008,plain,
( spl0_1240
| ~ spl0_36
| ~ spl0_127
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f2105,f1977,f1929,f1537,f29006]) ).
fof(f1537,plain,
( spl0_36
<=> class_Lattices_Olattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1977,plain,
( spl0_139
<=> ! [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_139])]) ).
fof(f2105,plain,
( ! [X0] :
( ~ class_Lattices_Olattice(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_127
| ~ spl0_139 ),
inference(resolution,[],[f1978,f1930]) ).
fof(f1978,plain,
( ! [X3,X0,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X4,X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1977]) ).
fof(f29004,plain,
spl0_1239,
inference(avatar_split_clause,[],[f1093,f29002]) ).
fof(f29002,plain,
( spl0_1239
<=> ! [X3,X4,X0,X23,X8] :
( ~ 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))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__trancl__trancl_0) ).
fof(f29000,plain,
spl0_1238,
inference(avatar_split_clause,[],[f1092,f28998]) ).
fof(f28998,plain,
( spl0_1238
<=> ! [X0,X8,X5,X2,X1] :
( ~ 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))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_trancl__rtrancl__trancl_0) ).
fof(f28996,plain,
spl0_1237,
inference(avatar_split_clause,[],[f1016,f28994]) ).
fof(f28994,plain,
( spl0_1237
<=> ! [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_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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__tranclE_0) ).
fof(f28992,plain,
spl0_1236,
inference(avatar_split_clause,[],[f1013,f28990]) ).
fof(f28990,plain,
( spl0_1236
<=> ! [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_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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_tranclE_1) ).
fof(f28988,plain,
spl0_1235,
inference(avatar_split_clause,[],[f23,f28986]) ).
fof(f28986,plain,
( spl0_1235
<=> ! [X5,X11,X0,X12,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X1),X2)),X11)),X12),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f23,axiom,
! [X2,X0,X11,X1,X5,X12] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X1),X2)),X11)),X12),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__add__iff2_1) ).
fof(f28984,plain,
spl0_1234,
inference(avatar_split_clause,[],[f22,f28982]) ).
fof(f28982,plain,
( spl0_1234
<=> ! [X5,X11,X0,X12,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X1),X2)),X11)),X12),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f22,axiom,
! [X2,X0,X11,X1,X5,X12] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(X5,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X1),X2)),X11)),X12),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__add__iff2_0) ).
fof(f28980,plain,
spl0_1233,
inference(avatar_split_clause,[],[f21,f28978]) ).
fof(f28978,plain,
( spl0_1233
<=> ! [X2,X11,X0,X12,X5,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X11)),X5),X12,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f21,axiom,
! [X2,X0,X11,X1,X5,X12] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X11)),X5),X12,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__add__iff1_1) ).
fof(f28976,plain,
spl0_1232,
inference(avatar_split_clause,[],[f20,f28974]) ).
fof(f28974,plain,
( spl0_1232
<=> ! [X2,X11,X0,X12,X5,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X11)),X5),X12,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f20,axiom,
! [X2,X0,X11,X1,X5,X12] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X11)),X5),X12,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__add__iff1_0) ).
fof(f28805,plain,
( spl0_1231
| ~ spl0_36
| ~ spl0_127
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f2097,f1973,f1929,f1537,f28803]) ).
fof(f1973,plain,
( spl0_138
<=> ! [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_138])]) ).
fof(f2097,plain,
( ! [X0] :
( ~ class_Lattices_Olattice(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
| ~ spl0_127
| ~ spl0_138 ),
inference(resolution,[],[f1974,f1930]) ).
fof(f1974,plain,
( ! [X3,X0,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X3,X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1973]) ).
fof(f28347,plain,
( spl0_1230
| ~ spl0_71
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1871,f1795,f1694,f28345]) ).
fof(f28345,plain,
( spl0_1230
<=> ! [X2,X3,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,tc_fun(X3,X4)) = X2
| ~ class_Lattices_Olattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f1694,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(f1795,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(f1871,plain,
( ! [X2,X3,X4] :
( c_Lattices_Olower__semilattice__class_Oinf(X2,X2,tc_fun(X3,X4)) = X2
| ~ class_Lattices_Olattice(X4) )
| ~ spl0_71
| ~ spl0_96 ),
inference(resolution,[],[f1796,f1695]) ).
fof(f1695,plain,
( ! [X68,X69] :
( class_Lattices_Olower__semilattice(tc_fun(X68,X69))
| ~ class_Lattices_Olattice(X69) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f1694]) ).
fof(f1796,plain,
( ! [X3,X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X3,X0) = X3 )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1795]) ).
fof(f28260,plain,
spl0_1229,
inference(avatar_split_clause,[],[f1195,f28258]) ).
fof(f28258,plain,
( spl0_1229
<=> ! [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_1229])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rel__compI_0) ).
fof(f28256,plain,
spl0_1228,
inference(avatar_split_clause,[],[f1017,f28254]) ).
fof(f28254,plain,
( spl0_1228
<=> ! [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_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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_trancl_Ocases_1) ).
fof(f28252,plain,
spl0_1227,
inference(avatar_split_clause,[],[f924,f28250]) ).
fof(f28250,plain,
( spl0_1227
<=> ! [X56,X58,X10,X59,X0,X18,X54,X57,X55,X25] :
( ~ c_Equiv__Relations_Ocongruent2(X59,X58,X18,X0,X10,X25)
| hAPP(hAPP(X18,X54),X55) = hAPP(hAPP(X18,X56),X57)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X54,X56,X0,X0)),X59))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X10)),c_Pair(X55,X57,X10,X10)),X58)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f924,axiom,
! [X58,X10,X59,X0,X18,X54,X56,X55,X57,X25] :
( ~ c_Equiv__Relations_Ocongruent2(X59,X58,X18,X0,X10,X25)
| hAPP(hAPP(X18,X54),X55) = hAPP(hAPP(X18,X56),X57)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X54,X56,X0,X0)),X59))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X10,X10)),c_Pair(X55,X57,X10,X10)),X58)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_congruent2_Ocongruent2_0) ).
fof(f28248,plain,
spl0_1226,
inference(avatar_split_clause,[],[f739,f28246]) ).
fof(f28246,plain,
( spl0_1226
<=> ! [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_1226])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__induct_1) ).
fof(f28244,plain,
spl0_1225,
inference(avatar_split_clause,[],[f738,f28242]) ).
fof(f28242,plain,
( spl0_1225
<=> ! [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_1225])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__rtrancl__induct_0) ).
fof(f28240,plain,
spl0_1224,
inference(avatar_split_clause,[],[f317,f28238]) ).
fof(f28238,plain,
( spl0_1224
<=> ! [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_1224])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__Un__disjoint_0) ).
fof(f28236,plain,
spl0_1223,
inference(avatar_split_clause,[],[f110,f28234]) ).
fof(f28234,plain,
( spl0_1223
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f110,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__divide__eq_7) ).
fof(f28232,plain,
spl0_1222,
inference(avatar_split_clause,[],[f109,f28230]) ).
fof(f28230,plain,
( spl0_1222
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f109,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__divide__eq_5) ).
fof(f28228,plain,
( spl0_1221
| ~ spl0_70
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1868,f1791,f1690,f28226]) ).
fof(f28226,plain,
( spl0_1221
<=> ! [X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X2,X2,tc_fun(X3,X4)) = X2
| ~ class_Lattices_Olattice(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f1690,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(f1791,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(f1868,plain,
( ! [X2,X3,X4] :
( c_Lattices_Oupper__semilattice__class_Osup(X2,X2,tc_fun(X3,X4)) = X2
| ~ class_Lattices_Olattice(X4) )
| ~ spl0_70
| ~ spl0_95 ),
inference(resolution,[],[f1792,f1691]) ).
fof(f1691,plain,
( ! [X68,X69] :
( class_Lattices_Oupper__semilattice(tc_fun(X68,X69))
| ~ class_Lattices_Olattice(X69) )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f1690]) ).
fof(f1792,plain,
( ! [X3,X0] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X3,X0) = X3 )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1791]) ).
fof(f28224,plain,
spl0_1220,
inference(avatar_split_clause,[],[f108,f28222]) ).
fof(f28222,plain,
( spl0_1220
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f108,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__divide__eq_4) ).
fof(f28220,plain,
spl0_1219,
inference(avatar_split_clause,[],[f107,f28218]) ).
fof(f28218,plain,
( spl0_1219
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f107,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__divide__eq_1) ).
fof(f28216,plain,
spl0_1218,
inference(avatar_split_clause,[],[f106,f28214]) ).
fof(f28214,plain,
( spl0_1218
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f106,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__eq_7) ).
fof(f28212,plain,
spl0_1217,
inference(avatar_split_clause,[],[f105,f28210]) ).
fof(f28210,plain,
( spl0_1217
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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)),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f105,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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)),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__eq_5) ).
fof(f28208,plain,
spl0_1216,
inference(avatar_split_clause,[],[f104,f28206]) ).
fof(f28206,plain,
( spl0_1216
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f104,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__eq_4) ).
fof(f28204,plain,
spl0_1215,
inference(avatar_split_clause,[],[f103,f28202]) ).
fof(f28202,plain,
( spl0_1215
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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_Oinverse__class_Odivide(X0),X1),X5)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f103,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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_Oinverse__class_Odivide(X0),X1),X5)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__eq_1) ).
fof(f27656,plain,
spl0_1214,
inference(avatar_split_clause,[],[f1177,f27654]) ).
fof(f27654,plain,
( spl0_1214
<=> ! [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_1214])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__rtrancl__into__rtrancl_0) ).
fof(f27652,plain,
( ~ spl0_1212
| spl0_1213
| ~ spl0_306
| ~ spl0_893 ),
inference(avatar_split_clause,[],[f15384,f15341,f3226,f27650,f27646]) ).
fof(f27646,plain,
( spl0_1212
<=> class_Ring__and__Field_Ocomm__ring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f27650,plain,
( spl0_1213
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Ouminus__class_Ouminus(tc_nat),X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f3226,plain,
( spl0_306
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f15341,plain,
( spl0_893
<=> ! [X29] : c_Ring__and__Field_Odvd__class_Odvd(X29,X29,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f15384,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Ouminus__class_Ouminus(tc_nat),X0),X0,tc_nat)
| ~ class_Ring__and__Field_Ocomm__ring__1(tc_nat) )
| ~ spl0_306
| ~ spl0_893 ),
inference(resolution,[],[f15342,f3227]) ).
fof(f3227,plain,
( ! [X3,X0,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4),X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
| ~ spl0_306 ),
inference(avatar_component_clause,[],[f3226]) ).
fof(f15342,plain,
( ! [X29] : c_Ring__and__Field_Odvd__class_Odvd(X29,X29,tc_nat)
| ~ spl0_893 ),
inference(avatar_component_clause,[],[f15341]) ).
fof(f27644,plain,
spl0_1211,
inference(avatar_split_clause,[],[f1176,f27642]) ).
fof(f27642,plain,
( spl0_1211
<=> ! [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_1211])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
fof(f27640,plain,
spl0_1210,
inference(avatar_split_clause,[],[f1175,f27638]) ).
fof(f27638,plain,
( spl0_1210
<=> ! [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_Otrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_trancl__into__trancl2_0) ).
fof(f27636,plain,
spl0_1209,
inference(avatar_split_clause,[],[f1174,f27634]) ).
fof(f27634,plain,
( spl0_1209
<=> ! [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_Otrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
fof(f27632,plain,
spl0_1208,
inference(avatar_split_clause,[],[f1085,f27630]) ).
fof(f27630,plain,
( spl0_1208
<=> ! [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_Otrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__into__trancl1_0) ).
fof(f27628,plain,
spl0_1207,
inference(avatar_split_clause,[],[f1084,f27626]) ).
fof(f27626,plain,
( spl0_1207
<=> ! [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_Otrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f1084,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_Otrancl(X8,X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__into__trancl2_0) ).
fof(f27624,plain,
spl0_1206,
inference(avatar_split_clause,[],[f729,f27622]) ).
fof(f27622,plain,
( spl0_1206
<=> ! [X4,X0,X23,X3,X26] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X26,X23,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X26))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X23)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X4),X26))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f729,axiom,
! [X3,X0,X26,X4,X23] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X26,X23,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X26))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X23)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X4),X26))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_frac__less_0) ).
fof(f27620,plain,
spl0_1205,
inference(avatar_split_clause,[],[f685,f27618]) ).
fof(f27618,plain,
( spl0_1205
<=> ! [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_1205])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__strict__mono_H_0) ).
fof(f27616,plain,
spl0_1204,
inference(avatar_split_clause,[],[f396,f27614]) ).
fof(f27614,plain,
( spl0_1204
<=> ! [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_1204])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_equiv__class__subset_0) ).
fof(f27612,plain,
spl0_1203,
inference(avatar_split_clause,[],[f368,f27610]) ).
fof(f27610,plain,
( spl0_1203
<=> ! [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_1203])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__le__less__imp__less_0) ).
fof(f27608,plain,
spl0_1202,
inference(avatar_split_clause,[],[f367,f27606]) ).
fof(f27606,plain,
( spl0_1202
<=> ! [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_1202])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__le__imp__less_0) ).
fof(f27561,plain,
spl0_1201,
inference(avatar_split_clause,[],[f147,f27559]) ).
fof(f27559,plain,
( spl0_1201
<=> ! [X5,X0,X12,X2,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| X5 = X12
| 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),X12)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f147,axiom,
! [X2,X0,X1,X5,X12] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| X5 = X12
| 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),X12)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X5)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__ringb_Onoteq__reduce_0) ).
fof(f27557,plain,
spl0_1200,
inference(avatar_split_clause,[],[f44,f27555]) ).
fof(f27555,plain,
( spl0_1200
<=> ! [X2,X11,X0,X12,X5,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X11)),X5) = X12
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f44,axiom,
! [X2,X0,X11,X1,X5,X12] :
( ~ class_Ring__and__Field_Oring(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X11)),X5) = X12
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),X12) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_eq__add__iff1_0) ).
fof(f27463,plain,
spl0_1199,
inference(avatar_split_clause,[],[f995,f27461]) ).
fof(f27461,plain,
( spl0_1199
<=> ! [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_1199])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__induct_0) ).
fof(f27459,plain,
spl0_1198,
inference(avatar_split_clause,[],[f994,f27457]) ).
fof(f27457,plain,
( spl0_1198
<=> ! [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_1198])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__rtrancl__induct_1) ).
fof(f27388,plain,
spl0_1197,
inference(avatar_split_clause,[],[f1196,f27386]) ).
fof(f27386,plain,
( spl0_1197
<=> ! [X15,X0,X5,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X15))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),X15))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Otrancl(X15,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f1196,axiom,
! [X2,X0,X1,X15,X5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X1,X0,X0)),X15))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X1,X5,X0,X0)),X15))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X5,X0,X0)),c_Transitive__Closure_Otrancl(X15,X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_r__r__into__trancl_0) ).
fof(f27345,plain,
spl0_1196,
inference(avatar_split_clause,[],[f986,f27343]) ).
fof(f27343,plain,
( spl0_1196
<=> ! [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_1196])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__addf_0) ).
fof(f27341,plain,
spl0_1195,
inference(avatar_split_clause,[],[f985,f27339]) ).
fof(f27339,plain,
( spl0_1195
<=> ! [X18,X10,X20,X0,X6] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(X0),X18,X0,tc_fun(X0,X0),X10),X20,X10,X0,X0)),X6) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_1195])]) ).
fof(f985,axiom,
! [X10,X0,X18,X6,X20] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(X0),X18,X0,tc_fun(X0,X0),X10),X20,X10,X0,X0)),X6) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__subtractf_0) ).
fof(f26994,plain,
spl0_1194,
inference(avatar_split_clause,[],[f1048,f26992]) ).
fof(f26992,plain,
( spl0_1194
<=> ! [X18,X10,X20,X0,X6] :
( ~ class_Ring__and__Field_Ofield(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Osetprod(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(X10),X18,X10,tc_fun(X10,X10),X0),X20,X0,X10,X10),X6,X0,X10) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X10),c_Finite__Set_Osetprod(X18,X6,X0,X10)),c_Finite__Set_Osetprod(X20,X6,X0,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f1048,axiom,
! [X10,X0,X18,X6,X20] :
( ~ class_Ring__and__Field_Ofield(X10)
| ~ class_Ring__and__Field_Odivision__by__zero(X10)
| ~ c_Finite__Set_Ofinite(X6,X0)
| c_Finite__Set_Osetprod(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(X10),X18,X10,tc_fun(X10,X10),X0),X20,X0,X10,X10),X6,X0,X10) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X10),c_Finite__Set_Osetprod(X18,X6,X0,X10)),c_Finite__Set_Osetprod(X20,X6,X0,X10)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__dividef_0) ).
fof(f26990,plain,
spl0_1193,
inference(avatar_split_clause,[],[f946,f26988]) ).
fof(f26988,plain,
( spl0_1193
<=> ! [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_1193])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_equiv__class__eq_0) ).
fof(f26986,plain,
spl0_1192,
inference(avatar_split_clause,[],[f748,f26984]) ).
fof(f26984,plain,
( spl0_1192
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f748,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__divide__eq_3) ).
fof(f26982,plain,
spl0_1191,
inference(avatar_split_clause,[],[f747,f26980]) ).
fof(f26980,plain,
( spl0_1191
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(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),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f747,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(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),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__divide__eq_2) ).
fof(f26978,plain,
spl0_1190,
inference(avatar_split_clause,[],[f746,f26976]) ).
fof(f26976,plain,
( spl0_1190
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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_Oinverse__class_Odivide(X0),X1),X5)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f746,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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_Oinverse__class_Odivide(X0),X1),X5)),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__eq_3) ).
fof(f26974,plain,
spl0_1189,
inference(avatar_split_clause,[],[f745,f26972]) ).
fof(f26972,plain,
( spl0_1189
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),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),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f745,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),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),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__eq_2) ).
fof(f26970,plain,
spl0_1188,
inference(avatar_split_clause,[],[f397,f26968]) ).
fof(f26968,plain,
( spl0_1188
<=> ! [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_1188])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_combine__common__factor_0) ).
fof(f26966,plain,
spl0_1187,
inference(avatar_split_clause,[],[f62,f26964]) ).
fof(f26964,plain,
( spl0_1187
<=> ! [X2,X11,X0,X5,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X11)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f62,axiom,
! [X2,X0,X11,X1,X5] :
( ~ class_Ring__and__Field_Oring(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X11)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X11)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X11)),X5)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_eq__add__iff1_1) ).
fof(f26962,plain,
spl0_1186,
inference(avatar_split_clause,[],[f60,f26960]) ).
fof(f26960,plain,
( spl0_1186
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ 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)))
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f60,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ 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)))
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__left__mono__neg_0) ).
fof(f26810,plain,
spl0_1185,
inference(avatar_split_clause,[],[f145,f26808]) ).
fof(f26808,plain,
( spl0_1185
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0)
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f145,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0)
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__divide__eq_8) ).
fof(f26806,plain,
spl0_1184,
inference(avatar_split_clause,[],[f144,f26804]) ).
fof(f26804,plain,
( spl0_1184
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f144,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__eq_8) ).
fof(f26461,plain,
spl0_1183,
inference(avatar_split_clause,[],[f1039,f26459]) ).
fof(f26459,plain,
( spl0_1183
<=> ! [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_1183])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__strict__decreasing_0) ).
fof(f26457,plain,
spl0_1182,
inference(avatar_split_clause,[],[f1020,f26455]) ).
fof(f26455,plain,
( spl0_1182
<=> ! [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_1182])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rel__compEpair_0) ).
fof(f26453,plain,
spl0_1181,
inference(avatar_split_clause,[],[f1019,f26451]) ).
fof(f26451,plain,
( spl0_1181
<=> ! [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_1181])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rel__compEpair_1) ).
fof(f26449,plain,
spl0_1180,
inference(avatar_split_clause,[],[f540,f26447]) ).
fof(f26447,plain,
( spl0_1180
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0)
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f540,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0)
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__divide__eq_4) ).
fof(f26445,plain,
spl0_1179,
inference(avatar_split_clause,[],[f539,f26443]) ).
fof(f26443,plain,
( spl0_1179
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f539,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__divide__eq_1) ).
fof(f26441,plain,
spl0_1178,
inference(avatar_split_clause,[],[f538,f26439]) ).
fof(f26439,plain,
( spl0_1178
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(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),X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f538,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(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),X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__eq_4) ).
fof(f26437,plain,
spl0_1177,
inference(avatar_split_clause,[],[f537,f26435]) ).
fof(f26435,plain,
( spl0_1177
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f537,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__eq_1) ).
fof(f26433,plain,
spl0_1176,
inference(avatar_split_clause,[],[f61,f26431]) ).
fof(f26431,plain,
( spl0_1176
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ 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)))
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f61,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ 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)))
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X5),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__left__mono_0) ).
fof(f26133,plain,
spl0_1175,
inference(avatar_split_clause,[],[f1057,f26131]) ).
fof(f26131,plain,
( spl0_1175
<=> ! [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_1175])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc_Oinduct_0) ).
fof(f26129,plain,
( spl0_1174
| ~ spl0_666
| ~ spl0_786 ),
inference(avatar_split_clause,[],[f17343,f12821,f9251,f26127]) ).
fof(f26127,plain,
( spl0_1174
<=> ! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_bool),tc_bool) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f9251,plain,
( spl0_666
<=> ! [X2,X3] : c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool),tc_bool) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f12821,plain,
( spl0_786
<=> ! [X2,X3] : c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f17343,plain,
( ! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_bool),tc_bool) = X1
| ~ spl0_666
| ~ spl0_786 ),
inference(superposition,[],[f9252,f12822]) ).
fof(f12822,plain,
( ! [X2,X3] : c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_bool)
| ~ spl0_786 ),
inference(avatar_component_clause,[],[f12821]) ).
fof(f9252,plain,
( ! [X2,X3] : c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool),tc_bool) = X2
| ~ spl0_666 ),
inference(avatar_component_clause,[],[f9251]) ).
fof(f26125,plain,
spl0_1173,
inference(avatar_split_clause,[],[f1055,f26123]) ).
fof(f26123,plain,
( spl0_1173
<=> ! [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_1173])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc_Oinducts_0) ).
fof(f26121,plain,
spl0_1172,
inference(avatar_split_clause,[],[f1037,f26119]) ).
fof(f26119,plain,
( spl0_1172
<=> ! [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_1172])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mlex__leq_0) ).
fof(f26117,plain,
spl0_1171,
inference(avatar_split_clause,[],[f1002,f26115]) ).
fof(f26115,plain,
( spl0_1171
<=> ! [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_1171])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtranclE_0) ).
fof(f26113,plain,
spl0_1170,
inference(avatar_split_clause,[],[f991,f26111]) ).
fof(f26111,plain,
( spl0_1170
<=> ! [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_1170])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__rtranclE_1) ).
fof(f26109,plain,
spl0_1169,
inference(avatar_split_clause,[],[f734,f26107]) ).
fof(f26107,plain,
( spl0_1169
<=> ! [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_1169])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__insert_0) ).
fof(f26105,plain,
spl0_1168,
inference(avatar_split_clause,[],[f345,f26103]) ).
fof(f26103,plain,
( spl0_1168
<=> ! [X3,X4,X0,X23,X26] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X23),X26)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f345,axiom,
! [X3,X0,X26,X4,X23] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X23),X26)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X26)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__frac__frac_0) ).
fof(f26101,plain,
spl0_1167,
inference(avatar_split_clause,[],[f331,f26099]) ).
fof(f26099,plain,
( spl0_1167
<=> ! [X3,X4,X0,X23,X26] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X26,X23,X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X26))
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X23),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X4),X26),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f331,axiom,
! [X3,X0,X26,X4,X23] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X26,X23,X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X26))
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X23),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X4),X26),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_frac__le_0) ).
fof(f26097,plain,
spl0_1166,
inference(avatar_split_clause,[],[f193,f26095]) ).
fof(f26095,plain,
( spl0_1166
<=> ! [X0,X12,X5,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f193,axiom,
! [X3,X0,X5,X12] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X5)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__ringb_Onoteq__reduce_1) ).
fof(f26005,plain,
( spl0_1165
| ~ spl0_490
| ~ spl0_785 ),
inference(avatar_split_clause,[],[f17243,f12285,f6195,f26003]) ).
fof(f26003,plain,
( spl0_1165
<=> ! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f6195,plain,
( spl0_490
<=> ! [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_490])]) ).
fof(f12285,plain,
( spl0_785
<=> ! [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_785])]) ).
fof(f17243,plain,
( ! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_nat),tc_nat) = X1
| ~ spl0_490
| ~ spl0_785 ),
inference(superposition,[],[f6196,f12286]) ).
fof(f12286,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_nat)
| ~ spl0_785 ),
inference(avatar_component_clause,[],[f12285]) ).
fof(f6196,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_490 ),
inference(avatar_component_clause,[],[f6195]) ).
fof(f25757,plain,
( spl0_1164
| ~ spl0_488
| ~ spl0_777 ),
inference(avatar_split_clause,[],[f16880,f11982,f6009,f25755]) ).
fof(f25755,plain,
( spl0_1164
<=> ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_bool),tc_bool) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f6009,plain,
( spl0_488
<=> ! [X2,X3] : c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_bool),tc_bool) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f11982,plain,
( spl0_777
<=> ! [X2,X3] : c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f16880,plain,
( ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_bool),tc_bool) = X1
| ~ spl0_488
| ~ spl0_777 ),
inference(superposition,[],[f6010,f11983]) ).
fof(f11983,plain,
( ! [X2,X3] : c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_bool)
| ~ spl0_777 ),
inference(avatar_component_clause,[],[f11982]) ).
fof(f6010,plain,
( ! [X2,X3] : c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_bool),tc_bool) = X2
| ~ spl0_488 ),
inference(avatar_component_clause,[],[f6009]) ).
fof(f25597,plain,
spl0_1163,
inference(avatar_split_clause,[],[f1264,f25595]) ).
fof(f25595,plain,
( spl0_1163
<=> ! [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_1163])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__mkbot_3) ).
fof(f25593,plain,
spl0_1162,
inference(avatar_split_clause,[],[f1263,f25591]) ).
fof(f25591,plain,
( spl0_1162
<=> ! [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_1162])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__mkbot_5) ).
fof(f25589,plain,
spl0_1161,
inference(avatar_split_clause,[],[f1237,f25587]) ).
fof(f25587,plain,
( spl0_1161
<=> ! [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_1161])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__mktop_3) ).
fof(f25585,plain,
spl0_1160,
inference(avatar_split_clause,[],[f1236,f25583]) ).
fof(f25583,plain,
( spl0_1160
<=> ! [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_1160])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__mktop_5) ).
fof(f25581,plain,
( spl0_1159
| ~ spl0_486
| ~ spl0_667 ),
inference(avatar_split_clause,[],[f16400,f9403,f5867,f25579]) ).
fof(f25579,plain,
( spl0_1159
<=> ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f5867,plain,
( spl0_486
<=> ! [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_486])]) ).
fof(f9403,plain,
( spl0_667
<=> ! [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_667])]) ).
fof(f16400,plain,
( ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_nat),tc_nat) = X1
| ~ spl0_486
| ~ spl0_667 ),
inference(superposition,[],[f5868,f9404]) ).
fof(f9404,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_nat)
| ~ spl0_667 ),
inference(avatar_component_clause,[],[f9403]) ).
fof(f5868,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_486 ),
inference(avatar_component_clause,[],[f5867]) ).
fof(f25577,plain,
spl0_1158,
inference(avatar_split_clause,[],[f998,f25575]) ).
fof(f25575,plain,
( spl0_1158
<=> ! [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_1158])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl_Ocases_0) ).
fof(f25573,plain,
spl0_1157,
inference(avatar_split_clause,[],[f983,f25571]) ).
fof(f25571,plain,
( spl0_1157
<=> ! [X18,X10,X0,X6,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(X0),X18,X0,tc_fun(X0,X0),X10),X10,X0,X0),X8)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f983,axiom,
! [X10,X0,X18,X8,X6] :
( ~ class_Ring__and__Field_Ofield(X0)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(X0),X18,X0,tc_fun(X0,X0),X10),X10,X0,X0),X8)),X6) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__divide__distrib_0) ).
fof(f25569,plain,
spl0_1156,
inference(avatar_split_clause,[],[f982,f25567]) ).
fof(f25567,plain,
( spl0_1156
<=> ! [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_1156])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__left__distrib_0) ).
fof(f25565,plain,
spl0_1155,
inference(avatar_split_clause,[],[f703,f25563]) ).
fof(f25563,plain,
( spl0_1155
<=> ! [X3,X4,X0,X23,X26] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X23
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X26),X23)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X26),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f703,axiom,
! [X3,X0,X26,X4,X23] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X23
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X26),X23)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X26),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X23) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_frac__eq__eq_0) ).
fof(f25561,plain,
spl0_1154,
inference(avatar_split_clause,[],[f702,f25559]) ).
fof(f25559,plain,
( spl0_1154
<=> ! [X4,X0,X23,X3,X26] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X23
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X26),X4) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X23)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X26),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f702,axiom,
! [X3,X0,X26,X4,X23] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X23
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X26),X4) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X23)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X26),X23) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_frac__eq__eq_1) ).
fof(f25557,plain,
spl0_1153,
inference(avatar_split_clause,[],[f701,f25555]) ).
fof(f25555,plain,
( spl0_1153
<=> ! [X44,X3,X0,X31,X12,X52] :
( ~ class_Ring__and__Field_Ocomm__ring(X0)
| ~ class_Ring__and__Field_Odvd(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X44,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X52),X0)
| c_Ring__and__Field_Odvd__class_Odvd(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X31),X44))),X52),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f701,axiom,
! [X31,X3,X0,X44,X52,X12] :
( ~ class_Ring__and__Field_Ocomm__ring(X0)
| ~ class_Ring__and__Field_Odvd(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X44,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X52),X0)
| c_Ring__and__Field_Odvd__class_Odvd(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X31),X44))),X52),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__period_I4_J_0) ).
fof(f25553,plain,
spl0_1152,
inference(avatar_split_clause,[],[f700,f25551]) ).
fof(f25551,plain,
( spl0_1152
<=> ! [X44,X3,X0,X31,X12,X52] :
( ~ class_Ring__and__Field_Ocomm__ring(X0)
| ~ class_Ring__and__Field_Odvd(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X44,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X52),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X31),X44))),X52),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f700,axiom,
! [X31,X3,X0,X44,X52,X12] :
( ~ class_Ring__and__Field_Ocomm__ring(X0)
| ~ class_Ring__and__Field_Odvd(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X44,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X52),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X12,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X31),X44))),X52),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__period_I4_J_1) ).
fof(f25549,plain,
spl0_1151,
inference(avatar_split_clause,[],[f648,f25547]) ).
fof(f25547,plain,
( spl0_1151
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f648,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__eq_9) ).
fof(f25545,plain,
spl0_1150,
inference(avatar_split_clause,[],[f645,f25543]) ).
fof(f25543,plain,
( spl0_1150
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0)
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f645,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0)
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__divide__eq_9) ).
fof(f25541,plain,
spl0_1149,
inference(avatar_split_clause,[],[f611,f25539]) ).
fof(f25539,plain,
( spl0_1149
<=> ! [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_1149])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__Suc__less_0) ).
fof(f25513,plain,
spl0_1148,
inference(avatar_split_clause,[],[f582,f25511]) ).
fof(f25511,plain,
( spl0_1148
<=> ! [X4,X0,X23,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X4))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f582,axiom,
! [X3,X0,X4,X23] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X4))),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),X23) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__frac__num_0) ).
fof(f25509,plain,
spl0_1147,
inference(avatar_split_clause,[],[f581,f25507]) ).
fof(f25507,plain,
( spl0_1147
<=> ! [X4,X0,X23,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X23),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X4))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f581,axiom,
! [X3,X0,X4,X23] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X23),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X4))),X4) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__num__frac_0) ).
fof(f25505,plain,
spl0_1146,
inference(avatar_split_clause,[],[f547,f25503]) ).
fof(f25503,plain,
( spl0_1146
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ 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),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f547,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ 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),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__divide__eq_0) ).
fof(f25501,plain,
spl0_1145,
inference(avatar_split_clause,[],[f545,f25499]) ).
fof(f25499,plain,
( spl0_1145
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ 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_Oinverse__class_Odivide(X0),X1),X5)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f545,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ 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_Oinverse__class_Odivide(X0),X1),X5)),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__eq_0) ).
fof(f25207,plain,
( spl0_1144
| ~ spl0_786
| ~ spl0_1130 ),
inference(avatar_split_clause,[],[f24894,f24822,f12821,f25205]) ).
fof(f25205,plain,
( spl0_1144
<=> ! [X2,X1] : c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f24822,plain,
( spl0_1130
<=> ! [X6,X7] : c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f24894,plain,
( ! [X2,X1] : c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_bool),tc_bool)
| ~ spl0_786
| ~ spl0_1130 ),
inference(superposition,[],[f24823,f12822]) ).
fof(f24823,plain,
( ! [X6,X7] : c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_bool),tc_bool)
| ~ spl0_1130 ),
inference(avatar_component_clause,[],[f24822]) ).
fof(f25201,plain,
( spl0_1143
| ~ spl0_201
| ~ spl0_1136 ),
inference(avatar_split_clause,[],[f24867,f24864,f2344,f25199]) ).
fof(f25199,plain,
( spl0_1143
<=> ! [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_1143])]) ).
fof(f24864,plain,
( spl0_1136
<=> ! [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_1136])]) ).
fof(f24867,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_201
| ~ spl0_1136 ),
inference(forward_demodulation,[],[f24865,f2346]) ).
fof(f24865,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_1136 ),
inference(avatar_component_clause,[],[f24864]) ).
fof(f24913,plain,
spl0_1142,
inference(avatar_split_clause,[],[f1018,f24911]) ).
fof(f24911,plain,
( spl0_1142
<=> ! [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_1142])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__timesf_0) ).
fof(f24909,plain,
spl0_1141,
inference(avatar_split_clause,[],[f992,f24907]) ).
fof(f24907,plain,
( spl0_1141
<=> ! [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_1141])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__rtranclE_0) ).
fof(f24905,plain,
spl0_1140,
inference(avatar_split_clause,[],[f990,f24903]) ).
fof(f24903,plain,
( spl0_1140
<=> ! [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_1140])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtranclE_1) ).
fof(f24879,plain,
spl0_1139,
inference(avatar_split_clause,[],[f763,f24877]) ).
fof(f24877,plain,
( spl0_1139
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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_1139])]) ).
fof(f763,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__cancel__left__disj_0) ).
fof(f24875,plain,
spl0_1138,
inference(avatar_split_clause,[],[f762,f24873]) ).
fof(f24873,plain,
( spl0_1138
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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_1138])]) ).
fof(f762,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__cancel__right__disj_0) ).
fof(f24871,plain,
spl0_1137,
inference(avatar_split_clause,[],[f580,f24869]) ).
fof(f24869,plain,
( spl0_1137
<=> ! [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_1137])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f24866,plain,
spl0_1136,
inference(avatar_split_clause,[],[f408,f24864]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__strict__mono_0) ).
fof(f24862,plain,
spl0_1135,
inference(avatar_split_clause,[],[f268,f24860]) ).
fof(f24860,plain,
( spl0_1135
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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)),X5))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f268,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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)),X5))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__eq_5) ).
fof(f24858,plain,
spl0_1134,
inference(avatar_split_clause,[],[f267,f24856]) ).
fof(f24856,plain,
( spl0_1134
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f267,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__eq_7) ).
fof(f24854,plain,
spl0_1133,
inference(avatar_split_clause,[],[f266,f24852]) ).
fof(f24852,plain,
( spl0_1133
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0)
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f266,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0)
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__divide__eq_5) ).
fof(f24850,plain,
spl0_1132,
inference(avatar_split_clause,[],[f265,f24848]) ).
fof(f24848,plain,
( spl0_1132
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0)
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f265,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0)
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__divide__eq_7) ).
fof(f24846,plain,
spl0_1131,
inference(avatar_split_clause,[],[f164,f24844]) ).
fof(f24844,plain,
( spl0_1131
<=> ! [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_1131])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f24824,plain,
( spl0_1130
| ~ spl0_666
| ~ spl0_1129 ),
inference(avatar_split_clause,[],[f24367,f23936,f9251,f24822]) ).
fof(f23936,plain,
( spl0_1129
<=> ! [X2,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_bool),X1,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f24367,plain,
( ! [X6,X7] : c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_bool),tc_bool)
| ~ spl0_666
| ~ spl0_1129 ),
inference(superposition,[],[f23937,f9252]) ).
fof(f23937,plain,
( ! [X2,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_bool),X1,tc_bool)
| ~ spl0_1129 ),
inference(avatar_component_clause,[],[f23936]) ).
fof(f23938,plain,
( spl0_1129
| ~ spl0_777
| ~ spl0_1117 ),
inference(avatar_split_clause,[],[f23512,f23455,f11982,f23936]) ).
fof(f23455,plain,
( spl0_1117
<=> ! [X4,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_bool),X4,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f23512,plain,
( ! [X2,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_bool),X1,tc_bool)
| ~ spl0_777
| ~ spl0_1117 ),
inference(superposition,[],[f23456,f11983]) ).
fof(f23456,plain,
( ! [X4,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_bool),X4,tc_bool)
| ~ spl0_1117 ),
inference(avatar_component_clause,[],[f23455]) ).
fof(f23523,plain,
spl0_1128,
inference(avatar_split_clause,[],[f1192,f23521]) ).
fof(f23521,plain,
( spl0_1128
<=> ! [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_1128])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__inv__image_0) ).
fof(f23497,plain,
spl0_1127,
inference(avatar_split_clause,[],[f1191,f23495]) ).
fof(f23495,plain,
( spl0_1127
<=> ! [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_1127])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__inv__image_1) ).
fof(f23493,plain,
spl0_1126,
inference(avatar_split_clause,[],[f1064,f23491]) ).
fof(f23491,plain,
( spl0_1126
<=> ! [X4,X0,X3,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))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_tranclD_1) ).
fof(f23489,plain,
spl0_1125,
inference(avatar_split_clause,[],[f1063,f23487]) ).
fof(f23487,plain,
( spl0_1125
<=> ! [X4,X0,X3,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))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_tranclD2_0) ).
fof(f23485,plain,
spl0_1124,
inference(avatar_split_clause,[],[f1000,f23483]) ).
fof(f23483,plain,
( spl0_1124
<=> ! [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_1124])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl_Ocases_1) ).
fof(f23481,plain,
spl0_1123,
inference(avatar_split_clause,[],[f909,f23479]) ).
fof(f23479,plain,
( spl0_1123
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| 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_1123])]) ).
fof(f909,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| 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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__cancel__left__disj_1) ).
fof(f23477,plain,
spl0_1122,
inference(avatar_split_clause,[],[f908,f23475]) ).
fof(f23475,plain,
( spl0_1122
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ 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_1122])]) ).
fof(f908,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ 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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__cancel__left__disj_2) ).
fof(f23473,plain,
spl0_1121,
inference(avatar_split_clause,[],[f907,f23471]) ).
fof(f23471,plain,
( spl0_1121
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| 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_1121])]) ).
fof(f907,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| 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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__cancel__right__disj_1) ).
fof(f23469,plain,
spl0_1120,
inference(avatar_split_clause,[],[f906,f23467]) ).
fof(f23467,plain,
( spl0_1120
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ 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_1120])]) ).
fof(f906,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ 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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__cancel__right__disj_2) ).
fof(f23465,plain,
spl0_1119,
inference(avatar_split_clause,[],[f875,f23463]) ).
fof(f23463,plain,
( spl0_1119
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X0),X2),X5)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f875,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X0),X2),X5)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__strict__right__mono_0) ).
fof(f23461,plain,
spl0_1118,
inference(avatar_split_clause,[],[f874,f23459]) ).
fof(f23459,plain,
( spl0_1118
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X5)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f874,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X5)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__strict__right__mono__neg_0) ).
fof(f23457,plain,
( ~ spl0_41
| spl0_1117
| ~ spl0_135
| ~ spl0_488 ),
inference(avatar_split_clause,[],[f15709,f6009,f1961,f23455,f1562]) ).
fof(f1562,plain,
( spl0_41
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1961,plain,
( spl0_135
<=> ! [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_135])]) ).
fof(f15709,plain,
( ! [X4,X5] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_bool),X4,tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_135
| ~ spl0_488 ),
inference(superposition,[],[f1962,f6010]) ).
fof(f1962,plain,
( ! [X3,X0,X4] :
( c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1961]) ).
fof(f23453,plain,
spl0_1116,
inference(avatar_split_clause,[],[f761,f23451]) ).
fof(f23451,plain,
( spl0_1116
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ 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_1116])]) ).
fof(f761,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| ~ 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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__cancel__left__neg_0) ).
fof(f23449,plain,
spl0_1115,
inference(avatar_split_clause,[],[f759,f23447]) ).
fof(f23447,plain,
( spl0_1115
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__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_1115])]) ).
fof(f759,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__cancel__left__pos_0) ).
fof(f23445,plain,
spl0_1114,
inference(avatar_split_clause,[],[f758,f23443]) ).
fof(f23443,plain,
( spl0_1114
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__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_1114])]) ).
fof(f758,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__cancel__left__pos_1) ).
fof(f23441,plain,
spl0_1113,
inference(avatar_split_clause,[],[f757,f23439]) ).
fof(f23439,plain,
( spl0_1113
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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_1113])]) ).
fof(f757,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__strict__left__mono__neg_0) ).
fof(f23437,plain,
spl0_1112,
inference(avatar_split_clause,[],[f756,f23435]) ).
fof(f23435,plain,
( spl0_1112
<=> ! [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_1112])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__strict__left__mono_0) ).
fof(f23433,plain,
spl0_1111,
inference(avatar_split_clause,[],[f752,f23431]) ).
fof(f23431,plain,
( spl0_1111
<=> ! [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_1111])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__strict__right__mono_0) ).
fof(f23429,plain,
spl0_1110,
inference(avatar_split_clause,[],[f751,f23427]) ).
fof(f23427,plain,
( spl0_1110
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__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_1110])]) ).
fof(f751,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__cancel__right__disj_4) ).
fof(f23425,plain,
spl0_1109,
inference(avatar_split_clause,[],[f750,f23423]) ).
fof(f23423,plain,
( spl0_1109
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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_1109])]) ).
fof(f750,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| 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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__cancel__right__disj_5) ).
fof(f23421,plain,
spl0_1108,
inference(avatar_split_clause,[],[f749,f23419]) ).
fof(f23419,plain,
( spl0_1108
<=> ! [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_1108])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__strict__left__mono__comm_0) ).
fof(f23417,plain,
spl0_1107,
inference(avatar_split_clause,[],[f650,f23415]) ).
fof(f23415,plain,
( spl0_1107
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f650,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__eq_2) ).
fof(f23389,plain,
spl0_1106,
inference(avatar_split_clause,[],[f649,f23387]) ).
fof(f23387,plain,
( spl0_1106
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f649,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__eq_3) ).
fof(f23385,plain,
spl0_1105,
inference(avatar_split_clause,[],[f647,f23383]) ).
fof(f23383,plain,
( spl0_1105
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f647,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__divide__eq_2) ).
fof(f23381,plain,
spl0_1104,
inference(avatar_split_clause,[],[f646,f23379]) ).
fof(f23379,plain,
( spl0_1104
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f646,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__divide__eq_3) ).
fof(f23377,plain,
spl0_1103,
inference(avatar_split_clause,[],[f623,f23375]) ).
fof(f23375,plain,
( spl0_1103
<=> ! [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_1103])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__mono_H_0) ).
fof(f23373,plain,
spl0_1102,
inference(avatar_split_clause,[],[f622,f23371]) ).
fof(f23371,plain,
( spl0_1102
<=> ! [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_1102])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__mono_0) ).
fof(f23369,plain,
spl0_1101,
inference(avatar_split_clause,[],[f544,f23367]) ).
fof(f23367,plain,
( spl0_1101
<=> ! [X4,X0,X23,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f544,axiom,
! [X3,X0,X4,X23] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X4)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),X23)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__imp__div__pos__less_0) ).
fof(f23365,plain,
spl0_1100,
inference(avatar_split_clause,[],[f543,f23363]) ).
fof(f23363,plain,
( spl0_1100
<=> ! [X4,X0,X23,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X4)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X23),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f543,axiom,
! [X3,X0,X4,X23] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X4)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X23),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__imp__less__div__pos_0) ).
fof(f23361,plain,
spl0_1099,
inference(avatar_split_clause,[],[f531,f23359]) ).
fof(f23359,plain,
( spl0_1099
<=> ! [X3,X0,X12,X5,X8] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X5 = X12
| c_HOL_Ozero__class_Ozero(X0) = X8
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X8),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X8),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f531,axiom,
! [X3,X0,X8,X5,X12] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X5 = X12
| c_HOL_Ozero__class_Ozero(X0) = X8
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X8),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X8),X12)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(f23357,plain,
spl0_1098,
inference(avatar_split_clause,[],[f219,f23355]) ).
fof(f23355,plain,
( spl0_1098
<=> ! [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_1098])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rel__comp__mono_0) ).
fof(f23334,plain,
( spl0_1097
| ~ spl0_785
| ~ spl0_1096 ),
inference(avatar_split_clause,[],[f23019,f22734,f12285,f23332]) ).
fof(f23332,plain,
( spl0_1097
<=> ! [X2,X1] : c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f22734,plain,
( spl0_1096
<=> ! [X6,X7] : c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f23019,plain,
( ! [X2,X1] : c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_nat),tc_nat)
| ~ spl0_785
| ~ spl0_1096 ),
inference(superposition,[],[f22735,f12286]) ).
fof(f22735,plain,
( ! [X6,X7] : c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_nat),tc_nat)
| ~ spl0_1096 ),
inference(avatar_component_clause,[],[f22734]) ).
fof(f22736,plain,
( spl0_1096
| ~ spl0_490
| ~ spl0_1082 ),
inference(avatar_split_clause,[],[f22506,f22442,f6195,f22734]) ).
fof(f22442,plain,
( spl0_1082
<=> ! [X2,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f22506,plain,
( ! [X6,X7] : c_lessequals(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_nat),tc_nat)
| ~ spl0_490
| ~ spl0_1082 ),
inference(superposition,[],[f22443,f6196]) ).
fof(f22443,plain,
( ! [X2,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_nat),X1,tc_nat)
| ~ spl0_1082 ),
inference(avatar_component_clause,[],[f22442]) ).
fof(f22525,plain,
spl0_1095,
inference(avatar_split_clause,[],[f1271,f22523]) ).
fof(f22523,plain,
( spl0_1095
<=> ! [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_1095])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__mkbot_2) ).
fof(f22521,plain,
spl0_1094,
inference(avatar_split_clause,[],[f1252,f22519]) ).
fof(f22519,plain,
( spl0_1094
<=> ! [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_1094])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__mktop_2) ).
fof(f22517,plain,
spl0_1093,
inference(avatar_split_clause,[],[f1209,f22515]) ).
fof(f22515,plain,
( spl0_1093
<=> ! [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_1093])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_SigmaI_0) ).
fof(f22484,plain,
spl0_1092,
inference(avatar_split_clause,[],[f1187,f22482]) ).
fof(f22482,plain,
( spl0_1092
<=> ! [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_1092])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_cuts__eq_0) ).
fof(f22480,plain,
spl0_1091,
inference(avatar_split_clause,[],[f1088,f22478]) ).
fof(f22478,plain,
( spl0_1091
<=> ! [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_Transitive__Closure_Otrancl(X15,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtranclD_0) ).
fof(f22476,plain,
spl0_1090,
inference(avatar_split_clause,[],[f1080,f22474]) ).
fof(f22474,plain,
( spl0_1090
<=> ! [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_1090])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc__downwards_0) ).
fof(f22472,plain,
spl0_1089,
inference(avatar_split_clause,[],[f1058,f22470]) ).
fof(f22470,plain,
( spl0_1089
<=> ! [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_1089])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc__induct_1) ).
fof(f22468,plain,
spl0_1088,
inference(avatar_split_clause,[],[f1052,f22466]) ).
fof(f22466,plain,
( spl0_1088
<=> ! [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_1088])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc__induct__rule_1) ).
fof(f22464,plain,
spl0_1087,
inference(avatar_split_clause,[],[f1045,f22462]) ).
fof(f22462,plain,
( spl0_1087
<=> ! [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_1087])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__eq__minimal_1) ).
fof(f22460,plain,
spl0_1086,
inference(avatar_split_clause,[],[f1044,f22458]) ).
fof(f22458,plain,
( spl0_1086
<=> ! [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_1086])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wfE__min_1) ).
fof(f22456,plain,
spl0_1085,
inference(avatar_split_clause,[],[f923,f22454]) ).
fof(f22454,plain,
( spl0_1085
<=> ! [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_1085])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_single__valuedD_0) ).
fof(f22452,plain,
spl0_1084,
inference(avatar_split_clause,[],[f905,f22450]) ).
fof(f22450,plain,
( spl0_1084
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f905,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__less__divide__iff_3) ).
fof(f22448,plain,
spl0_1083,
inference(avatar_split_clause,[],[f904,f22446]) ).
fof(f22446,plain,
( spl0_1083
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),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_Oinverse__class_Odivide(X0),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f904,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),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_Oinverse__class_Odivide(X0),X2),X1))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__less__divide__iff_2) ).
fof(f22444,plain,
( spl0_1082
| ~ spl0_667
| ~ spl0_1066 ),
inference(avatar_split_clause,[],[f22390,f22165,f9403,f22442]) ).
fof(f22165,plain,
( spl0_1066
<=> ! [X4,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_nat),X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f22390,plain,
( ! [X2,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_nat),X1,tc_nat)
| ~ spl0_667
| ~ spl0_1066 ),
inference(superposition,[],[f22166,f9404]) ).
fof(f22166,plain,
( ! [X4,X5] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_nat),X4,tc_nat)
| ~ spl0_1066 ),
inference(avatar_component_clause,[],[f22165]) ).
fof(f22440,plain,
spl0_1081,
inference(avatar_split_clause,[],[f903,f22438]) ).
fof(f22438,plain,
( spl0_1081
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f903,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__less__divide__iff_1) ).
fof(f22436,plain,
spl0_1080,
inference(avatar_split_clause,[],[f902,f22434]) ).
fof(f22434,plain,
( spl0_1080
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),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_Oinverse__class_Odivide(X0),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f902,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),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_Oinverse__class_Odivide(X0),X2),X1))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__less__divide__iff_0) ).
fof(f22432,plain,
spl0_1079,
inference(avatar_split_clause,[],[f847,f22430]) ).
fof(f22430,plain,
( spl0_1079
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),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),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f847,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),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),X5))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__cancel__right__disj_3) ).
fof(f22428,plain,
spl0_1078,
inference(avatar_split_clause,[],[f846,f22426]) ).
fof(f22426,plain,
( spl0_1078
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ 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_1078])]) ).
fof(f846,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),X2))
| ~ 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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__cancel__left__disj_3) ).
fof(f22424,plain,
spl0_1077,
inference(avatar_split_clause,[],[f834,f22422]) ).
fof(f22422,plain,
( spl0_1077
<=> ! [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_1077])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__strict__mono_0) ).
fof(f22420,plain,
spl0_1076,
inference(avatar_split_clause,[],[f771,f22418]) ).
fof(f22418,plain,
( spl0_1076
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f771,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__0__iff_3) ).
fof(f22416,plain,
spl0_1075,
inference(avatar_split_clause,[],[f770,f22414]) ).
fof(f22414,plain,
( spl0_1075
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X2),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f770,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X2),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__0__iff_2) ).
fof(f22412,plain,
spl0_1074,
inference(avatar_split_clause,[],[f769,f22410]) ).
fof(f22410,plain,
( spl0_1074
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f769,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__0__iff_1) ).
fof(f22408,plain,
spl0_1073,
inference(avatar_split_clause,[],[f768,f22406]) ).
fof(f22406,plain,
( spl0_1073
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Ozero__class_Ozero(X0)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f768,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Ozero__class_Ozero(X0)),X2))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__0__iff_0) ).
fof(f22404,plain,
spl0_1072,
inference(avatar_split_clause,[],[f735,f22402]) ).
fof(f22402,plain,
( spl0_1072
<=> ! [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_1072])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__insert_0) ).
fof(f22371,plain,
spl0_1071,
inference(avatar_split_clause,[],[f591,f22369]) ).
fof(f22369,plain,
( spl0_1071
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f591,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0)))),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_gt__half__sum_0) ).
fof(f22367,plain,
spl0_1070,
inference(avatar_split_clause,[],[f590,f22365]) ).
fof(f22365,plain,
( spl0_1070
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),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_1070])]) ).
fof(f590,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Oone__class_Oone(X0)),c_HOL_Oone__class_Oone(X0))))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__half__sum_0) ).
fof(f22363,plain,
spl0_1069,
inference(avatar_split_clause,[],[f237,f22361]) ).
fof(f22361,plain,
( spl0_1069
<=> ! [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_1069])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Image__subset__eq_0) ).
fof(f22359,plain,
spl0_1068,
inference(avatar_split_clause,[],[f236,f22357]) ).
fof(f22357,plain,
( spl0_1068
<=> ! [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_1068])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Image__subset__eq_1) ).
fof(f22355,plain,
spl0_1067,
inference(avatar_split_clause,[],[f131,f22353]) ).
fof(f22353,plain,
( spl0_1067
<=> ! [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_ODomain(X8,X0,X0),c_Relation_ORange(X9,X0,X0),tc_fun(X0,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__Un_0) ).
fof(f22167,plain,
( ~ spl0_21
| spl0_1066
| ~ spl0_135
| ~ spl0_486 ),
inference(avatar_split_clause,[],[f15437,f5867,f1961,f22165,f1462]) ).
fof(f1462,plain,
( spl0_21
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f15437,plain,
( ! [X4,X5] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,tc_nat),X4,tc_nat)
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_135
| ~ spl0_486 ),
inference(superposition,[],[f1962,f5868]) ).
fof(f21861,plain,
( spl0_1065
| ~ spl0_201
| ~ spl0_1052 ),
inference(avatar_split_clause,[],[f21625,f21621,f2344,f21859]) ).
fof(f21859,plain,
( spl0_1065
<=> ! [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_1065])]) ).
fof(f21621,plain,
( spl0_1052
<=> ! [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_1052])]) ).
fof(f21625,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_201
| ~ spl0_1052 ),
inference(forward_demodulation,[],[f21624,f2346]) ).
fof(f21624,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_201
| ~ spl0_1052 ),
inference(forward_demodulation,[],[f21622,f2346]) ).
fof(f21622,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_1052 ),
inference(avatar_component_clause,[],[f21621]) ).
fof(f21848,plain,
( spl0_1064
| ~ spl0_201
| ~ spl0_1050 ),
inference(avatar_split_clause,[],[f21615,f21612,f2344,f21846]) ).
fof(f21846,plain,
( spl0_1064
<=> ! [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_1064])]) ).
fof(f21612,plain,
( spl0_1050
<=> ! [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_1050])]) ).
fof(f21615,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_201
| ~ spl0_1050 ),
inference(forward_demodulation,[],[f21613,f2346]) ).
fof(f21613,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_1050 ),
inference(avatar_component_clause,[],[f21612]) ).
fof(f21833,plain,
( spl0_1063
| ~ spl0_152
| ~ spl0_701 ),
inference(avatar_split_clause,[],[f10381,f10016,f2029,f21831]) ).
fof(f21831,plain,
( spl0_1063
<=> ! [X9,X8,X10] :
( c_Relation_Oirrefl(c_Wellfounded_Omlex__prod(X8,X9,X10),X10)
| ~ c_Wellfounded_Owf(X9,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f2029,plain,
( spl0_152
<=> ! [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_152])]) ).
fof(f10016,plain,
( spl0_701
<=> ! [X0,X1] :
( c_Relation_Oirrefl(X0,X1)
| ~ c_Wellfounded_Owf(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f10381,plain,
( ! [X10,X8,X9] :
( c_Relation_Oirrefl(c_Wellfounded_Omlex__prod(X8,X9,X10),X10)
| ~ c_Wellfounded_Owf(X9,X10) )
| ~ spl0_152
| ~ spl0_701 ),
inference(resolution,[],[f10017,f2030]) ).
fof(f2030,plain,
( ! [X0,X18,X15] :
( c_Wellfounded_Owf(c_Wellfounded_Omlex__prod(X18,X15,X0),X0)
| ~ c_Wellfounded_Owf(X15,X0) )
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f2029]) ).
fof(f10017,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Relation_Oirrefl(X0,X1) )
| ~ spl0_701 ),
inference(avatar_component_clause,[],[f10016]) ).
fof(f21665,plain,
spl0_1062,
inference(avatar_split_clause,[],[f1356,f21663]) ).
fof(f21663,plain,
( spl0_1062
<=> ! [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_1062])]) ).
fof(f1356,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,[],[f1355,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rel__comp__distrib2_0) ).
fof(f1355,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__union__merge_1) ).
fof(f21661,plain,
spl0_1061,
inference(avatar_split_clause,[],[f1354,f21659]) ).
fof(f21659,plain,
( spl0_1061
<=> ! [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_1061])]) ).
fof(f1354,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,[],[f1353,f459]) ).
fof(f1353,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__union__merge_0) ).
fof(f21657,plain,
spl0_1060,
inference(avatar_split_clause,[],[f1183,f21655]) ).
fof(f21655,plain,
( spl0_1060
<=> ! [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_1060])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_antisym__def_0) ).
fof(f21653,plain,
spl0_1059,
inference(avatar_split_clause,[],[f1056,f21651]) ).
fof(f21651,plain,
( spl0_1059
<=> ! [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_1059])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc_Oinducts_1) ).
fof(f21649,plain,
spl0_1058,
inference(avatar_split_clause,[],[f1053,f21647]) ).
fof(f21647,plain,
( spl0_1058
<=> ! [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_1058])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc_Oinduct_1) ).
fof(f21645,plain,
spl0_1057,
inference(avatar_split_clause,[],[f1028,f21643]) ).
fof(f21643,plain,
( spl0_1057
<=> ! [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_1057])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_cuts__eq_1) ).
fof(f21641,plain,
spl0_1056,
inference(avatar_split_clause,[],[f1015,f21639]) ).
fof(f21639,plain,
( spl0_1056
<=> ! [X4,X0,X3,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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_tranclD2_1) ).
fof(f21637,plain,
spl0_1055,
inference(avatar_split_clause,[],[f1010,f21635]) ).
fof(f21635,plain,
( spl0_1055
<=> ! [X4,X0,X3,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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_tranclD_0) ).
fof(f21633,plain,
( spl0_1054
| ~ spl0_127
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2388,f2344,f1929,f21631]) ).
fof(f21631,plain,
( spl0_1054
<=> ! [X0] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f2388,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X0 )
| ~ spl0_127
| ~ spl0_201 ),
inference(superposition,[],[f1930,f2346]) ).
fof(f21629,plain,
spl0_1053,
inference(avatar_split_clause,[],[f1008,f21627]) ).
fof(f21627,plain,
( spl0_1053
<=> ! [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_Transitive__Closure_Otrancl(X8,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_irrefl__trancl__rD_0) ).
fof(f21623,plain,
spl0_1052,
inference(avatar_split_clause,[],[f732,f21621]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__pos__nat__iff_0) ).
fof(f21619,plain,
spl0_1051,
inference(avatar_split_clause,[],[f657,f21617]) ).
fof(f21617,plain,
( spl0_1051
<=> ! [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_1051])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_cuts__eq_2) ).
fof(f21614,plain,
spl0_1050,
inference(avatar_split_clause,[],[f594,f21612]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__eq__imp__eq__base_0) ).
fof(f21610,plain,
spl0_1049,
inference(avatar_split_clause,[],[f521,f21608]) ).
fof(f21608,plain,
( spl0_1049
<=> ! [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_1049])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Image__Int__eq_0) ).
fof(f21606,plain,
spl0_1048,
inference(avatar_split_clause,[],[f460,f21604]) ).
fof(f21604,plain,
( spl0_1048
<=> ! [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_1048])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rel__comp__distrib_0) ).
fof(f21602,plain,
spl0_1047,
inference(avatar_split_clause,[],[f459,f21600]) ).
fof(f21600,plain,
( spl0_1047
<=> ! [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_1047])]) ).
fof(f21000,plain,
spl0_1046,
inference(avatar_split_clause,[],[f1212,f20998]) ).
fof(f20998,plain,
( spl0_1046
<=> ! [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_1046])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rev__ImageI_0) ).
fof(f20996,plain,
spl0_1045,
inference(avatar_split_clause,[],[f1210,f20994]) ).
fof(f20994,plain,
( spl0_1045
<=> ! [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_1045])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc__downward_0) ).
fof(f20992,plain,
spl0_1044,
inference(avatar_split_clause,[],[f1001,f20990]) ).
fof(f20990,plain,
( spl0_1044
<=> ! [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_1044])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__rtrancl__induct_3) ).
fof(f20988,plain,
spl0_1043,
inference(avatar_split_clause,[],[f999,f20986]) ).
fof(f20986,plain,
( spl0_1043
<=> ! [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_1043])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__induct_2) ).
fof(f20984,plain,
spl0_1042,
inference(avatar_split_clause,[],[f996,f20982]) ).
fof(f20982,plain,
( spl0_1042
<=> ! [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_1042])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__induct_3) ).
fof(f20980,plain,
spl0_1041,
inference(avatar_split_clause,[],[f993,f20978]) ).
fof(f20978,plain,
( spl0_1041
<=> ! [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_1041])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__rtrancl__induct_2) ).
fof(f20976,plain,
spl0_1040,
inference(avatar_split_clause,[],[f920,f20974]) ).
fof(f20974,plain,
( spl0_1040
<=> ! [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_1040])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__1__mult_0) ).
fof(f20972,plain,
spl0_1039,
inference(avatar_split_clause,[],[f899,f20970]) ).
fof(f20970,plain,
( spl0_1039
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f899,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X3))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__pos__neg_0) ).
fof(f20967,plain,
spl0_1038,
inference(avatar_split_clause,[],[f898,f20965]) ).
fof(f20965,plain,
( spl0_1038
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f898,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__neg__pos_0) ).
fof(f20963,plain,
spl0_1037,
inference(avatar_split_clause,[],[f895,f20961]) ).
fof(f20961,plain,
( spl0_1037
<=> ! [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_1037])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__pos__neg_0) ).
fof(f20959,plain,
spl0_1036,
inference(avatar_split_clause,[],[f894,f20957]) ).
fof(f20957,plain,
( spl0_1036
<=> ! [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_1036])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__pos__neg2_0) ).
fof(f20955,plain,
spl0_1035,
inference(avatar_split_clause,[],[f891,f20953]) ).
fof(f20953,plain,
( spl0_1035
<=> ! [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_1035])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__pos__pos_0) ).
fof(f20951,plain,
spl0_1034,
inference(avatar_split_clause,[],[f889,f20949]) ).
fof(f20949,plain,
( spl0_1034
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f889,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__neg__neg_0) ).
fof(f20947,plain,
spl0_1033,
inference(avatar_split_clause,[],[f888,f20945]) ).
fof(f20945,plain,
( spl0_1033
<=> ! [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_1033])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__pos__pos_0) ).
fof(f20943,plain,
spl0_1032,
inference(avatar_split_clause,[],[f887,f20941]) ).
fof(f20941,plain,
( spl0_1032
<=> ! [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_1032])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__less__mult__pos_0) ).
fof(f20939,plain,
spl0_1031,
inference(avatar_split_clause,[],[f886,f20937]) ).
fof(f20937,plain,
( spl0_1031
<=> ! [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_1031])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__less__mult__pos2_0) ).
fof(f20935,plain,
spl0_1030,
inference(avatar_split_clause,[],[f877,f20933]) ).
fof(f20933,plain,
( spl0_1030
<=> ! [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_1030])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__neg__neg_0) ).
fof(f20931,plain,
spl0_1029,
inference(avatar_split_clause,[],[f765,f20929]) ).
fof(f20929,plain,
( spl0_1029
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f765,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__pos__pos_0) ).
fof(f20927,plain,
spl0_1028,
inference(avatar_split_clause,[],[f764,f20925]) ).
fof(f20925,plain,
( spl0_1028
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f764,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),c_HOL_Ozero__class_Ozero(X0)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),c_HOL_Ozero__class_Ozero(X0)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__neg__neg_0) ).
fof(f20923,plain,
spl0_1027,
inference(avatar_split_clause,[],[f598,f20921]) ).
fof(f20921,plain,
( spl0_1027
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_1027])]) ).
fof(f598,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__divide__mult__cancel__right_0) ).
fof(f20919,plain,
spl0_1026,
inference(avatar_split_clause,[],[f597,f20917]) ).
fof(f20917,plain,
( spl0_1026
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_1026])]) ).
fof(f597,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__divide__mult__cancel__left_0) ).
fof(f20915,plain,
spl0_1025,
inference(avatar_split_clause,[],[f88,f20913]) ).
fof(f20913,plain,
( spl0_1025
<=> ! [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_1025])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__left__less__imp__less_0) ).
fof(f20911,plain,
spl0_1024,
inference(avatar_split_clause,[],[f87,f20909]) ).
fof(f20909,plain,
( spl0_1024
<=> ! [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_1024])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__right__less__imp__less_0) ).
fof(f20907,plain,
spl0_1023,
inference(avatar_split_clause,[],[f86,f20905]) ).
fof(f20905,plain,
( spl0_1023
<=> ! [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_1023])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__imp__less__left_0) ).
fof(f20903,plain,
spl0_1022,
inference(avatar_split_clause,[],[f85,f20901]) ).
fof(f20901,plain,
( spl0_1022
<=> ! [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_1022])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__less__imp__less__right_0) ).
fof(f20820,plain,
( spl0_1021
| ~ spl0_719
| ~ spl0_999 ),
inference(avatar_split_clause,[],[f20612,f20281,f10621,f20818]) ).
fof(f20818,plain,
( spl0_1021
<=> ! [X1] : ~ c_Wellfounded_Oacyclic(c_Relation_OId(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f10621,plain,
( spl0_719
<=> ! [X8,X7] :
( c_Relation_Oirrefl(c_Transitive__Closure_Otrancl(X7,X8),X8)
| ~ c_Wellfounded_Oacyclic(X7,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f20281,plain,
( spl0_999
<=> ! [X13] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Otrancl(c_Relation_OId(X13),X13),X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f20612,plain,
( ! [X1] : ~ c_Wellfounded_Oacyclic(c_Relation_OId(X1),X1)
| ~ spl0_719
| ~ spl0_999 ),
inference(resolution,[],[f20282,f10622]) ).
fof(f10622,plain,
( ! [X8,X7] :
( c_Relation_Oirrefl(c_Transitive__Closure_Otrancl(X7,X8),X8)
| ~ c_Wellfounded_Oacyclic(X7,X8) )
| ~ spl0_719 ),
inference(avatar_component_clause,[],[f10621]) ).
fof(f20282,plain,
( ! [X13] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Otrancl(c_Relation_OId(X13),X13),X13)
| ~ spl0_999 ),
inference(avatar_component_clause,[],[f20281]) ).
fof(f20506,plain,
spl0_1020,
inference(avatar_split_clause,[],[f1060,f20504]) ).
fof(f20504,plain,
( spl0_1020
<=> ! [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_1020])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__insert_2) ).
fof(f20502,plain,
spl0_1019,
inference(avatar_split_clause,[],[f978,f20500]) ).
fof(f20500,plain,
( spl0_1019
<=> ! [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_1019])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__strict__increasing_0) ).
fof(f20498,plain,
spl0_1018,
inference(avatar_split_clause,[],[f977,f20496]) ).
fof(f20496,plain,
( spl0_1018
<=> ! [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_1018])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__less__imp__less__exp_0) ).
fof(f20494,plain,
spl0_1017,
inference(avatar_split_clause,[],[f945,f20492]) ).
fof(f20492,plain,
( spl0_1017
<=> ! [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_Transitive__Closure_Otrancl(X8,X0)))
| hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),X48),c_Transitive__Closure_Otrancl(X9,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_trancl__mono_0) ).
fof(f20490,plain,
( spl0_1016
| ~ spl0_687
| ~ spl0_855 ),
inference(avatar_split_clause,[],[f19808,f14196,f9627,f20488]) ).
fof(f20488,plain,
( spl0_1016
<=> ! [X23] : c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(c_Relation_OId(X23),X23),X23) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f9627,plain,
( spl0_687
<=> ! [X2,X1] : c_Nitpick_Orefl_H(c_Transitive__Closure_Ortrancl(X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f14196,plain,
( spl0_855
<=> ! [X2] : c_Transitive__Closure_Ortrancl(c_Relation_OId(X2),X2) = c_Transitive__Closure_Otrancl(c_Relation_OId(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f19808,plain,
( ! [X23] : c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(c_Relation_OId(X23),X23),X23)
| ~ spl0_687
| ~ spl0_855 ),
inference(superposition,[],[f9628,f14197]) ).
fof(f14197,plain,
( ! [X2] : c_Transitive__Closure_Ortrancl(c_Relation_OId(X2),X2) = c_Transitive__Closure_Otrancl(c_Relation_OId(X2),X2)
| ~ spl0_855 ),
inference(avatar_component_clause,[],[f14196]) ).
fof(f9628,plain,
( ! [X2,X1] : c_Nitpick_Orefl_H(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ spl0_687 ),
inference(avatar_component_clause,[],[f9627]) ).
fof(f20486,plain,
spl0_1015,
inference(avatar_split_clause,[],[f935,f20484]) ).
fof(f20484,plain,
( spl0_1015
<=> ! [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_1015])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Image__singleton__iff_1) ).
fof(f20482,plain,
spl0_1014,
inference(avatar_split_clause,[],[f934,f20480]) ).
fof(f20480,plain,
( spl0_1014
<=> ! [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_1014])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Image__singleton__iff_0) ).
fof(f20478,plain,
spl0_1013,
inference(avatar_split_clause,[],[f933,f20476]) ).
fof(f20476,plain,
( spl0_1013
<=> ! [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_1013])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_pred__subset__eq_1) ).
fof(f20474,plain,
spl0_1012,
inference(avatar_split_clause,[],[f932,f20472]) ).
fof(f20472,plain,
( spl0_1012
<=> ! [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_1012])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_pred__subset__eq_0) ).
fof(f20470,plain,
spl0_1011,
inference(avatar_split_clause,[],[f928,f20468]) ).
fof(f20468,plain,
( spl0_1011
<=> ! [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_1011])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__right__distrib_0) ).
fof(f20466,plain,
spl0_1010,
inference(avatar_split_clause,[],[f774,f20464]) ).
fof(f20464,plain,
( spl0_1010
<=> ! [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_1010])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__less__le__mono_0) ).
fof(f20462,plain,
spl0_1009,
inference(avatar_split_clause,[],[f773,f20460]) ).
fof(f20460,plain,
( spl0_1009
<=> ! [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_1009])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__le__less__mono_0) ).
fof(f20458,plain,
spl0_1008,
inference(avatar_split_clause,[],[f736,f20456]) ).
fof(f20456,plain,
( spl0_1008
<=> ! [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_1008])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acyclic__insert_2) ).
fof(f20454,plain,
spl0_1007,
inference(avatar_split_clause,[],[f726,f20452]) ).
fof(f20452,plain,
( spl0_1007
<=> ! [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_1007])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Omul__d_0) ).
fof(f20450,plain,
spl0_1006,
inference(avatar_split_clause,[],[f725,f20448]) ).
fof(f20448,plain,
( spl0_1006
<=> ! [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_1006])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_comm__semiring__class_Odistrib_0) ).
fof(f20446,plain,
( spl0_1005
| ~ spl0_533
| ~ spl0_855 ),
inference(avatar_split_clause,[],[f19802,f14196,f6668,f20444]) ).
fof(f20444,plain,
( spl0_1005
<=> ! [X14] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(c_Relation_OId(X14),X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f6668,plain,
( spl0_533
<=> ! [X2,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f19802,plain,
( ! [X14] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(c_Relation_OId(X14),X14),X14)
| ~ spl0_533
| ~ spl0_855 ),
inference(superposition,[],[f6669,f14197]) ).
fof(f6669,plain,
( ! [X2,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ spl0_533 ),
inference(avatar_component_clause,[],[f6668]) ).
fof(f20442,plain,
spl0_1004,
inference(avatar_split_clause,[],[f724,f20440]) ).
fof(f20440,plain,
( spl0_1004
<=> ! [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_1004])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f20438,plain,
spl0_1003,
inference(avatar_split_clause,[],[f664,f20436]) ).
fof(f20436,plain,
( spl0_1003
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X5)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f664,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X5)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__divide__distrib_0) ).
fof(f20434,plain,
spl0_1002,
inference(avatar_split_clause,[],[f116,f20432]) ).
fof(f20432,plain,
( spl0_1002
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X5)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f116,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X5)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_diff__divide__distrib_0) ).
fof(f20430,plain,
spl0_1001,
inference(avatar_split_clause,[],[f81,f20428]) ).
fof(f20428,plain,
( spl0_1001
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f81,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__divide__eq_0) ).
fof(f20426,plain,
spl0_1000,
inference(avatar_split_clause,[],[f79,f20424]) ).
fof(f20424,plain,
( spl0_1000
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f79,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X5))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X2,X0)
| c_lessequals(X1,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__eq_0) ).
fof(f20283,plain,
( spl0_999
| ~ spl0_527
| ~ spl0_855 ),
inference(avatar_split_clause,[],[f19801,f14196,f6618,f20281]) ).
fof(f6618,plain,
( spl0_527
<=> ! [X2,X1] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Ortrancl(X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f19801,plain,
( ! [X13] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Otrancl(c_Relation_OId(X13),X13),X13)
| ~ spl0_527
| ~ spl0_855 ),
inference(superposition,[],[f6619,f14197]) ).
fof(f6619,plain,
( ! [X2,X1] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ spl0_527 ),
inference(avatar_component_clause,[],[f6618]) ).
fof(f19959,plain,
( spl0_998
| ~ spl0_201
| ~ spl0_987 ),
inference(avatar_split_clause,[],[f19450,f19447,f2344,f19957]) ).
fof(f19957,plain,
( spl0_998
<=> ! [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_998])]) ).
fof(f19447,plain,
( spl0_987
<=> ! [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_987])]) ).
fof(f19450,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_201
| ~ spl0_987 ),
inference(forward_demodulation,[],[f19448,f2346]) ).
fof(f19448,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_987 ),
inference(avatar_component_clause,[],[f19447]) ).
fof(f19494,plain,
spl0_997,
inference(avatar_split_clause,[],[f1194,f19492]) ).
fof(f19492,plain,
( spl0_997
<=> ! [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_997])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_symD_0) ).
fof(f19490,plain,
spl0_996,
inference(avatar_split_clause,[],[f1182,f19488]) ).
fof(f19488,plain,
( spl0_996
<=> ! [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_996])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__asym_0) ).
fof(f19486,plain,
spl0_995,
inference(avatar_split_clause,[],[f1172,f19484]) ).
fof(f19484,plain,
( spl0_995
<=> ! [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_995])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converseD_0) ).
fof(f19482,plain,
spl0_994,
inference(avatar_split_clause,[],[f1071,f19480]) ).
fof(f19480,plain,
( spl0_994
<=> ! [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_994])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converseI_0) ).
fof(f19478,plain,
spl0_993,
inference(avatar_split_clause,[],[f1047,f19476]) ).
fof(f19476,plain,
( spl0_993
<=> ! [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_993])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Image__iff_1) ).
fof(f19474,plain,
spl0_992,
inference(avatar_split_clause,[],[f1046,f19472]) ).
fof(f19472,plain,
( spl0_992
<=> ! [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_992])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_ImageE_0) ).
fof(f19466,plain,
spl0_991,
inference(avatar_split_clause,[],[f942,f19464]) ).
fof(f19464,plain,
( spl0_991
<=> ! [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_991])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__rtrancl__UnI_1) ).
fof(f19462,plain,
spl0_990,
inference(avatar_split_clause,[],[f941,f19460]) ).
fof(f19460,plain,
( spl0_990
<=> ! [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_990])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__rtrancl__UnI_0) ).
fof(f19458,plain,
spl0_989,
inference(avatar_split_clause,[],[f897,f19456]) ).
fof(f19456,plain,
( spl0_989
<=> ! [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_989])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_pos__add__strict_0) ).
fof(f19454,plain,
spl0_988,
inference(avatar_split_clause,[],[f818,f19452]) ).
fof(f19452,plain,
( spl0_988
<=> ! [X38,X4,X0,X3,X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X38),X39))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X38),X39) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f818,axiom,
! [X38,X3,X39,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X38),X39))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X38),X39) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X4) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__eqI_1) ).
fof(f19449,plain,
spl0_987,
inference(avatar_split_clause,[],[f733,f19447]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_one__less__power_0) ).
fof(f19445,plain,
spl0_986,
inference(avatar_split_clause,[],[f689,f19443]) ).
fof(f19443,plain,
( spl0_986
<=> ! [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_986])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__insert_0) ).
fof(f19441,plain,
spl0_985,
inference(avatar_split_clause,[],[f644,f19439]) ).
fof(f19439,plain,
( spl0_985
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f644,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sum__squares__gt__zero__iff_0) ).
fof(f19437,plain,
spl0_984,
inference(avatar_split_clause,[],[f579,f19435]) ).
fof(f19435,plain,
( spl0_984
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f579,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sum__squares__gt__zero__iff_2) ).
fof(f19433,plain,
spl0_983,
inference(avatar_split_clause,[],[f578,f19431]) ).
fof(f19431,plain,
( spl0_983
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f578,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sum__squares__gt__zero__iff_1) ).
fof(f19429,plain,
spl0_982,
inference(avatar_split_clause,[],[f127,f19427]) ).
fof(f19427,plain,
( spl0_982
<=> ! [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_982])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__union__compatible_0) ).
fof(f19395,plain,
spl0_981,
inference(avatar_split_clause,[],[f101,f19393]) ).
fof(f19393,plain,
( spl0_981
<=> ! [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_981])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__Int__assoc__eq_1) ).
fof(f19391,plain,
spl0_980,
inference(avatar_split_clause,[],[f100,f19389]) ).
fof(f19389,plain,
( spl0_980
<=> ! [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_980])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__Int__assoc__eq_0) ).
fof(f17572,plain,
spl0_979,
inference(avatar_split_clause,[],[f1078,f17570]) ).
fof(f17570,plain,
( spl0_979
<=> ! [X4,X0,X3,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))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Not__Domain__rtrancl_0) ).
fof(f17568,plain,
spl0_978,
inference(avatar_split_clause,[],[f981,f17566]) ).
fof(f17566,plain,
( spl0_978
<=> ! [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_978])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__pos_1) ).
fof(f17564,plain,
spl0_977,
inference(avatar_split_clause,[],[f740,f17562]) ).
fof(f17562,plain,
( spl0_977
<=> ! [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_977])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_equiv__class__self_0) ).
fof(f17560,plain,
spl0_976,
inference(avatar_split_clause,[],[f716,f17558]) ).
fof(f17558,plain,
( spl0_976
<=> ! [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_976])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Image__mono_0) ).
fof(f17556,plain,
spl0_975,
inference(avatar_split_clause,[],[f680,f17554]) ).
fof(f17554,plain,
( spl0_975
<=> ! [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_975])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__mono_0) ).
fof(f17552,plain,
spl0_974,
inference(avatar_split_clause,[],[f605,f17550]) ).
fof(f17550,plain,
( spl0_974
<=> ! [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_974])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Compl__Un_0) ).
fof(f17548,plain,
spl0_973,
inference(avatar_split_clause,[],[f587,f17546]) ).
fof(f17546,plain,
( spl0_973
<=> ! [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_973])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Compl__Int_0) ).
fof(f17438,plain,
spl0_972,
inference(avatar_split_clause,[],[f523,f17436]) ).
fof(f17436,plain,
( spl0_972
<=> ! [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_972])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__less__power__Suc_0) ).
fof(f17434,plain,
spl0_971,
inference(avatar_split_clause,[],[f522,f17432]) ).
fof(f17432,plain,
( spl0_971
<=> ! [X0,X14,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),X14,X0) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X1,X14,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f522,axiom,
! [X2,X0,X1,X14] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),X14,X0) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X1,X14,X0)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_nonzero__power__divide_0) ).
fof(f17430,plain,
spl0_970,
inference(avatar_split_clause,[],[f507,f17428]) ).
fof(f17428,plain,
( spl0_970
<=> ! [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_970])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__Int__distrib2_0) ).
fof(f17426,plain,
spl0_969,
inference(avatar_split_clause,[],[f506,f17424]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__Int__distrib_0) ).
fof(f17422,plain,
spl0_968,
inference(avatar_split_clause,[],[f475,f17420]) ).
fof(f17420,plain,
( spl0_968
<=> ! [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_968])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__mono_0) ).
fof(f17418,plain,
spl0_967,
inference(avatar_split_clause,[],[f424,f17416]) ).
fof(f17416,plain,
( spl0_967
<=> ! [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_967])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__pos__nonneg_0) ).
fof(f17414,plain,
spl0_966,
inference(avatar_split_clause,[],[f423,f17412]) ).
fof(f17412,plain,
( spl0_966
<=> ! [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_966])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__nonneg__pos_0) ).
fof(f17410,plain,
spl0_965,
inference(avatar_split_clause,[],[f264,f17408]) ).
fof(f17408,plain,
( spl0_965
<=> ! [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_965])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__right__le__imp__le_0) ).
fof(f17406,plain,
spl0_964,
inference(avatar_split_clause,[],[f263,f17404]) ).
fof(f17404,plain,
( spl0_964
<=> ! [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_964])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__left__le__imp__le_0) ).
fof(f17402,plain,
spl0_963,
inference(avatar_split_clause,[],[f262,f17400]) ).
fof(f17400,plain,
( spl0_963
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__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_963])]) ).
fof(f262,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__le__cancel__left__pos_1) ).
fof(f17334,plain,
spl0_962,
inference(avatar_split_clause,[],[f261,f17332]) ).
fof(f17332,plain,
( spl0_962
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__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_962])]) ).
fof(f261,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__le__cancel__left__pos_0) ).
fof(f17330,plain,
spl0_961,
inference(avatar_split_clause,[],[f260,f17328]) ).
fof(f17328,plain,
( spl0_961
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(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_961])]) ).
fof(f260,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__le__cancel__left__neg_1) ).
fof(f17326,plain,
spl0_960,
inference(avatar_split_clause,[],[f259,f17324]) ).
fof(f17324,plain,
( spl0_960
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(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_960])]) ).
fof(f259,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X5),c_HOL_Ozero__class_Ozero(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__le__cancel__left__neg_0) ).
fof(f17322,plain,
spl0_959,
inference(avatar_split_clause,[],[f251,f17320]) ).
fof(f17320,plain,
( spl0_959
<=> ! [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_959])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__strict__increasing2_0) ).
fof(f17318,plain,
spl0_958,
inference(avatar_split_clause,[],[f235,f17316]) ).
fof(f17316,plain,
( spl0_958
<=> ! [X23,X0,X4,X36,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X23) = X36
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X23)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f235,axiom,
! [X3,X0,X36,X4,X23] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X23) = X36
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X23)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X36) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__cancel__21_0) ).
fof(f17314,plain,
spl0_957,
inference(avatar_split_clause,[],[f205,f17312]) ).
fof(f17312,plain,
( spl0_957
<=> ! [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_957])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__Un__distrib_0) ).
fof(f17310,plain,
spl0_956,
inference(avatar_split_clause,[],[f204,f17308]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__Un__distrib2_0) ).
fof(f17306,plain,
spl0_955,
inference(avatar_split_clause,[],[f182,f17304]) ).
fof(f17304,plain,
( spl0_955
<=> ! [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_955])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__strict__increasing_0) ).
fof(f17302,plain,
spl0_954,
inference(avatar_split_clause,[],[f155,f17300]) ).
fof(f17300,plain,
( spl0_954
<=> ! [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_954])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__neg__nonpos_0) ).
fof(f17298,plain,
spl0_953,
inference(avatar_split_clause,[],[f154,f17296]) ).
fof(f17296,plain,
( spl0_953
<=> ! [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_953])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__nonpos__neg_0) ).
fof(f17238,plain,
spl0_952,
inference(avatar_split_clause,[],[f99,f17236]) ).
fof(f17236,plain,
( spl0_952
<=> ! [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_952])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Image__Int__subset_0) ).
fof(f17234,plain,
spl0_951,
inference(avatar_split_clause,[],[f84,f17232]) ).
fof(f17232,plain,
( spl0_951
<=> ! [X4,X0,X23,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X4),X3,X0)
| c_lessequals(X23,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f84,axiom,
! [X3,X0,X4,X23] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X4),X3,X0)
| c_lessequals(X23,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__imp__le__div__pos_0) ).
fof(f17230,plain,
spl0_950,
inference(avatar_split_clause,[],[f83,f17228]) ).
fof(f17228,plain,
( spl0_950
<=> ! [X4,X0,X23,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| ~ c_lessequals(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X4),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4),X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f83,axiom,
! [X3,X0,X4,X23] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| ~ c_lessequals(X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X23),X4),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4),X23,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__imp__div__pos__le_0) ).
fof(f17226,plain,
spl0_949,
inference(avatar_split_clause,[],[f59,f17224]) ).
fof(f17224,plain,
( spl0_949
<=> ! [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_949])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__Un__subset_0) ).
fof(f16515,plain,
spl0_948,
inference(avatar_split_clause,[],[f1229,f16513]) ).
fof(f16513,plain,
( spl0_948
<=> ! [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_948])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mlex__less_0) ).
fof(f16511,plain,
spl0_947,
inference(avatar_split_clause,[],[f1062,f16509]) ).
fof(f16509,plain,
( spl0_947
<=> ! [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_947])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Range__iff_0) ).
fof(f16507,plain,
spl0_946,
inference(avatar_split_clause,[],[f1061,f16505]) ).
fof(f16505,plain,
( spl0_946
<=> ! [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_946])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_RangeE_0) ).
fof(f16503,plain,
spl0_945,
inference(avatar_split_clause,[],[f1059,f16501]) ).
fof(f16501,plain,
( spl0_945
<=> ! [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_945])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__insert_1) ).
fof(f16499,plain,
spl0_944,
inference(avatar_split_clause,[],[f1050,f16497]) ).
fof(f16497,plain,
( spl0_944
<=> ! [X0,X8,X10,X2] :
( ~ 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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Domain__iff_0) ).
fof(f16495,plain,
spl0_943,
inference(avatar_split_clause,[],[f1049,f16493]) ).
fof(f16493,plain,
( spl0_943
<=> ! [X0,X8,X10,X2] :
( ~ 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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_DomainE_0) ).
fof(f16491,plain,
( spl0_942
| ~ spl0_667
| ~ spl0_924 ),
inference(avatar_split_clause,[],[f16398,f15507,f9403,f16489]) ).
fof(f16489,plain,
( spl0_942
<=> ! [X7] : c_Orderings_Obot__class_Obot(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f15507,plain,
( spl0_924
<=> ! [X2] : c_Orderings_Obot__class_Obot(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f16398,plain,
( ! [X7] : c_Orderings_Obot__class_Obot(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X7,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_667
| ~ spl0_924 ),
inference(superposition,[],[f9404,f15508]) ).
fof(f15508,plain,
( ! [X2] : c_Orderings_Obot__class_Obot(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| ~ spl0_924 ),
inference(avatar_component_clause,[],[f15507]) ).
fof(f16487,plain,
spl0_941,
inference(avatar_split_clause,[],[f1006,f16485]) ).
fof(f16485,plain,
( spl0_941
<=> ! [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_941])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__induct_0) ).
fof(f16483,plain,
spl0_940,
inference(avatar_split_clause,[],[f1005,f16481]) ).
fof(f16481,plain,
( spl0_940
<=> ! [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_940])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_tfl__wf__induct_0) ).
fof(f16479,plain,
spl0_939,
inference(avatar_split_clause,[],[f1004,f16477]) ).
fof(f16477,plain,
( spl0_939
<=> ! [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_939])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__def_0) ).
fof(f16475,plain,
spl0_938,
inference(avatar_split_clause,[],[f1003,f16473]) ).
fof(f16473,plain,
( spl0_938
<=> ! [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_938])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__induct__rule_0) ).
fof(f16471,plain,
spl0_937,
inference(avatar_split_clause,[],[f737,f16469]) ).
fof(f16469,plain,
( spl0_937
<=> ! [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_937])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acyclic__insert_1) ).
fof(f16467,plain,
spl0_936,
inference(avatar_split_clause,[],[f705,f16465]) ).
fof(f16465,plain,
( spl0_936
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f705,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__right__mono_0) ).
fof(f16463,plain,
spl0_935,
inference(avatar_split_clause,[],[f704,f16461]) ).
fof(f16461,plain,
( spl0_935
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f704,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__right__mono__neg_0) ).
fof(f16459,plain,
spl0_934,
inference(avatar_split_clause,[],[f688,f16457]) ).
fof(f16457,plain,
( spl0_934
<=> ! [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_934])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_subset__singletonD_0) ).
fof(f16455,plain,
spl0_933,
inference(avatar_split_clause,[],[f609,f16453]) ).
fof(f16453,plain,
( spl0_933
<=> ! [X4,X0,X23,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),X23) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X23)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f609,axiom,
! [X3,X0,X4,X23] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4)),X23) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X23)),X4) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__frac__num_0) ).
fof(f16451,plain,
spl0_932,
inference(avatar_split_clause,[],[f434,f16449]) ).
fof(f16449,plain,
( spl0_932
<=> ! [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_932])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Sigma__Un__distrib1_0) ).
fof(f16397,plain,
spl0_931,
inference(avatar_split_clause,[],[f336,f16395]) ).
fof(f16395,plain,
( spl0_931
<=> ! [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_931])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_doubleton__eq__iff_3) ).
fof(f16393,plain,
spl0_930,
inference(avatar_split_clause,[],[f334,f16391]) ).
fof(f16391,plain,
( spl0_930
<=> ! [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_930])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_doubleton__eq__iff_1) ).
fof(f16389,plain,
spl0_929,
inference(avatar_split_clause,[],[f230,f16387]) ).
fof(f16387,plain,
( spl0_929
<=> ! [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_929])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__Image_0) ).
fof(f16385,plain,
spl0_928,
inference(avatar_split_clause,[],[f126,f16383]) ).
fof(f16383,plain,
( spl0_928
<=> ! [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_928])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__less__imp__less__base_0) ).
fof(f15554,plain,
( spl0_927
| ~ spl0_201
| ~ spl0_883 ),
inference(avatar_split_clause,[],[f15303,f15299,f2344,f15552]) ).
fof(f15552,plain,
( spl0_927
<=> ! [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_927])]) ).
fof(f15299,plain,
( spl0_883
<=> ! [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_883])]) ).
fof(f15303,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_201
| ~ spl0_883 ),
inference(forward_demodulation,[],[f15302,f2346]) ).
fof(f15302,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_201
| ~ spl0_883 ),
inference(forward_demodulation,[],[f15300,f2346]) ).
fof(f15300,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_883 ),
inference(avatar_component_clause,[],[f15299]) ).
fof(f15517,plain,
spl0_926,
inference(avatar_split_clause,[],[f1231,f15515]) ).
fof(f15515,plain,
( spl0_926
<=> ! [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_926])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__measure_0) ).
fof(f15513,plain,
spl0_925,
inference(avatar_split_clause,[],[f1230,f15511]) ).
fof(f15511,plain,
( spl0_925
<=> ! [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_925])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__measure_1) ).
fof(f15509,plain,
( spl0_924
| ~ spl0_486
| ~ spl0_829 ),
inference(avatar_split_clause,[],[f15434,f13829,f5867,f15507]) ).
fof(f13829,plain,
( spl0_829
<=> ! [X20] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_nat),X20,tc_nat) = X20 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f15434,plain,
( ! [X2] : c_Orderings_Obot__class_Obot(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| ~ spl0_486
| ~ spl0_829 ),
inference(superposition,[],[f5868,f13830]) ).
fof(f13830,plain,
( ! [X20] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_nat),X20,tc_nat) = X20
| ~ spl0_829 ),
inference(avatar_component_clause,[],[f13829]) ).
fof(f15505,plain,
spl0_923,
inference(avatar_split_clause,[],[f1222,f15503]) ).
fof(f15503,plain,
( spl0_923
<=> ! [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_923])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_SigmaD2_0) ).
fof(f15501,plain,
spl0_922,
inference(avatar_split_clause,[],[f1108,f15499]) ).
fof(f15499,plain,
( spl0_922
<=> ! [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_922])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__zero_0) ).
fof(f15497,plain,
spl0_921,
inference(avatar_split_clause,[],[f1043,f15495]) ).
fof(f15495,plain,
( spl0_921
<=> ! [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_921])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__zero__iff_0) ).
fof(f15493,plain,
spl0_920,
inference(avatar_split_clause,[],[f1022,f15491]) ).
fof(f15491,plain,
( spl0_920
<=> ! [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_920])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_of__nat__setsum_0) ).
fof(f15489,plain,
spl0_919,
inference(avatar_split_clause,[],[f974,f15487]) ).
fof(f15487,plain,
( spl0_919
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f974,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__0__1__iff_0) ).
fof(f15485,plain,
spl0_918,
inference(avatar_split_clause,[],[f973,f15483]) ).
fof(f15483,plain,
( spl0_918
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f973,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__less__0__1__iff_1) ).
fof(f15481,plain,
spl0_917,
inference(avatar_split_clause,[],[f927,f15479]) ).
fof(f15479,plain,
( spl0_917
<=> ! [X18,X10,X0,X6] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),c_COMBB(c_HOL_Ouminus__class_Ouminus(X0),X18,X0,X0,X10)),X6) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),X18),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f927,axiom,
! [X10,X0,X18,X6] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),c_COMBB(c_HOL_Ouminus__class_Ouminus(X0),X18,X0,X0,X10)),X6) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_Finite__Set_Osetsum(X10,X0),X18),X6)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__negf_0) ).
fof(f15477,plain,
spl0_916,
inference(avatar_split_clause,[],[f871,f15475]) ).
fof(f15475,plain,
( spl0_916
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f871,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__less__divide__1__iff_1) ).
fof(f15473,plain,
spl0_915,
inference(avatar_split_clause,[],[f870,f15471]) ).
fof(f15471,plain,
( spl0_915
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f870,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__less__divide__1__iff_0) ).
fof(f15469,plain,
spl0_914,
inference(avatar_split_clause,[],[f829,f15467]) ).
fof(f15467,plain,
( spl0_914
<=> ! [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_914])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__strict__right__mono_0) ).
fof(f15432,plain,
spl0_913,
inference(avatar_split_clause,[],[f828,f15430]) ).
fof(f15430,plain,
( spl0_913
<=> ! [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_913])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__less__cancel__right_1) ).
fof(f15428,plain,
spl0_912,
inference(avatar_split_clause,[],[f827,f15426]) ).
fof(f15426,plain,
( spl0_912
<=> ! [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_912])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__less__cancel__right_0) ).
fof(f15424,plain,
spl0_911,
inference(avatar_split_clause,[],[f826,f15422]) ).
fof(f15422,plain,
( spl0_911
<=> ! [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_911])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__strict__left__mono_0) ).
fof(f15420,plain,
spl0_910,
inference(avatar_split_clause,[],[f825,f15418]) ).
fof(f15418,plain,
( spl0_910
<=> ! [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_910])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__less__cancel__left_1) ).
fof(f15416,plain,
spl0_909,
inference(avatar_split_clause,[],[f824,f15414]) ).
fof(f15414,plain,
( spl0_909
<=> ! [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_909])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__less__cancel__left_0) ).
fof(f15412,plain,
spl0_908,
inference(avatar_split_clause,[],[f808,f15410]) ).
fof(f15410,plain,
( spl0_908
<=> ! [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_908])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__ident_0) ).
fof(f15408,plain,
spl0_907,
inference(avatar_split_clause,[],[f798,f15406]) ).
fof(f15406,plain,
( spl0_907
<=> ! [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_907])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_UnE_0) ).
fof(f15404,plain,
spl0_906,
inference(avatar_split_clause,[],[f783,f15402]) ).
fof(f15402,plain,
( spl0_906
<=> ! [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_906])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__iff_2) ).
fof(f15400,plain,
spl0_905,
inference(avatar_split_clause,[],[f477,f15398]) ).
fof(f15398,plain,
( spl0_905
<=> ! [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_905])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__Un_0) ).
fof(f15396,plain,
spl0_904,
inference(avatar_split_clause,[],[f450,f15394]) ).
fof(f15394,plain,
( spl0_904
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X3),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f450,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X3),X3,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__left__le__one__le_0) ).
fof(f15383,plain,
spl0_903,
inference(avatar_split_clause,[],[f449,f15381]) ).
fof(f15381,plain,
( spl0_903
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X4),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f449,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X4),X3,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__right__le__one__le_0) ).
fof(f15379,plain,
spl0_902,
inference(avatar_split_clause,[],[f413,f15377]) ).
fof(f15377,plain,
( spl0_902
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f413,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sum__squares__le__zero__iff_1) ).
fof(f15375,plain,
spl0_901,
inference(avatar_split_clause,[],[f412,f15373]) ).
fof(f15373,plain,
( spl0_901
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f412,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sum__squares__le__zero__iff_0) ).
fof(f15371,plain,
spl0_900,
inference(avatar_split_clause,[],[f371,f15369]) ).
fof(f15369,plain,
( spl0_900
<=> ! [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_900])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__insert__right_0) ).
fof(f15367,plain,
spl0_899,
inference(avatar_split_clause,[],[f370,f15365]) ).
fof(f15365,plain,
( spl0_899
<=> ! [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_899])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__insert__left_0) ).
fof(f15363,plain,
spl0_898,
inference(avatar_split_clause,[],[f305,f15361]) ).
fof(f15361,plain,
( spl0_898
<=> ! [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_898])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__gt1__lemma_0) ).
fof(f15359,plain,
spl0_897,
inference(avatar_split_clause,[],[f304,f15357]) ).
fof(f15357,plain,
( spl0_897
<=> ! [X0,X14,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),X14,X0) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X1,X14,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f304,axiom,
! [X2,X0,X1,X14] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),X14,X0) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_Power_Opower__class_Opower(X2,X14,X0)),c_Power_Opower__class_Opower(X1,X14,X0)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__divide_0) ).
fof(f15355,plain,
spl0_896,
inference(avatar_split_clause,[],[f281,f15353]) ).
fof(f15353,plain,
( spl0_896
<=> ! [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_896])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(f15351,plain,
spl0_895,
inference(avatar_split_clause,[],[f280,f15349]) ).
fof(f15349,plain,
( spl0_895
<=> ! [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_895])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(f15347,plain,
spl0_894,
inference(avatar_split_clause,[],[f246,f15345]) ).
fof(f15345,plain,
( spl0_894
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0)),X5) = c_Lattices_Olower__semilattice__class_Oinf(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_894])]) ).
fof(f246,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0)),X5) = c_Lattices_Olower__semilattice__class_Oinf(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).
fof(f15343,plain,
( ~ spl0_33
| spl0_893
| ~ spl0_204
| ~ spl0_479 ),
inference(avatar_split_clause,[],[f15222,f5757,f2357,f15341,f1522]) ).
fof(f1522,plain,
( spl0_33
<=> class_Ring__and__Field_Odvd(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f2357,plain,
( spl0_204
<=> ! [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_204])]) ).
fof(f5757,plain,
( spl0_479
<=> ! [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_479])]) ).
fof(f15222,plain,
( ! [X29] :
( c_Ring__and__Field_Odvd__class_Odvd(X29,X29,tc_nat)
| ~ class_Ring__and__Field_Odvd(tc_nat) )
| ~ spl0_204
| ~ spl0_479 ),
inference(superposition,[],[f2358,f5758]) ).
fof(f5758,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)) = X0
| ~ spl0_479 ),
inference(avatar_component_clause,[],[f5757]) ).
fof(f2358,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_204 ),
inference(avatar_component_clause,[],[f2357]) ).
fof(f15339,plain,
spl0_892,
inference(avatar_split_clause,[],[f245,f15337]) ).
fof(f15337,plain,
( spl0_892
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f245,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).
fof(f15335,plain,
spl0_891,
inference(avatar_split_clause,[],[f244,f15333]) ).
fof(f15333,plain,
( spl0_891
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0)),X5) = c_Lattices_Olower__semilattice__class_Oinf(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_891])]) ).
fof(f244,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0)),X5) = c_Lattices_Olower__semilattice__class_Oinf(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__inf__distrib__right_0) ).
fof(f15331,plain,
spl0_890,
inference(avatar_split_clause,[],[f243,f15329]) ).
fof(f15329,plain,
( spl0_890
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f243,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_Lattices_Olower__semilattice__class_Oinf(X1,X5,X0)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__inf__distrib__left_0) ).
fof(f15327,plain,
spl0_889,
inference(avatar_split_clause,[],[f215,f15325]) ).
fof(f15325,plain,
( spl0_889
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0)),X5) = c_Lattices_Oupper__semilattice__class_Osup(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_889])]) ).
fof(f215,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0)),X5) = c_Lattices_Oupper__semilattice__class_Osup(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).
fof(f15323,plain,
spl0_888,
inference(avatar_split_clause,[],[f214,f15321]) ).
fof(f15321,plain,
( spl0_888
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f214,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).
fof(f15319,plain,
spl0_887,
inference(avatar_split_clause,[],[f213,f15317]) ).
fof(f15317,plain,
( spl0_887
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0)),X5) = c_Lattices_Oupper__semilattice__class_Osup(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_887])]) ).
fof(f213,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0)),X5) = c_Lattices_Oupper__semilattice__class_Osup(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__sup__distrib__right_0) ).
fof(f15315,plain,
spl0_886,
inference(avatar_split_clause,[],[f212,f15313]) ).
fof(f15313,plain,
( spl0_886
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f212,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),c_Lattices_Oupper__semilattice__class_Osup(X1,X5,X0)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__sup__distrib__left_0) ).
fof(f15311,plain,
spl0_885,
inference(avatar_split_clause,[],[f157,f15309]) ).
fof(f15309,plain,
( spl0_885
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f157,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sum__squares__le__zero__iff_2) ).
fof(f15307,plain,
spl0_884,
inference(avatar_split_clause,[],[f73,f15305]) ).
fof(f15305,plain,
( spl0_884
<=> ! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oring__1(X0)
| c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X14,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Oone__class_Oone(X0)),X14,X0)),c_Power_Opower__class_Opower(X2,X14,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f73,axiom,
! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oring__1(X0)
| c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X14,X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Oone__class_Oone(X0)),X14,X0)),c_Power_Opower__class_Opower(X2,X14,X0)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__minus_0) ).
fof(f15301,plain,
spl0_883,
inference(avatar_split_clause,[],[f43,f15299]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__eq__0__iff_0) ).
fof(f15205,plain,
spl0_882,
inference(avatar_split_clause,[],[f26,f15203]) ).
fof(f15203,plain,
( spl0_882
<=> ! [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_882])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__decreasing_0) ).
fof(f14819,plain,
( ~ spl0_33
| spl0_881
| ~ spl0_204
| ~ spl0_468 ),
inference(avatar_split_clause,[],[f14490,f5712,f2357,f14817,f1522]) ).
fof(f14817,plain,
( spl0_881
<=> ! [X23] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X23,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f5712,plain,
( spl0_468
<=> ! [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_468])]) ).
fof(f14490,plain,
( ! [X23] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X23,tc_nat)
| ~ class_Ring__and__Field_Odvd(tc_nat) )
| ~ spl0_204
| ~ spl0_468 ),
inference(superposition,[],[f2358,f5713]) ).
fof(f5713,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) = X0
| ~ spl0_468 ),
inference(avatar_component_clause,[],[f5712]) ).
fof(f14298,plain,
spl0_880,
inference(avatar_split_clause,[],[f1185,f14296]) ).
fof(f14296,plain,
( spl0_880
<=> ! [X18,X23,X0,X4,X10,X8] :
( ~ c_Equiv__Relations_Ocongruent(X8,X18,X0,X10)
| hAPP(X18,X4) = hAPP(X18,X23)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,X23,X0,X0)),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f1185,axiom,
! [X10,X0,X18,X8,X4,X23] :
( ~ c_Equiv__Relations_Ocongruent(X8,X18,X0,X10)
| hAPP(X18,X4) = hAPP(X18,X23)
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X4,X23,X0,X0)),X8)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_congruent_Ocongruent_0) ).
fof(f14294,plain,
spl0_879,
inference(avatar_split_clause,[],[f1073,f14292]) ).
fof(f14292,plain,
( spl0_879
<=> ! [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_879])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_tfl__cut__apply_0) ).
fof(f14290,plain,
spl0_878,
inference(avatar_split_clause,[],[f1054,f14288]) ).
fof(f14288,plain,
( spl0_878
<=> ! [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_878])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc_OaccI_0) ).
fof(f14286,plain,
( spl0_877
| ~ spl0_249
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f4949,f4107,f2550,f14284]) ).
fof(f14284,plain,
( spl0_877
<=> ! [X2,X3] : hBOOL(hAPP(c_Relation_OId(X2),c_Pair(X3,X3,X2,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f2550,plain,
( spl0_249
<=> ! [X22,X0,X3] :
( hBOOL(hAPP(X22,X3))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f4107,plain,
( spl0_397
<=> ! [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_397])]) ).
fof(f4949,plain,
( ! [X2,X3] : hBOOL(hAPP(c_Relation_OId(X2),c_Pair(X3,X3,X2,X2)))
| ~ spl0_249
| ~ spl0_397 ),
inference(resolution,[],[f4108,f2551]) ).
fof(f2551,plain,
( ! [X3,X0,X22] :
( ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X22))
| hBOOL(hAPP(X22,X3)) )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2550]) ).
fof(f4108,plain,
( ! [X2,X0] : hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X2,X2,X0,X0)),c_Relation_OId(X0)))
| ~ spl0_397 ),
inference(avatar_component_clause,[],[f4107]) ).
fof(f14282,plain,
spl0_876,
inference(avatar_split_clause,[],[f1051,f14280]) ).
fof(f14280,plain,
( spl0_876
<=> ! [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_876])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_not__acc__down_0) ).
fof(f14278,plain,
spl0_875,
inference(avatar_split_clause,[],[f1040,f14276]) ).
fof(f14276,plain,
( spl0_875
<=> ! [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_875])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__pos_0) ).
fof(f14274,plain,
spl0_874,
inference(avatar_split_clause,[],[f1036,f14272]) ).
fof(f14272,plain,
( spl0_874
<=> ! [X59,X10,X58,X0,X18,X6,X25,X2] :
( ~ c_Equiv__Relations_Oequiv(X6,X59,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| ~ c_Equiv__Relations_Ocongruent2(X59,X58,X18,X0,X10,X25)
| c_Equiv__Relations_Ocongruent(X58,hAPP(X18,X2),X10,X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f1036,axiom,
! [X2,X58,X10,X59,X0,X18,X6,X25] :
( ~ c_Equiv__Relations_Oequiv(X6,X59,X0)
| ~ hBOOL(hAPP(hAPP(c_in(X0),X2),X6))
| ~ c_Equiv__Relations_Ocongruent2(X59,X58,X18,X0,X10,X25)
| c_Equiv__Relations_Ocongruent(X58,hAPP(X18,X2),X10,X25) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_congruent2__implies__congruent_0) ).
fof(f14270,plain,
spl0_873,
inference(avatar_split_clause,[],[f989,f14268]) ).
fof(f14268,plain,
( spl0_873
<=> ! [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_873])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_SigmaE_0) ).
fof(f14266,plain,
spl0_872,
inference(avatar_split_clause,[],[f988,f14264]) ).
fof(f14264,plain,
( spl0_872
<=> ! [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_872])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__zero__iff_1) ).
fof(f14262,plain,
spl0_871,
inference(avatar_split_clause,[],[f955,f14260]) ).
fof(f14260,plain,
( spl0_871
<=> ! [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_871])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc__induct_0) ).
fof(f14258,plain,
spl0_870,
inference(avatar_split_clause,[],[f950,f14256]) ).
fof(f14256,plain,
( spl0_870
<=> ! [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_870])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc__induct__rule_0) ).
fof(f14254,plain,
spl0_869,
inference(avatar_split_clause,[],[f775,f14252]) ).
fof(f14252,plain,
( spl0_869
<=> ! [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_869])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__Int_0) ).
fof(f14250,plain,
spl0_868,
inference(avatar_split_clause,[],[f722,f14248]) ).
fof(f14248,plain,
( spl0_868
<=> ! [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_868])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f14246,plain,
spl0_867,
inference(avatar_split_clause,[],[f721,f14244]) ).
fof(f14244,plain,
( spl0_867
<=> ! [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_867])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(f14242,plain,
( spl0_866
| ~ spl0_283
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f3824,f3362,f3106,f14240]) ).
fof(f14240,plain,
( spl0_866
<=> ! [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_866])]) ).
fof(f3106,plain,
( spl0_283
<=> ! [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_283])]) ).
fof(f3362,plain,
( spl0_335
<=> ! [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_335])]) ).
fof(f3824,plain,
( ! [X0,X1] :
( c_Finite__Set_Ofinite(X0,X1)
| c_Finite__Set_Ocard(X0,X1) = c_Orderings_Obot__class_Obot(tc_nat) )
| ~ spl0_283
| ~ spl0_335 ),
inference(resolution,[],[f3363,f3107]) ).
fof(f3107,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_283 ),
inference(avatar_component_clause,[],[f3106]) ).
fof(f3363,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_335 ),
inference(avatar_component_clause,[],[f3362]) ).
fof(f14238,plain,
spl0_865,
inference(avatar_split_clause,[],[f719,f14236]) ).
fof(f14236,plain,
( spl0_865
<=> ! [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_865])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f14234,plain,
spl0_864,
inference(avatar_split_clause,[],[f718,f14232]) ).
fof(f14232,plain,
( spl0_864
<=> ! [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_864])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f14230,plain,
spl0_863,
inference(avatar_split_clause,[],[f690,f14228]) ).
fof(f14228,plain,
( spl0_863
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f690,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sum__squares__eq__zero__iff_2) ).
fof(f14226,plain,
spl0_862,
inference(avatar_split_clause,[],[f682,f14224]) ).
fof(f14224,plain,
( spl0_862
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f682,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__nonpos__pos_0) ).
fof(f14222,plain,
spl0_861,
inference(avatar_split_clause,[],[f681,f14220]) ).
fof(f14220,plain,
( spl0_861
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),c_HOL_Ozero__class_Ozero(X0)))
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f681,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),c_HOL_Ozero__class_Ozero(X0)))
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__nonneg__neg_0) ).
fof(f14218,plain,
spl0_860,
inference(avatar_split_clause,[],[f614,f14216]) ).
fof(f14216,plain,
( spl0_860
<=> ! [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_860])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__Un__rtrancl_0) ).
fof(f14214,plain,
spl0_859,
inference(avatar_split_clause,[],[f610,f14212]) ).
fof(f14212,plain,
( spl0_859
<=> ! [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_859])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__Un_0) ).
fof(f14210,plain,
spl0_858,
inference(avatar_split_clause,[],[f573,f14208]) ).
fof(f14208,plain,
( spl0_858
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f573,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_nonzero__minus__divide__divide_0) ).
fof(f14206,plain,
spl0_857,
inference(avatar_split_clause,[],[f534,f14204]) ).
fof(f14204,plain,
( spl0_857
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f534,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sum__squares__eq__zero__iff_0) ).
fof(f14202,plain,
spl0_856,
inference(avatar_split_clause,[],[f533,f14200]) ).
fof(f14200,plain,
( spl0_856
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f533,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sum__squares__eq__zero__iff_1) ).
fof(f14198,plain,
( spl0_855
| ~ spl0_148
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3117,f2833,f2013,f14196]) ).
fof(f2013,plain,
( spl0_148
<=> ! [X10,X0,X15] : c_Relation_Orel__comp(X15,c_Relation_OId(X10),X0,X10,X10) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f2833,plain,
( spl0_279
<=> ! [X0,X8] : c_Transitive__Closure_Otrancl(X8,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X8,X0),X8,X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f3117,plain,
( ! [X2] : c_Transitive__Closure_Ortrancl(c_Relation_OId(X2),X2) = c_Transitive__Closure_Otrancl(c_Relation_OId(X2),X2)
| ~ spl0_148
| ~ spl0_279 ),
inference(superposition,[],[f2834,f2014]) ).
fof(f2014,plain,
( ! [X10,X0,X15] : c_Relation_Orel__comp(X15,c_Relation_OId(X10),X0,X10,X10) = X15
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f2013]) ).
fof(f2834,plain,
( ! [X0,X8] : c_Transitive__Closure_Otrancl(X8,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X8,X0),X8,X0,X0,X0)
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f2833]) ).
fof(f14194,plain,
spl0_854,
inference(avatar_split_clause,[],[f529,f14192]) ).
fof(f14192,plain,
( spl0_854
<=> ! [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_854])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__mono1_0) ).
fof(f14190,plain,
spl0_853,
inference(avatar_split_clause,[],[f528,f14188]) ).
fof(f14188,plain,
( spl0_853
<=> ! [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_853])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__left__mono_0) ).
fof(f14186,plain,
spl0_852,
inference(avatar_split_clause,[],[f527,f14184]) ).
fof(f14184,plain,
( spl0_852
<=> ! [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_852])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__right__mono_0) ).
fof(f14182,plain,
spl0_851,
inference(avatar_split_clause,[],[f526,f14180]) ).
fof(f14180,plain,
( spl0_851
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),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_851])]) ).
fof(f526,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__left__mono__neg_0) ).
fof(f14178,plain,
spl0_850,
inference(avatar_split_clause,[],[f525,f14176]) ).
fof(f14176,plain,
( spl0_850
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),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_850])]) ).
fof(f525,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X0),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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__right__mono__neg_0) ).
fof(f14174,plain,
spl0_849,
inference(avatar_split_clause,[],[f452,f14172]) ).
fof(f14172,plain,
( spl0_849
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f452,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X4))
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__nonneg__pos_0) ).
fof(f14170,plain,
spl0_848,
inference(avatar_split_clause,[],[f451,f14168]) ).
fof(f14168,plain,
( spl0_848
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),c_HOL_Ozero__class_Ozero(X0)))
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f451,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),c_HOL_Ozero__class_Ozero(X0)))
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X4),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__nonpos__neg_0) ).
fof(f14166,plain,
spl0_847,
inference(avatar_split_clause,[],[f399,f14164]) ).
fof(f14164,plain,
( spl0_847
<=> ! [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_847])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__subset_0) ).
fof(f14162,plain,
spl0_846,
inference(avatar_split_clause,[],[f284,f14160]) ).
fof(f14160,plain,
( spl0_846
<=> ! [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_846])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_disjoint__iff__not__equal_0) ).
fof(f14158,plain,
spl0_845,
inference(avatar_split_clause,[],[f231,f14156]) ).
fof(f14156,plain,
( spl0_845
<=> ! [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_845])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Image__Un_0) ).
fof(f14154,plain,
( spl0_844
| ~ spl0_249
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f3109,f2825,f2550,f14152]) ).
fof(f14152,plain,
( spl0_844
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f2825,plain,
( spl0_277
<=> ! [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_277])]) ).
fof(f3109,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| hBOOL(hAPP(c_Wellfounded_Oacc(X0,X1),X2)) )
| ~ spl0_249
| ~ spl0_277 ),
inference(resolution,[],[f2826,f2551]) ).
fof(f2826,plain,
( ! [X3,X0,X8] :
( hBOOL(hAPP(hAPP(c_in(X0),X3),c_Wellfounded_Oacc(X8,X0)))
| ~ c_Wellfounded_Owf(X8,X0) )
| ~ spl0_277 ),
inference(avatar_component_clause,[],[f2825]) ).
fof(f14150,plain,
spl0_843,
inference(avatar_split_clause,[],[f228,f14148]) ).
fof(f14148,plain,
( spl0_843
<=> ! [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_843])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f14146,plain,
spl0_842,
inference(avatar_split_clause,[],[f227,f14144]) ).
fof(f14144,plain,
( spl0_842
<=> ! [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_842])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f14142,plain,
spl0_841,
inference(avatar_split_clause,[],[f226,f14140]) ).
fof(f14140,plain,
( spl0_841
<=> ! [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_841])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(f14138,plain,
spl0_840,
inference(avatar_split_clause,[],[f225,f14136]) ).
fof(f14136,plain,
( spl0_840
<=> ! [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_840])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f14134,plain,
spl0_839,
inference(avatar_split_clause,[],[f224,f14132]) ).
fof(f14132,plain,
( spl0_839
<=> ! [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_839])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f14130,plain,
spl0_838,
inference(avatar_split_clause,[],[f223,f14128]) ).
fof(f14128,plain,
( spl0_838
<=> ! [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_838])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f14126,plain,
spl0_837,
inference(avatar_split_clause,[],[f222,f14124]) ).
fof(f14124,plain,
( spl0_837
<=> ! [X4,X0,X23,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X23)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X23)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f222,axiom,
! [X3,X0,X4,X23] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X23)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X23)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__cancel__21_1) ).
fof(f14122,plain,
spl0_836,
inference(avatar_split_clause,[],[f191,f14120]) ).
fof(f14120,plain,
( spl0_836
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f191,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_nonzero__minus__divide__right_0) ).
fof(f14118,plain,
spl0_835,
inference(avatar_split_clause,[],[f188,f14116]) ).
fof(f14116,plain,
( spl0_835
<=> ! [X2,X0,X14] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),c_Power_Opower__class_Opower(X2,X14,X0)) = c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X2),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f188,axiom,
! [X2,X0,X14] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),c_Power_Opower__class_Opower(X2,X14,X0)) = c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X2),X14,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__one__over_0) ).
fof(f14114,plain,
spl0_834,
inference(avatar_split_clause,[],[f143,f14112]) ).
fof(f14112,plain,
( spl0_834
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4))),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f143,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4))),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_not__sum__squares__lt__zero_0) ).
fof(f14110,plain,
( spl0_833
| ~ spl0_57
| ~ spl0_201
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3068,f2799,f2344,f1638,f14108]) ).
fof(f14108,plain,
( spl0_833
<=> ! [X2,X3] :
( ~ c_lessequals(X2,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| c_lessequals(X2,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f1638,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(f2799,plain,
( spl0_271
<=> ! [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_271])]) ).
fof(f3068,plain,
( ! [X2,X3] :
( ~ c_lessequals(X2,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| c_lessequals(X2,X3,tc_nat) )
| ~ spl0_57
| ~ spl0_201
| ~ spl0_271 ),
inference(forward_demodulation,[],[f3047,f2346]) ).
fof(f3047,plain,
( ! [X2,X3] :
( ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_lessequals(X2,X3,tc_nat) )
| ~ spl0_57
| ~ spl0_271 ),
inference(resolution,[],[f2800,f1639]) ).
fof(f1639,plain,
( ! [X14] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1638]) ).
fof(f2800,plain,
( ! [X31,X46,X45] :
( ~ c_lessequals(X46,X31,tc_nat)
| ~ c_lessequals(X45,X46,tc_nat)
| c_lessequals(X45,X31,tc_nat) )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f2799]) ).
fof(f14106,plain,
spl0_832,
inference(avatar_split_clause,[],[f113,f14104]) ).
fof(f14104,plain,
( spl0_832
<=> ! [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_832])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__nonneg__eq__0__iff_0) ).
fof(f14102,plain,
spl0_831,
inference(avatar_split_clause,[],[f112,f14100]) ).
fof(f14100,plain,
( spl0_831
<=> ! [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_831])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__nonneg__eq__0__iff_1) ).
fof(f14098,plain,
spl0_830,
inference(avatar_split_clause,[],[f102,f14096]) ).
fof(f14096,plain,
( spl0_830
<=> ! [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_830])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__dvd__setprod__subset_0) ).
fof(f13831,plain,
( ~ spl0_21
| spl0_829
| ~ spl0_57
| ~ spl0_201
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2952,f2767,f2344,f1638,f13829,f1462]) ).
fof(f2767,plain,
( spl0_263
<=> ! [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_263])]) ).
fof(f2952,plain,
( ! [X20] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_nat),X20,tc_nat) = X20
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_57
| ~ spl0_201
| ~ spl0_263 ),
inference(forward_demodulation,[],[f2927,f2346]) ).
fof(f2927,plain,
( ! [X20] :
( ~ class_Lattices_Oupper__semilattice(tc_nat)
| c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ozero__class_Ozero(tc_nat),X20,tc_nat) = X20 )
| ~ spl0_57
| ~ spl0_263 ),
inference(resolution,[],[f2768,f1639]) ).
fof(f2768,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_263 ),
inference(avatar_component_clause,[],[f2767]) ).
fof(f13299,plain,
( ~ spl0_21
| spl0_828
| ~ spl0_57
| ~ spl0_201
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2902,f2759,f2344,f1638,f13297,f1462]) ).
fof(f13297,plain,
( spl0_828
<=> ! [X20] : c_Lattices_Oupper__semilattice__class_Osup(X20,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X20 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f2759,plain,
( spl0_261
<=> ! [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_261])]) ).
fof(f2902,plain,
( ! [X20] :
( c_Lattices_Oupper__semilattice__class_Osup(X20,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X20
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_57
| ~ spl0_201
| ~ spl0_261 ),
inference(forward_demodulation,[],[f2878,f2346]) ).
fof(f2878,plain,
( ! [X20] :
( ~ class_Lattices_Oupper__semilattice(tc_nat)
| c_Lattices_Oupper__semilattice__class_Osup(X20,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X20 )
| ~ spl0_57
| ~ spl0_261 ),
inference(resolution,[],[f2760,f1639]) ).
fof(f2760,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_261 ),
inference(avatar_component_clause,[],[f2759]) ).
fof(f13295,plain,
spl0_827,
inference(avatar_split_clause,[],[f1228,f13293]) ).
fof(f13293,plain,
( spl0_827
<=> ! [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_827])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_refl__onD_0) ).
fof(f13291,plain,
spl0_826,
inference(avatar_split_clause,[],[f1227,f13289]) ).
fof(f13289,plain,
( spl0_826
<=> ! [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_826])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_refl__onD1_0) ).
fof(f13287,plain,
spl0_825,
inference(avatar_split_clause,[],[f1226,f13285]) ).
fof(f13285,plain,
( spl0_825
<=> ! [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_825])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_refl__onD2_0) ).
fof(f13283,plain,
spl0_824,
inference(avatar_split_clause,[],[f1223,f13281]) ).
fof(f13281,plain,
( spl0_824
<=> ! [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_824])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_SigmaD1_0) ).
fof(f13279,plain,
spl0_823,
inference(avatar_split_clause,[],[f1217,f13277]) ).
fof(f13277,plain,
( spl0_823
<=> ! [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_823])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_equiv__class__eq__iff_1) ).
fof(f13275,plain,
spl0_822,
inference(avatar_split_clause,[],[f1216,f13273]) ).
fof(f13273,plain,
( spl0_822
<=> ! [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_822])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_equiv__class__eq__iff_2) ).
fof(f13271,plain,
spl0_821,
inference(avatar_split_clause,[],[f1101,f13269]) ).
fof(f13269,plain,
( spl0_821
<=> ! [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_821])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_pred__equals__eq_0) ).
fof(f13267,plain,
spl0_820,
inference(avatar_split_clause,[],[f1027,f13265]) ).
fof(f13265,plain,
( spl0_820
<=> ! [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_820])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Id__onE_1) ).
fof(f13263,plain,
spl0_819,
inference(avatar_split_clause,[],[f1025,f13261]) ).
fof(f13261,plain,
( spl0_819
<=> ! [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_819])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_of__nat__setprod_0) ).
fof(f13259,plain,
spl0_818,
inference(avatar_split_clause,[],[f728,f13257]) ).
fof(f13257,plain,
( spl0_818
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f728,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__add_0) ).
fof(f13255,plain,
( spl0_817
| ~ spl0_208
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2680,f2482,f2373,f13253]) ).
fof(f13253,plain,
( spl0_817
<=> ! [X2,X3] :
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f2373,plain,
( spl0_208
<=> ! [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_208])]) ).
fof(f2482,plain,
( spl0_233
<=> ! [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_233])]) ).
fof(f2680,plain,
( ! [X2,X3] :
( c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),X3) )
| ~ spl0_208
| ~ spl0_233 ),
inference(superposition,[],[f2483,f2374]) ).
fof(f2374,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_208 ),
inference(avatar_component_clause,[],[f2373]) ).
fof(f2483,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_233 ),
inference(avatar_component_clause,[],[f2482]) ).
fof(f13251,plain,
spl0_816,
inference(avatar_split_clause,[],[f727,f13249]) ).
fof(f13249,plain,
( spl0_816
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f727,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__add__distrib_0) ).
fof(f13247,plain,
spl0_815,
inference(avatar_split_clause,[],[f697,f13245]) ).
fof(f13245,plain,
( spl0_815
<=> ! [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_815])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Opwr__mul_0) ).
fof(f13243,plain,
spl0_814,
inference(avatar_split_clause,[],[f696,f13241]) ).
fof(f13241,plain,
( spl0_814
<=> ! [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_814])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__mult__distrib_0) ).
fof(f13239,plain,
spl0_813,
inference(avatar_split_clause,[],[f678,f13237]) ).
fof(f13237,plain,
( spl0_813
<=> ! [X2,X0,X12,X5,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X5,X12,X0)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5),X0)
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X12),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f678,axiom,
! [X2,X0,X1,X5,X12] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X5,X12,X0)
| ~ c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X5),X0)
| c_lessequals(X2,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X12),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__add__right__mono_0) ).
fof(f13235,plain,
spl0_812,
inference(avatar_split_clause,[],[f660,f13233]) ).
fof(f13233,plain,
( spl0_812
<=> ! [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_812])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__increasing__iff_1) ).
fof(f13231,plain,
spl0_811,
inference(avatar_split_clause,[],[f659,f13229]) ).
fof(f13229,plain,
( spl0_811
<=> ! [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_811])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__increasing__iff_0) ).
fof(f13227,plain,
spl0_810,
inference(avatar_split_clause,[],[f635,f13225]) ).
fof(f13225,plain,
( spl0_810
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,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),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f635,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,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),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__mult__cancel__right_0) ).
fof(f13223,plain,
spl0_809,
inference(avatar_split_clause,[],[f634,f13221]) ).
fof(f13221,plain,
( spl0_809
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(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_809])]) ).
fof(f634,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__mult__cancel__left_0) ).
fof(f13219,plain,
spl0_808,
inference(avatar_split_clause,[],[f595,f13217]) ).
fof(f13217,plain,
( spl0_808
<=> ! [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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Domain__Un__eq_0) ).
fof(f13215,plain,
spl0_807,
inference(avatar_split_clause,[],[f535,f13213]) ).
fof(f13213,plain,
( spl0_807
<=> ! [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_807])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Range__Un__eq_0) ).
fof(f13211,plain,
( spl0_806
| ~ spl0_45
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2677,f2473,f1582,f13209]) ).
fof(f13209,plain,
( spl0_806
<=> ! [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_806])]) ).
fof(f2473,plain,
( spl0_231
<=> ! [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_231])]) ).
fof(f2677,plain,
( ! [X0] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X0)) = X0
| ~ spl0_45
| ~ spl0_231 ),
inference(resolution,[],[f2474,f1584]) ).
fof(f2474,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_231 ),
inference(avatar_component_clause,[],[f2473]) ).
fof(f13207,plain,
spl0_805,
inference(avatar_split_clause,[],[f524,f13205]) ).
fof(f13205,plain,
( spl0_805
<=> ! [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_805])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__dvd__mono_0) ).
fof(f13203,plain,
spl0_804,
inference(avatar_split_clause,[],[f330,f13201]) ).
fof(f13201,plain,
( spl0_804
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f330,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__divide__iff_5) ).
fof(f13199,plain,
spl0_803,
inference(avatar_split_clause,[],[f329,f13197]) ).
fof(f13197,plain,
( spl0_803
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(X0),X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f329,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(X0),X2),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__divide__iff_4) ).
fof(f13195,plain,
spl0_802,
inference(avatar_split_clause,[],[f250,f13193]) ).
fof(f13193,plain,
( spl0_802
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f250,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__divide__iff_0) ).
fof(f13191,plain,
spl0_801,
inference(avatar_split_clause,[],[f249,f13189]) ).
fof(f13189,plain,
( spl0_801
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f249,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__divide__iff_1) ).
fof(f13187,plain,
spl0_800,
inference(avatar_split_clause,[],[f248,f13185]) ).
fof(f13185,plain,
( spl0_800
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f248,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__divide__iff_2) ).
fof(f13183,plain,
spl0_799,
inference(avatar_split_clause,[],[f247,f13181]) ).
fof(f13181,plain,
( spl0_799
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f247,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__divide__iff_3) ).
fof(f13179,plain,
spl0_798,
inference(avatar_split_clause,[],[f203,f13177]) ).
fof(f13177,plain,
( spl0_798
<=> ! [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_798])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__mono_0) ).
fof(f13175,plain,
spl0_797,
inference(avatar_split_clause,[],[f200,f13173]) ).
fof(f13173,plain,
( spl0_797
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Ozero__class_Ozero(X0)))
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2) = c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f200,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Ozero__class_Ozero(X0)))
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2) = c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__eq__if_0) ).
fof(f13171,plain,
spl0_796,
inference(avatar_split_clause,[],[f135,f13169]) ).
fof(f13169,plain,
( spl0_796
<=> ! [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_796])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_refl__on__Un_0) ).
fof(f13167,plain,
( spl0_795
| ~ spl0_19
| ~ spl0_201
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2668,f2453,f2344,f1452,f13165]) ).
fof(f13165,plain,
( spl0_795
<=> ! [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_795])]) ).
fof(f1452,plain,
( spl0_19
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f2453,plain,
( spl0_226
<=> ! [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_226])]) ).
fof(f2668,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat)) = X0
| ~ spl0_19
| ~ spl0_201
| ~ spl0_226 ),
inference(forward_demodulation,[],[f2667,f2346]) ).
fof(f2667,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = X0
| ~ spl0_19
| ~ spl0_226 ),
inference(resolution,[],[f2454,f1454]) ).
fof(f1454,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f1452]) ).
fof(f2454,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_226 ),
inference(avatar_component_clause,[],[f2453]) ).
fof(f13163,plain,
spl0_794,
inference(avatar_split_clause,[],[f89,f13161]) ).
fof(f13161,plain,
( spl0_794
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1) = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f89,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1) = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_square__eq__iff_0) ).
fof(f13159,plain,
spl0_793,
inference(avatar_split_clause,[],[f25,f13157]) ).
fof(f13157,plain,
( spl0_793
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f25,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__0__iff_4) ).
fof(f13155,plain,
spl0_792,
inference(avatar_split_clause,[],[f24,f13153]) ).
fof(f13153,plain,
( spl0_792
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f24,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__0__iff_5) ).
fof(f13151,plain,
spl0_791,
inference(avatar_split_clause,[],[f4,f13149]) ).
fof(f13149,plain,
( spl0_791
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__0__iff_0) ).
fof(f13147,plain,
spl0_790,
inference(avatar_split_clause,[],[f3,f13145]) ).
fof(f13145,plain,
( spl0_790
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__0__iff_1) ).
fof(f13143,plain,
spl0_789,
inference(avatar_split_clause,[],[f2,f13141]) ).
fof(f13141,plain,
( spl0_789
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__0__iff_2) ).
fof(f13139,plain,
spl0_788,
inference(avatar_split_clause,[],[f1,f13137]) ).
fof(f13137,plain,
( spl0_788
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__0__iff_3) ).
fof(f13030,plain,
( spl0_787
| ~ spl0_19
| ~ spl0_201
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2661,f2449,f2344,f1452,f13028]) ).
fof(f13028,plain,
( spl0_787
<=> ! [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_787])]) ).
fof(f2449,plain,
( spl0_225
<=> ! [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_225])]) ).
fof(f2661,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0) = X0
| ~ spl0_19
| ~ spl0_201
| ~ spl0_225 ),
inference(forward_demodulation,[],[f2660,f2346]) ).
fof(f2660,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X0) = X0
| ~ spl0_19
| ~ spl0_225 ),
inference(resolution,[],[f2450,f1454]) ).
fof(f2450,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_225 ),
inference(avatar_component_clause,[],[f2449]) ).
fof(f12823,plain,
( spl0_786
| ~ spl0_41
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2655,f2433,f1562,f12821]) ).
fof(f2433,plain,
( spl0_221
<=> ! [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_221])]) ).
fof(f2655,plain,
( ! [X2,X3] : c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X3,X2,tc_bool)
| ~ spl0_41
| ~ spl0_221 ),
inference(resolution,[],[f2434,f1564]) ).
fof(f1564,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f1562]) ).
fof(f2434,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_221 ),
inference(avatar_component_clause,[],[f2433]) ).
fof(f12287,plain,
( spl0_785
| ~ spl0_21
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2654,f2433,f1462,f12285]) ).
fof(f2654,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_221 ),
inference(resolution,[],[f2434,f1464]) ).
fof(f1464,plain,
( class_Lattices_Oupper__semilattice(tc_nat)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f1462]) ).
fof(f12012,plain,
spl0_784,
inference(avatar_split_clause,[],[f1262,f12010]) ).
fof(f12010,plain,
( spl0_784
<=> ! [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_784])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_xt1_I10_J_0) ).
fof(f12008,plain,
spl0_783,
inference(avatar_split_clause,[],[f1261,f12006]) ).
fof(f12006,plain,
( spl0_783
<=> ! [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_783])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_order__less__trans_0) ).
fof(f12004,plain,
spl0_782,
inference(avatar_split_clause,[],[f1221,f12002]) ).
fof(f12002,plain,
( spl0_782
<=> ! [X0,X8,X10,X2,X1] :
( 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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_DomainI_0) ).
fof(f12000,plain,
spl0_781,
inference(avatar_split_clause,[],[f1219,f11998]) ).
fof(f11998,plain,
( spl0_781
<=> ! [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_781])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_RangeI_0) ).
fof(f11996,plain,
spl0_780,
inference(avatar_split_clause,[],[f1138,f11994]) ).
fof(f11994,plain,
( spl0_780
<=> ! [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_780])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_O__assoc_0) ).
fof(f11992,plain,
spl0_779,
inference(avatar_split_clause,[],[f976,f11990]) ).
fof(f11990,plain,
( spl0_779
<=> ! [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_779])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__0_H_0) ).
fof(f11988,plain,
spl0_778,
inference(avatar_split_clause,[],[f940,f11986]) ).
fof(f11986,plain,
( spl0_778
<=> ! [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_778])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Image__iff_0) ).
fof(f11984,plain,
( spl0_777
| ~ spl0_42
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2629,f2405,f1567,f11982]) ).
fof(f1567,plain,
( spl0_42
<=> class_Lattices_Olower__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f2405,plain,
( spl0_214
<=> ! [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_214])]) ).
fof(f2629,plain,
( ! [X2,X3] : c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X3,X2,tc_bool)
| ~ spl0_42
| ~ spl0_214 ),
inference(resolution,[],[f2406,f1569]) ).
fof(f1569,plain,
( class_Lattices_Olower__semilattice(tc_bool)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f1567]) ).
fof(f2406,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_214 ),
inference(avatar_component_clause,[],[f2405]) ).
fof(f11980,plain,
spl0_776,
inference(avatar_split_clause,[],[f939,f11978]) ).
fof(f11978,plain,
( spl0_776
<=> ! [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_776])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_ImageE_1) ).
fof(f11976,plain,
spl0_775,
inference(avatar_split_clause,[],[f885,f11974]) ).
fof(f11974,plain,
( spl0_775
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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),X2)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f885,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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),X2)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_even__less__0__iff_1) ).
fof(f11972,plain,
spl0_774,
inference(avatar_split_clause,[],[f884,f11970]) ).
fof(f11970,plain,
( spl0_774
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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),X2)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f884,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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),X2)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_even__less__0__iff_0) ).
fof(f11968,plain,
spl0_773,
inference(avatar_split_clause,[],[f883,f11966]) ).
fof(f11966,plain,
( spl0_773
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f883,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(f11964,plain,
spl0_772,
inference(avatar_split_clause,[],[f882,f11962]) ).
fof(f11962,plain,
( spl0_772
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f882,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(f11960,plain,
spl0_771,
inference(avatar_split_clause,[],[f744,f11958]) ).
fof(f11958,plain,
( spl0_771
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__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)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f744,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__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)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(f11956,plain,
spl0_770,
inference(avatar_split_clause,[],[f743,f11954]) ).
fof(f11954,plain,
( spl0_770
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__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)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f743,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__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)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(f11952,plain,
spl0_769,
inference(avatar_split_clause,[],[f695,f11950]) ).
fof(f11950,plain,
( spl0_769
<=> ! [X38,X4,X0,X3,X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X39,X38,X0)
| c_lessequals(X4,X3,X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X38),X39) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f695,axiom,
! [X38,X3,X39,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X39,X38,X0)
| c_lessequals(X4,X3,X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X38),X39) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X4) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__eqI_1) ).
fof(f11948,plain,
spl0_768,
inference(avatar_split_clause,[],[f662,f11946]) ).
fof(f11946,plain,
( spl0_768
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f662,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__divide__right_0) ).
fof(f11944,plain,
spl0_767,
inference(avatar_split_clause,[],[f490,f11942]) ).
fof(f11942,plain,
( spl0_767
<=> ! [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_767])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__subset__iff_2) ).
fof(f11937,plain,
spl0_766,
inference(avatar_split_clause,[],[f448,f11935]) ).
fof(f11935,plain,
( spl0_766
<=> ! [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_766])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__insert__left_1) ).
fof(f11933,plain,
spl0_765,
inference(avatar_split_clause,[],[f447,f11931]) ).
fof(f11931,plain,
( spl0_765
<=> ! [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_765])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__insert__right_1) ).
fof(f11929,plain,
spl0_764,
inference(avatar_split_clause,[],[f381,f11927]) ).
fof(f11927,plain,
( spl0_764
<=> ! [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_764])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__subset__iff_2) ).
fof(f11925,plain,
spl0_763,
inference(avatar_split_clause,[],[f375,f11923]) ).
fof(f11923,plain,
( spl0_763
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f375,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__divide__divide_0) ).
fof(f11921,plain,
spl0_762,
inference(avatar_split_clause,[],[f270,f11919]) ).
fof(f11919,plain,
( spl0_762
<=> ! [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_762])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__assoc_0) ).
fof(f11917,plain,
spl0_761,
inference(avatar_split_clause,[],[f269,f11915]) ).
fof(f11915,plain,
( spl0_761
<=> ! [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_761])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__left__commute_0) ).
fof(f11913,plain,
spl0_760,
inference(avatar_split_clause,[],[f220,f11911]) ).
fof(f11911,plain,
( spl0_760
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X3))
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Oone__class_Oone(X0)) = c_HOL_Osgn__class_Osgn(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f220,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X3))
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Oone__class_Oone(X0)) = c_HOL_Osgn__class_Osgn(X3,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn__if_2) ).
fof(f11909,plain,
spl0_759,
inference(avatar_split_clause,[],[f141,f11907]) ).
fof(f11907,plain,
( spl0_759
<=> ! [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_759])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__left__commute_0) ).
fof(f11905,plain,
spl0_758,
inference(avatar_split_clause,[],[f140,f11903]) ).
fof(f11903,plain,
( spl0_758
<=> ! [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_758])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__assoc_0) ).
fof(f11744,plain,
( spl0_757
| ~ spl0_109
| ~ spl0_701 ),
inference(avatar_split_clause,[],[f10379,f10016,f1847,f11742]) ).
fof(f11742,plain,
( spl0_757
<=> ! [X4,X5] :
( c_Relation_Oirrefl(c_Transitive__Closure_Otrancl(X4,X5),X5)
| ~ c_Wellfounded_Owf(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f1847,plain,
( spl0_109
<=> ! [X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f10379,plain,
( ! [X4,X5] :
( c_Relation_Oirrefl(c_Transitive__Closure_Otrancl(X4,X5),X5)
| ~ c_Wellfounded_Owf(X4,X5) )
| ~ spl0_109
| ~ spl0_701 ),
inference(resolution,[],[f10017,f1848]) ).
fof(f1848,plain,
( ! [X0,X8] :
( c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X8,X0),X0)
| ~ c_Wellfounded_Owf(X8,X0) )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1847]) ).
fof(f11480,plain,
( spl0_756
| ~ spl0_333
| ~ spl0_687 ),
inference(avatar_split_clause,[],[f9674,f9627,f3334,f11478]) ).
fof(f11478,plain,
( spl0_756
<=> ! [X4,X5] : c_Nitpick_Orefl_H(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f3334,plain,
( spl0_333
<=> ! [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_333])]) ).
fof(f9674,plain,
( ! [X4,X5] : c_Nitpick_Orefl_H(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X5)
| ~ spl0_333
| ~ spl0_687 ),
inference(superposition,[],[f9628,f3335]) ).
fof(f3335,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_333 ),
inference(avatar_component_clause,[],[f3334]) ).
fof(f10770,plain,
spl0_755,
inference(avatar_split_clause,[],[f1215,f10768]) ).
fof(f10768,plain,
( spl0_755
<=> ! [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_755])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Id__on__eqI_0) ).
fof(f10766,plain,
spl0_754,
inference(avatar_split_clause,[],[f1214,f10764]) ).
fof(f10764,plain,
( spl0_754
<=> ! [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_754])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Id__on__iff_1) ).
fof(f10762,plain,
spl0_753,
inference(avatar_split_clause,[],[f1201,f10760]) ).
fof(f10760,plain,
( spl0_753
<=> ! [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_753])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_of__nat__less__iff_1) ).
fof(f10758,plain,
spl0_752,
inference(avatar_split_clause,[],[f1200,f10756]) ).
fof(f10756,plain,
( spl0_752
<=> ! [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_752])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_of__nat__less__iff_0) ).
fof(f10751,plain,
spl0_751,
inference(avatar_split_clause,[],[f1129,f10749]) ).
fof(f10749,plain,
( spl0_751
<=> ! [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_751])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__rel__comp_0) ).
fof(f10747,plain,
spl0_750,
inference(avatar_split_clause,[],[f984,f10745]) ).
fof(f10745,plain,
( spl0_750
<=> ! [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_750])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__setprod_0) ).
fof(f10743,plain,
spl0_749,
inference(avatar_split_clause,[],[f925,f10741]) ).
fof(f10741,plain,
( spl0_749
<=> ! [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_749])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__0_H_1) ).
fof(f10739,plain,
spl0_748,
inference(avatar_split_clause,[],[f922,f10737]) ).
fof(f10737,plain,
( spl0_748
<=> ! [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_748])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__inject__exp_0) ).
fof(f10735,plain,
spl0_747,
inference(avatar_split_clause,[],[f893,f10733]) ).
fof(f10733,plain,
( spl0_747
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__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_Ominus__class_Ominus(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f893,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__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_Ominus__class_Ominus(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__iff__diff__less__0_0) ).
fof(f10731,plain,
spl0_746,
inference(avatar_split_clause,[],[f892,f10729]) ).
fof(f10729,plain,
( spl0_746
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__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_Ominus__class_Ominus(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f892,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__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_Ominus__class_Ominus(X0),X2),X1)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__iff__diff__less__0_1) ).
fof(f10727,plain,
spl0_745,
inference(avatar_split_clause,[],[f852,f10725]) ).
fof(f10725,plain,
( spl0_745
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f852,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__less__iff_0) ).
fof(f10723,plain,
spl0_744,
inference(avatar_split_clause,[],[f851,f10721]) ).
fof(f10721,plain,
( spl0_744
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f851,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__minus__iff_1) ).
fof(f10719,plain,
spl0_743,
inference(avatar_split_clause,[],[f837,f10717]) ).
fof(f10717,plain,
( spl0_743
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f837,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__less__iff__less_1) ).
fof(f10715,plain,
spl0_742,
inference(avatar_split_clause,[],[f836,f10713]) ).
fof(f10713,plain,
( spl0_742
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f836,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__less__iff__less_0) ).
fof(f10711,plain,
( spl0_741
| ~ spl0_178
| ~ spl0_656 ),
inference(avatar_split_clause,[],[f9480,f8694,f2218,f10709]) ).
fof(f10709,plain,
( spl0_741
<=> ! [X18] : c_Nitpick_Orefl_H(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X18,X18),tc_bool)),X18) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f2218,plain,
( spl0_178
<=> ! [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_178])]) ).
fof(f8694,plain,
( spl0_656
<=> ! [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_656])]) ).
fof(f9480,plain,
( ! [X18] : c_Nitpick_Orefl_H(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X18,X18),tc_bool)),X18)
| ~ spl0_178
| ~ spl0_656 ),
inference(resolution,[],[f8695,f2219]) ).
fof(f2219,plain,
( ! [X3,X0] : hBOOL(hAPP(hAPP(c_in(X0),X3),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))))
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f2218]) ).
fof(f8695,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_656 ),
inference(avatar_component_clause,[],[f8694]) ).
fof(f10707,plain,
spl0_740,
inference(avatar_split_clause,[],[f713,f10705]) ).
fof(f10705,plain,
( spl0_740
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(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_740])]) ).
fof(f713,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_split__mult__pos__le_0) ).
fof(f10703,plain,
spl0_739,
inference(avatar_split_clause,[],[f711,f10701]) ).
fof(f10701,plain,
( spl0_739
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),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_739])]) ).
fof(f711,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__nonpos__nonpos_0) ).
fof(f10699,plain,
spl0_738,
inference(avatar_split_clause,[],[f709,f10697]) ).
fof(f10697,plain,
( spl0_738
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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_738])]) ).
fof(f709,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__mult__iff_4) ).
fof(f10695,plain,
spl0_737,
inference(avatar_split_clause,[],[f708,f10693]) ).
fof(f10693,plain,
( spl0_737
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),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_737])]) ).
fof(f708,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__mult__iff_5) ).
fof(f10691,plain,
spl0_736,
inference(avatar_split_clause,[],[f707,f10689]) ).
fof(f10689,plain,
( spl0_736
<=> ! [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_736])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__nonneg__nonneg_0) ).
fof(f10687,plain,
spl0_735,
inference(avatar_split_clause,[],[f655,f10685]) ).
fof(f10685,plain,
( spl0_735
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),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_735])]) ).
fof(f655,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__mult__iff_3) ).
fof(f10683,plain,
spl0_734,
inference(avatar_split_clause,[],[f654,f10681]) ).
fof(f10681,plain,
( spl0_734
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),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_734])]) ).
fof(f654,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__mult__iff_2) ).
fof(f10679,plain,
spl0_733,
inference(avatar_split_clause,[],[f653,f10677]) ).
fof(f10677,plain,
( spl0_733
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,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_733])]) ).
fof(f653,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__mult__iff_1) ).
fof(f10675,plain,
spl0_732,
inference(avatar_split_clause,[],[f652,f10673]) ).
fof(f10673,plain,
( spl0_732
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,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_732])]) ).
fof(f652,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__mult__iff_0) ).
fof(f10671,plain,
spl0_731,
inference(avatar_split_clause,[],[f633,f10669]) ).
fof(f10669,plain,
( spl0_731
<=> ! [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_731])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_disjoint__eq__subset__Compl_0) ).
fof(f10667,plain,
( spl0_730
| ~ spl0_177
| ~ spl0_655 ),
inference(avatar_split_clause,[],[f9465,f8690,f2214,f10665]) ).
fof(f10665,plain,
( spl0_730
<=> ! [X26] : c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X26,X26),tc_bool)),X26) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f2214,plain,
( spl0_177
<=> ! [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_177])]) ).
fof(f8690,plain,
( spl0_655
<=> ! [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_655])]) ).
fof(f9465,plain,
( ! [X26] : c_Relation_Oirrefl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X26,X26),tc_bool)),X26)
| ~ spl0_177
| ~ spl0_655 ),
inference(resolution,[],[f8691,f2215]) ).
fof(f2215,plain,
( ! [X0,X5] : ~ hBOOL(hAPP(hAPP(c_in(X0),X5),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))))
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f2214]) ).
fof(f8691,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_655 ),
inference(avatar_component_clause,[],[f8690]) ).
fof(f10663,plain,
spl0_729,
inference(avatar_split_clause,[],[f632,f10661]) ).
fof(f10661,plain,
( spl0_729
<=> ! [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_729])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_disjoint__eq__subset__Compl_1) ).
fof(f10659,plain,
spl0_728,
inference(avatar_split_clause,[],[f559,f10657]) ).
fof(f10657,plain,
( spl0_728
<=> ! [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_728])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__nonpos__nonpos_0) ).
fof(f10655,plain,
spl0_727,
inference(avatar_split_clause,[],[f509,f10653]) ).
fof(f10653,plain,
( spl0_727
<=> ! [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_727])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__subset_2) ).
fof(f10651,plain,
spl0_726,
inference(avatar_split_clause,[],[f500,f10649]) ).
fof(f10649,plain,
( spl0_726
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,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_726])]) ).
fof(f500,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__le__0__iff_0) ).
fof(f10647,plain,
spl0_725,
inference(avatar_split_clause,[],[f499,f10645]) ).
fof(f10645,plain,
( spl0_725
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,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_725])]) ).
fof(f499,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__le__0__iff_1) ).
fof(f10643,plain,
spl0_724,
inference(avatar_split_clause,[],[f498,f10641]) ).
fof(f10641,plain,
( spl0_724
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),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_724])]) ).
fof(f498,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__le__0__iff_2) ).
fof(f10639,plain,
spl0_723,
inference(avatar_split_clause,[],[f497,f10637]) ).
fof(f10637,plain,
( spl0_723
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,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_723])]) ).
fof(f497,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__le__0__iff_3) ).
fof(f10635,plain,
spl0_722,
inference(avatar_split_clause,[],[f476,f10633]) ).
fof(f10633,plain,
( spl0_722
<=> ! [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_722])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__singleton__eq_0) ).
fof(f10631,plain,
spl0_721,
inference(avatar_split_clause,[],[f458,f10629]) ).
fof(f10629,plain,
( spl0_721
<=> ! [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_721])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_card__eq__UNIV__imp__eq__UNIV_0) ).
fof(f10627,plain,
spl0_720,
inference(avatar_split_clause,[],[f443,f10625]) ).
fof(f10625,plain,
( spl0_720
<=> ! [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_720])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_subset__insert_0) ).
fof(f10623,plain,
( spl0_719
| ~ spl0_558
| ~ spl0_655 ),
inference(avatar_split_clause,[],[f9457,f8690,f7385,f10621]) ).
fof(f7385,plain,
( spl0_558
<=> ! [X0,X8,X3] :
( ~ 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))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f9457,plain,
( ! [X8,X7] :
( c_Relation_Oirrefl(c_Transitive__Closure_Otrancl(X7,X8),X8)
| ~ c_Wellfounded_Oacyclic(X7,X8) )
| ~ spl0_558
| ~ spl0_655 ),
inference(resolution,[],[f8691,f7386]) ).
fof(f7386,plain,
( ! [X3,X0,X8] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(X0,X0)),c_Pair(X3,X3,X0,X0)),c_Transitive__Closure_Otrancl(X8,X0)))
| ~ c_Wellfounded_Oacyclic(X8,X0) )
| ~ spl0_558 ),
inference(avatar_component_clause,[],[f7385]) ).
fof(f10619,plain,
spl0_718,
inference(avatar_split_clause,[],[f429,f10617]) ).
fof(f10617,plain,
( spl0_718
<=> ! [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_718])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_split__mult__neg__le_1) ).
fof(f10615,plain,
spl0_717,
inference(avatar_split_clause,[],[f428,f10613]) ).
fof(f10613,plain,
( spl0_717
<=> ! [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_717])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_split__mult__neg__le_0) ).
fof(f10611,plain,
spl0_716,
inference(avatar_split_clause,[],[f427,f10609]) ).
fof(f10609,plain,
( spl0_716
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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_716])]) ).
fof(f427,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__le__0__iff_5) ).
fof(f10607,plain,
spl0_715,
inference(avatar_split_clause,[],[f426,f10605]) ).
fof(f10605,plain,
( spl0_715
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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_715])]) ).
fof(f426,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__le__0__iff_4) ).
fof(f10603,plain,
spl0_714,
inference(avatar_split_clause,[],[f404,f10601]) ).
fof(f10601,plain,
( spl0_714
<=> ! [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_714])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_compl__unique_0) ).
fof(f10599,plain,
spl0_713,
inference(avatar_split_clause,[],[f349,f10597]) ).
fof(f10597,plain,
( spl0_713
<=> ! [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_713])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__subset__rtrancl_0) ).
fof(f10595,plain,
spl0_712,
inference(avatar_split_clause,[],[f216,f10593]) ).
fof(f10593,plain,
( spl0_712
<=> ! [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_712])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__nonneg__nonneg_0) ).
fof(f10591,plain,
spl0_711,
inference(avatar_split_clause,[],[f111,f10589]) ).
fof(f10589,plain,
( spl0_711
<=> ! [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_711])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(f10587,plain,
spl0_710,
inference(avatar_split_clause,[],[f49,f10585]) ).
fof(f10585,plain,
( spl0_710
<=> ! [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_710])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Compl__anti__mono_0) ).
fof(f10583,plain,
spl0_709,
inference(avatar_split_clause,[],[f48,f10581]) ).
fof(f10581,plain,
( spl0_709
<=> ! [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_709])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Compl__subset__Compl__iff_0) ).
fof(f10579,plain,
spl0_708,
inference(avatar_split_clause,[],[f33,f10577]) ).
fof(f10577,plain,
( spl0_708
<=> ! [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_708])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__inter__insert_0) ).
fof(f10575,plain,
spl0_707,
inference(avatar_split_clause,[],[f32,f10573]) ).
fof(f10573,plain,
( spl0_707
<=> ! [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_707])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__increasing_0) ).
fof(f10571,plain,
spl0_706,
inference(avatar_split_clause,[],[f31,f10569]) ).
fof(f10569,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,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_706])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__increasing2_0) ).
fof(f10567,plain,
spl0_705,
inference(avatar_split_clause,[],[f12,f10565]) ).
fof(f10565,plain,
( spl0_705
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f12,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X4),X4)),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sum__squares__ge__zero_0) ).
fof(f10528,plain,
( spl0_704
| ~ spl0_201
| ~ spl0_700 ),
inference(avatar_split_clause,[],[f9689,f9686,f2344,f10526]) ).
fof(f10526,plain,
( spl0_704
<=> ! [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_704])]) ).
fof(f9686,plain,
( spl0_700
<=> ! [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_700])]) ).
fof(f9689,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_201
| ~ spl0_700 ),
inference(forward_demodulation,[],[f9687,f2346]) ).
fof(f9687,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_700 ),
inference(avatar_component_clause,[],[f9686]) ).
fof(f10524,plain,
( spl0_703
| ~ spl0_201
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f9684,f9681,f2344,f10522]) ).
fof(f10522,plain,
( spl0_703
<=> ! [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_703])]) ).
fof(f9681,plain,
( spl0_699
<=> ! [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_699])]) ).
fof(f9684,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_201
| ~ spl0_699 ),
inference(forward_demodulation,[],[f9682,f2346]) ).
fof(f9682,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_699 ),
inference(avatar_component_clause,[],[f9681]) ).
fof(f10511,plain,
( spl0_702
| ~ spl0_61
| ~ spl0_701 ),
inference(avatar_split_clause,[],[f10380,f10016,f1654,f10509]) ).
fof(f10509,plain,
( spl0_702
<=> ! [X6,X7] : c_Relation_Oirrefl(c_Wellfounded_Omeasure(X6,X7),X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f1654,plain,
( spl0_61
<=> ! [X18,X0] : c_Wellfounded_Owf(c_Wellfounded_Omeasure(X18,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f10380,plain,
( ! [X6,X7] : c_Relation_Oirrefl(c_Wellfounded_Omeasure(X6,X7),X7)
| ~ spl0_61
| ~ spl0_701 ),
inference(resolution,[],[f10017,f1655]) ).
fof(f1655,plain,
( ! [X0,X18] : c_Wellfounded_Owf(c_Wellfounded_Omeasure(X18,X0),X0)
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f1654]) ).
fof(f10018,plain,
( spl0_701
| ~ spl0_481
| ~ spl0_655 ),
inference(avatar_split_clause,[],[f9453,f8690,f5765,f10016]) ).
fof(f5765,plain,
( spl0_481
<=> ! [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_481])]) ).
fof(f9453,plain,
( ! [X0,X1] :
( c_Relation_Oirrefl(X0,X1)
| ~ c_Wellfounded_Owf(X0,X1) )
| ~ spl0_481
| ~ spl0_655 ),
inference(resolution,[],[f8691,f5766]) ).
fof(f5766,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_481 ),
inference(avatar_component_clause,[],[f5765]) ).
fof(f9688,plain,
spl0_700,
inference(avatar_split_clause,[],[f1042,f9686]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_of__nat__0__less__iff_1) ).
fof(f9683,plain,
spl0_699,
inference(avatar_split_clause,[],[f1041,f9681]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_of__nat__0__less__iff_0) ).
fof(f9679,plain,
spl0_698,
inference(avatar_split_clause,[],[f1026,f9677]) ).
fof(f9677,plain,
( spl0_698
<=> ! [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_698])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Id__onE_0) ).
fof(f9669,plain,
spl0_697,
inference(avatar_split_clause,[],[f1021,f9667]) ).
fof(f9667,plain,
( spl0_697
<=> ! [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_697])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_IdE_0) ).
fof(f9665,plain,
spl0_696,
inference(avatar_split_clause,[],[f987,f9663]) ).
fof(f9663,plain,
( spl0_696
<=> ! [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_696])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__1_H_0) ).
fof(f9661,plain,
spl0_695,
inference(avatar_split_clause,[],[f954,f9659]) ).
fof(f9659,plain,
( spl0_695
<=> ! [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_695])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc_OaccI_1) ).
fof(f9657,plain,
spl0_694,
inference(avatar_split_clause,[],[f951,f9655]) ).
fof(f9655,plain,
( spl0_694
<=> ! [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_694])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_not__acc__down_1) ).
fof(f9653,plain,
spl0_693,
inference(avatar_split_clause,[],[f911,f9651]) ).
fof(f9651,plain,
( spl0_693
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__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),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f911,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__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),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__0__less__iff__less_0) ).
fof(f9649,plain,
spl0_692,
inference(avatar_split_clause,[],[f910,f9647]) ).
fof(f9647,plain,
( spl0_692
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__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),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f910,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__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),c_HOL_Ozero__class_Ozero(X0)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__0__less__iff__less_1) ).
fof(f9645,plain,
spl0_691,
inference(avatar_split_clause,[],[f890,f9643]) ).
fof(f9643,plain,
( spl0_691
<=> ! [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_691])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__less__power_0) ).
fof(f9641,plain,
spl0_690,
inference(avatar_split_clause,[],[f879,f9639]) ).
fof(f9639,plain,
( spl0_690
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__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),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f879,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__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),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__less__0__iff__less_0) ).
fof(f9637,plain,
spl0_689,
inference(avatar_split_clause,[],[f878,f9635]) ).
fof(f9635,plain,
( spl0_689
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__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),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f878,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__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),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__less__0__iff__less_1) ).
fof(f9633,plain,
spl0_688,
inference(avatar_split_clause,[],[f706,f9631]) ).
fof(f9631,plain,
( spl0_688
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Osgn__class_Osgn(X2,X0)),c_HOL_Osgn__class_Osgn(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f706,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Osgn__class_Osgn(X2,X0)),c_HOL_Osgn__class_Osgn(X1,X0)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn__times_0) ).
fof(f9629,plain,
( spl0_687
| ~ spl0_438
| ~ spl0_656 ),
inference(avatar_split_clause,[],[f9473,f8694,f5103,f9627]) ).
fof(f5103,plain,
( spl0_438
<=> ! [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_438])]) ).
fof(f9473,plain,
( ! [X2,X1] : c_Nitpick_Orefl_H(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ spl0_438
| ~ spl0_656 ),
inference(resolution,[],[f8695,f5104]) ).
fof(f5104,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_438 ),
inference(avatar_component_clause,[],[f5103]) ).
fof(f9625,plain,
spl0_686,
inference(avatar_split_clause,[],[f663,f9623]) ).
fof(f9623,plain,
( spl0_686
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f663,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),X1) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__divide__left_0) ).
fof(f9621,plain,
spl0_685,
inference(avatar_split_clause,[],[f631,f9619]) ).
fof(f9619,plain,
( spl0_685
<=> ! [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_685])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Range__insert_0) ).
fof(f9617,plain,
spl0_684,
inference(avatar_split_clause,[],[f625,f9615]) ).
fof(f9615,plain,
( spl0_684
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f625,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__mult__minus_0) ).
fof(f9613,plain,
spl0_683,
inference(avatar_split_clause,[],[f624,f9611]) ).
fof(f9611,plain,
( spl0_683
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f624,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_square__eq__iff_1) ).
fof(f9609,plain,
spl0_682,
inference(avatar_split_clause,[],[f596,f9607]) ).
fof(f9607,plain,
( spl0_682
<=> ! [X4,X0,X23,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X23) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X23)) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f596,axiom,
! [X3,X0,X4,X23] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X23) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X23)) != X4 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__cancel__end_0) ).
fof(f9605,plain,
spl0_681,
inference(avatar_split_clause,[],[f530,f9603]) ).
fof(f9603,plain,
( spl0_681
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Ozero__class_Ozero(X0)))
| c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f530,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Ozero__class_Ozero(X0)))
| c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__eq__if_1) ).
fof(f9601,plain,
spl0_680,
inference(avatar_split_clause,[],[f495,f9599]) ).
fof(f9599,plain,
( spl0_680
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f495,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),X1) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__mult__commute_0) ).
fof(f9597,plain,
spl0_679,
inference(avatar_split_clause,[],[f425,f9595]) ).
fof(f9595,plain,
( spl0_679
<=> ! [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_679])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__Compl_0) ).
fof(f9593,plain,
spl0_678,
inference(avatar_split_clause,[],[f398,f9591]) ).
fof(f9591,plain,
( spl0_678
<=> ! [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_678])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_distrib__inf__le_0) ).
fof(f9589,plain,
spl0_677,
inference(avatar_split_clause,[],[f347,f9587]) ).
fof(f9587,plain,
( spl0_677
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f347,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),X1) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__mult__left_0) ).
fof(f9583,plain,
spl0_676,
inference(avatar_split_clause,[],[f346,f9581]) ).
fof(f9581,plain,
( spl0_676
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f346,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__mult__right_0) ).
fof(f9579,plain,
spl0_675,
inference(avatar_split_clause,[],[f289,f9577]) ).
fof(f9577,plain,
( spl0_675
<=> ! [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_675])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_distrib__sup__le_0) ).
fof(f9575,plain,
spl0_674,
inference(avatar_split_clause,[],[f254,f9573]) ).
fof(f9573,plain,
( spl0_674
<=> ! [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_674])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__mono_0) ).
fof(f9571,plain,
spl0_673,
inference(avatar_split_clause,[],[f252,f9569]) ).
fof(f9569,plain,
( spl0_673
<=> ! [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_673])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__increasing_0) ).
fof(f9567,plain,
spl0_672,
inference(avatar_split_clause,[],[f168,f9565]) ).
fof(f9565,plain,
( spl0_672
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)),X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f168,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),X5)),X5) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_eq__divide__eq_0) ).
fof(f9563,plain,
spl0_671,
inference(avatar_split_clause,[],[f98,f9561]) ).
fof(f9561,plain,
( spl0_671
<=> ! [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_671])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__commutes_0) ).
fof(f9559,plain,
spl0_670,
inference(avatar_split_clause,[],[f28,f9557]) ).
fof(f9557,plain,
( spl0_670
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0)),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f28,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0)),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__eq__inf__sup_0) ).
fof(f9555,plain,
spl0_669,
inference(avatar_split_clause,[],[f17,f9553]) ).
fof(f9553,plain,
( spl0_669
<=> ! [X0,X8,X10,X2,X1] : 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) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Domain__insert_0) ).
fof(f9539,plain,
( spl0_668
| ~ spl0_397
| ~ spl0_656 ),
inference(avatar_split_clause,[],[f9472,f8694,f4107,f9537]) ).
fof(f9537,plain,
( spl0_668
<=> ! [X0] : c_Nitpick_Orefl_H(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f9472,plain,
( ! [X0] : c_Nitpick_Orefl_H(c_Relation_OId(X0),X0)
| ~ spl0_397
| ~ spl0_656 ),
inference(resolution,[],[f8695,f4108]) ).
fof(f9405,plain,
( spl0_667
| ~ spl0_22
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2628,f2405,f1467,f9403]) ).
fof(f2628,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_214 ),
inference(resolution,[],[f2406,f1469]) ).
fof(f1469,plain,
( class_Lattices_Olower__semilattice(tc_nat)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1467]) ).
fof(f9253,plain,
( spl0_666
| ~ spl0_48
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2620,f2385,f1597,f9251]) ).
fof(f1597,plain,
( spl0_48
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f2385,plain,
( spl0_211
<=> ! [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_211])]) ).
fof(f2620,plain,
( ! [X2,X3] : c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,tc_bool),tc_bool) = X2
| ~ spl0_48
| ~ spl0_211 ),
inference(resolution,[],[f2386,f1599]) ).
fof(f1599,plain,
( class_Lattices_Olattice(tc_bool)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1597]) ).
fof(f2386,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_211 ),
inference(avatar_component_clause,[],[f2385]) ).
fof(f9054,plain,
( spl0_665
| ~ spl0_201
| ~ spl0_624 ),
inference(avatar_split_clause,[],[f8561,f8558,f2344,f9052]) ).
fof(f9052,plain,
( spl0_665
<=> ! [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_665])]) ).
fof(f8558,plain,
( spl0_624
<=> ! [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_624])]) ).
fof(f8561,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_201
| ~ spl0_624 ),
inference(forward_demodulation,[],[f8559,f2346]) ).
fof(f8559,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_624 ),
inference(avatar_component_clause,[],[f8558]) ).
fof(f8823,plain,
( spl0_664
| ~ spl0_333
| ~ spl0_533 ),
inference(avatar_split_clause,[],[f7044,f6668,f3334,f8821]) ).
fof(f8821,plain,
( spl0_664
<=> ! [X4,X5] : ~ c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f7044,plain,
( ! [X4,X5] : ~ c_Wellfounded_Owf(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X5)
| ~ spl0_333
| ~ spl0_533 ),
inference(superposition,[],[f6669,f3335]) ).
fof(f8724,plain,
spl0_663,
inference(avatar_split_clause,[],[f1348,f8722]) ).
fof(f8722,plain,
( spl0_663
<=> ! [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_663])]) ).
fof(f1348,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__mktop_4) ).
fof(f8720,plain,
spl0_662,
inference(avatar_split_clause,[],[f1347,f8718]) ).
fof(f8718,plain,
( spl0_662
<=> ! [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_662])]) ).
fof(f1347,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__mkbot_4) ).
fof(f8716,plain,
( spl0_661
| ~ spl0_333
| ~ spl0_527 ),
inference(avatar_split_clause,[],[f6734,f6618,f3334,f8714]) ).
fof(f8714,plain,
( spl0_661
<=> ! [X4,X5] : ~ c_Relation_Oirrefl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f6734,plain,
( ! [X4,X5] : ~ c_Relation_Oirrefl(c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X4,X5),X5,X5),X5)
| ~ spl0_333
| ~ spl0_527 ),
inference(superposition,[],[f6619,f3335]) ).
fof(f8712,plain,
spl0_660,
inference(avatar_split_clause,[],[f1098,f8710]) ).
fof(f8710,plain,
( spl0_660
<=> ! [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_660])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimageI_0) ).
fof(f8708,plain,
spl0_659,
inference(avatar_split_clause,[],[f1096,f8706]) ).
fof(f8706,plain,
( spl0_659
<=> ! [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_659])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimageD_0) ).
fof(f8704,plain,
spl0_658,
inference(avatar_split_clause,[],[f1083,f8702]) ).
fof(f8702,plain,
( spl0_658
<=> ! [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))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_r__into__trancl_H_0) ).
fof(f8700,plain,
spl0_657,
inference(avatar_split_clause,[],[f1082,f8698]) ).
fof(f8698,plain,
( spl0_657
<=> ! [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_657])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_r__into__rtrancl_0) ).
fof(f8696,plain,
spl0_656,
inference(avatar_split_clause,[],[f1038,f8694]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Nitpick_Orefl_H__def_1) ).
fof(f8692,plain,
spl0_655,
inference(avatar_split_clause,[],[f1035,f8690]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_irrefl__def_1) ).
fof(f8688,plain,
spl0_654,
inference(avatar_split_clause,[],[f1033,f8686]) ).
fof(f8686,plain,
( spl0_654
<=> ! [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_654])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_refl__on__comp__subset_0) ).
fof(f8684,plain,
spl0_653,
inference(avatar_split_clause,[],[f972,f8682]) ).
fof(f8682,plain,
( spl0_653
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X3,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f972,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X3,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X3)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn__if_1) ).
fof(f8680,plain,
spl0_652,
inference(avatar_split_clause,[],[f952,f8678]) ).
fof(f8678,plain,
( spl0_652
<=> ! [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_652])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc__induct__rule_2) ).
fof(f8676,plain,
spl0_651,
inference(avatar_split_clause,[],[f948,f8674]) ).
fof(f8674,plain,
( spl0_651
<=> ! [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_651])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc__induct_2) ).
fof(f8668,plain,
spl0_650,
inference(avatar_split_clause,[],[f943,f8666]) ).
fof(f8666,plain,
( spl0_650
<=> ! [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_650])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__1_H_1) ).
fof(f8664,plain,
spl0_649,
inference(avatar_split_clause,[],[f937,f8662]) ).
fof(f8662,plain,
( spl0_649
<=> ! [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_649])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wfE__min_0) ).
fof(f8660,plain,
spl0_648,
inference(avatar_split_clause,[],[f936,f8658]) ).
fof(f8658,plain,
( spl0_648
<=> ! [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_648])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__eq__minimal_0) ).
fof(f8656,plain,
spl0_647,
inference(avatar_split_clause,[],[f913,f8654]) ).
fof(f8654,plain,
( spl0_647
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f913,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__minus__self__iff_1) ).
fof(f8652,plain,
spl0_646,
inference(avatar_split_clause,[],[f912,f8650]) ).
fof(f8650,plain,
( spl0_646
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f912,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__minus__self__iff_0) ).
fof(f8648,plain,
spl0_645,
inference(avatar_split_clause,[],[f881,f8646]) ).
fof(f8646,plain,
( spl0_645
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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_HOL_Osgn__class_Osgn(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f881,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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_HOL_Osgn__class_Osgn(X2,X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn__greater_0) ).
fof(f8644,plain,
spl0_644,
inference(avatar_split_clause,[],[f880,f8642]) ).
fof(f8642,plain,
( spl0_644
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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_HOL_Osgn__class_Osgn(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f880,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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_HOL_Osgn__class_Osgn(X2,X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn__greater_1) ).
fof(f8640,plain,
spl0_643,
inference(avatar_split_clause,[],[f873,f8638]) ).
fof(f8638,plain,
( spl0_643
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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),c_HOL_Osgn__class_Osgn(X2,X0)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f873,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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),c_HOL_Osgn__class_Osgn(X2,X0)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn__less_0) ).
fof(f8636,plain,
spl0_642,
inference(avatar_split_clause,[],[f872,f8634]) ).
fof(f8634,plain,
( spl0_642
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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),c_HOL_Osgn__class_Osgn(X2,X0)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f872,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(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),c_HOL_Osgn__class_Osgn(X2,X0)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn__less_1) ).
fof(f8632,plain,
spl0_641,
inference(avatar_split_clause,[],[f823,f8630]) ).
fof(f8630,plain,
( spl0_641
<=> ! [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_641])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_xt1_I7_J_0) ).
fof(f8625,plain,
spl0_640,
inference(avatar_split_clause,[],[f822,f8623]) ).
fof(f8623,plain,
( spl0_640
<=> ! [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_640])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_xt1_I8_J_0) ).
fof(f8621,plain,
spl0_639,
inference(avatar_split_clause,[],[f821,f8619]) ).
fof(f8619,plain,
( spl0_639
<=> ! [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_639])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_order__le__less__trans_0) ).
fof(f8617,plain,
spl0_638,
inference(avatar_split_clause,[],[f820,f8615]) ).
fof(f8615,plain,
( spl0_638
<=> ! [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_638])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_order__less__le__trans_0) ).
fof(f8613,plain,
spl0_637,
inference(avatar_split_clause,[],[f797,f8611]) ).
fof(f8611,plain,
( spl0_637
<=> ! [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_637])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insertE_0) ).
fof(f8609,plain,
spl0_636,
inference(avatar_split_clause,[],[f787,f8607]) ).
fof(f8607,plain,
( spl0_636
<=> ! [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_636])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_subset__iff_0) ).
fof(f8605,plain,
spl0_635,
inference(avatar_split_clause,[],[f693,f8603]) ).
fof(f8603,plain,
( spl0_635
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f693,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__eq__neg__inf_0) ).
fof(f8601,plain,
spl0_634,
inference(avatar_split_clause,[],[f687,f8599]) ).
fof(f8599,plain,
( spl0_634
<=> ! [X10,X0,X9,X8] :
( ~ 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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Domain__mono_0) ).
fof(f8597,plain,
spl0_633,
inference(avatar_split_clause,[],[f607,f8595]) ).
fof(f8595,plain,
( spl0_633
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f607,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__sup__eq__inf_0) ).
fof(f8593,plain,
spl0_632,
inference(avatar_split_clause,[],[f606,f8591]) ).
fof(f8591,plain,
( spl0_632
<=> ! [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_632])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_compl__sup_0) ).
fof(f8589,plain,
spl0_631,
inference(avatar_split_clause,[],[f589,f8587]) ).
fof(f8587,plain,
( spl0_631
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f589,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__inf__eq__sup_0) ).
fof(f8585,plain,
spl0_630,
inference(avatar_split_clause,[],[f588,f8583]) ).
fof(f8583,plain,
( spl0_630
<=> ! [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_630])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_compl__inf_0) ).
fof(f8581,plain,
spl0_629,
inference(avatar_split_clause,[],[f583,f8579]) ).
fof(f8579,plain,
( spl0_629
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f583,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__eq__neg__sup_0) ).
fof(f8577,plain,
spl0_628,
inference(avatar_split_clause,[],[f560,f8575]) ).
fof(f8575,plain,
( spl0_628
<=> ! [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_628])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__le__dvd_0) ).
fof(f8573,plain,
spl0_627,
inference(avatar_split_clause,[],[f505,f8571]) ).
fof(f8571,plain,
( spl0_627
<=> ! [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_627])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__inf__distrib1_0) ).
fof(f8569,plain,
spl0_626,
inference(avatar_split_clause,[],[f504,f8567]) ).
fof(f8567,plain,
( spl0_626
<=> ! [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_626])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__inf__distrib2_0) ).
fof(f8565,plain,
spl0_625,
inference(avatar_split_clause,[],[f496,f8563]) ).
fof(f8563,plain,
( spl0_625
<=> ! [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_625])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__power__le_0) ).
fof(f8560,plain,
spl0_624,
inference(avatar_split_clause,[],[f479,f8558]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__eq__0__iff_2) ).
fof(f8556,plain,
spl0_623,
inference(avatar_split_clause,[],[f445,f8554]) ).
fof(f8554,plain,
( spl0_623
<=> ! [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_623])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__mono_0) ).
fof(f8552,plain,
spl0_622,
inference(avatar_split_clause,[],[f436,f8550]) ).
fof(f8550,plain,
( spl0_622
<=> ! [X4,X0,X23,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X4 = X23
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f436,axiom,
! [X3,X0,X4,X23] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X4 = X23
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X23) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__ringb_Oadd__cancel_0) ).
fof(f8548,plain,
spl0_621,
inference(avatar_split_clause,[],[f361,f8546]) ).
fof(f8546,plain,
( spl0_621
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f361,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X4)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__left__idem_0) ).
fof(f8544,plain,
spl0_620,
inference(avatar_split_clause,[],[f348,f8542]) ).
fof(f8542,plain,
( spl0_620
<=> ! [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_620])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_card__insert__if_0) ).
fof(f8540,plain,
spl0_619,
inference(avatar_split_clause,[],[f344,f8538]) ).
fof(f8538,plain,
( spl0_619
<=> ! [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_619])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__left__mono_0) ).
fof(f8536,plain,
spl0_618,
inference(avatar_split_clause,[],[f343,f8534]) ).
fof(f8534,plain,
( spl0_618
<=> ! [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_618])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__right__mono_0) ).
fof(f8532,plain,
spl0_617,
inference(avatar_split_clause,[],[f342,f8530]) ).
fof(f8530,plain,
( spl0_617
<=> ! [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_617])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__le__cancel__left_0) ).
fof(f8528,plain,
spl0_616,
inference(avatar_split_clause,[],[f341,f8526]) ).
fof(f8526,plain,
( spl0_616
<=> ! [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_616])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__le__cancel__left_1) ).
fof(f8524,plain,
spl0_615,
inference(avatar_split_clause,[],[f340,f8522]) ).
fof(f8522,plain,
( spl0_615
<=> ! [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_615])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__le__cancel__right_0) ).
fof(f8520,plain,
spl0_614,
inference(avatar_split_clause,[],[f339,f8518]) ).
fof(f8518,plain,
( spl0_614
<=> ! [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_614])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__le__cancel__right_1) ).
fof(f8516,plain,
spl0_613,
inference(avatar_split_clause,[],[f291,f8514]) ).
fof(f8514,plain,
( spl0_613
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f291,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__0__1__iff_1) ).
fof(f8512,plain,
spl0_612,
inference(avatar_split_clause,[],[f290,f8510]) ).
fof(f8510,plain,
( spl0_612
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f290,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__le__0__1__iff_0) ).
fof(f8508,plain,
spl0_611,
inference(avatar_split_clause,[],[f277,f8506]) ).
fof(f8506,plain,
( spl0_611
<=> ! [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_611])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_card__seteq_0) ).
fof(f8504,plain,
spl0_610,
inference(avatar_split_clause,[],[f207,f8502]) ).
fof(f8502,plain,
( spl0_610
<=> ! [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_610])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__distrib2_0) ).
fof(f8500,plain,
spl0_609,
inference(avatar_split_clause,[],[f206,f8498]) ).
fof(f8498,plain,
( spl0_609
<=> ! [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_609])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__distrib1_0) ).
fof(f8496,plain,
spl0_608,
inference(avatar_split_clause,[],[f58,f8494]) ).
fof(f8494,plain,
( spl0_608
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,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),X5),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f58,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,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),X5),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__mult__cancel__right_2) ).
fof(f8492,plain,
spl0_607,
inference(avatar_split_clause,[],[f57,f8490]) ).
fof(f8490,plain,
( spl0_607
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| c_Ring__and__Field_Odvd__class_Odvd(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_607])]) ).
fof(f57,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| c_Ring__and__Field_Odvd__class_Odvd(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__mult__cancel__left_2) ).
fof(f8488,plain,
spl0_606,
inference(avatar_split_clause,[],[f15,f8486]) ).
fof(f8486,plain,
( spl0_606
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f15,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__divide__1__iff_0) ).
fof(f8484,plain,
spl0_605,
inference(avatar_split_clause,[],[f14,f8482]) ).
fof(f8482,plain,
( spl0_605
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f14,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_HOL_Oone__class_Oone(X0)),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__divide__1__iff_1) ).
fof(f8480,plain,
spl0_604,
inference(avatar_split_clause,[],[f13,f8478]) ).
fof(f8478,plain,
( spl0_604
<=> ! [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_604])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__mono_0) ).
fof(f8441,plain,
( spl0_603
| ~ spl0_108
| ~ spl0_148
| ~ spl0_183
| ~ spl0_559 ),
inference(avatar_split_clause,[],[f7637,f7389,f2238,f2013,f1843,f8439]) ).
fof(f8439,plain,
( spl0_603
<=> ! [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_603])]) ).
fof(f1843,plain,
( spl0_108
<=> ! [X0] : c_Relation_OId(X0) = c_Relation_Oconverse(c_Relation_OId(X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f2238,plain,
( spl0_183
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ODomain(c_Relation_OId(X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f7389,plain,
( spl0_559
<=> ! [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 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f7637,plain,
( ! [X0] : c_Equiv__Relations_Oequiv(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),c_Relation_OId(X0),X0)
| ~ spl0_108
| ~ spl0_148
| ~ spl0_183
| ~ spl0_559 ),
inference(forward_demodulation,[],[f7636,f2239]) ).
fof(f2239,plain,
( ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ODomain(c_Relation_OId(X0),X0,X0)
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f2238]) ).
fof(f7636,plain,
( ! [X0] : c_Equiv__Relations_Oequiv(c_Relation_ODomain(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0)
| ~ spl0_108
| ~ spl0_148
| ~ spl0_559 ),
inference(trivial_inequality_removal,[],[f7635]) ).
fof(f7635,plain,
( ! [X0] :
( c_Relation_OId(X0) != c_Relation_OId(X0)
| c_Equiv__Relations_Oequiv(c_Relation_ODomain(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0) )
| ~ spl0_108
| ~ spl0_148
| ~ spl0_559 ),
inference(forward_demodulation,[],[f7630,f2014]) ).
fof(f7630,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_ODomain(c_Relation_OId(X0),X0,X0),c_Relation_OId(X0),X0) )
| ~ spl0_108
| ~ spl0_559 ),
inference(superposition,[],[f7390,f1844]) ).
fof(f1844,plain,
( ! [X0] : c_Relation_OId(X0) = c_Relation_Oconverse(c_Relation_OId(X0),X0,X0)
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1843]) ).
fof(f7390,plain,
( ! [X0,X8] :
( c_Relation_Orel__comp(c_Relation_Oconverse(X8,X0,X0),X8,X0,X0,X0) != X8
| c_Equiv__Relations_Oequiv(c_Relation_ODomain(X8,X0,X0),X8,X0) )
| ~ spl0_559 ),
inference(avatar_component_clause,[],[f7389]) ).
fof(f8107,plain,
( spl0_602
| ~ spl0_480
| ~ spl0_558 ),
inference(avatar_split_clause,[],[f7625,f7385,f5761,f8105]) ).
fof(f8105,plain,
( spl0_602
<=> ! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f5761,plain,
( spl0_480
<=> ! [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_480])]) ).
fof(f7625,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X0,X1)
| ~ c_Nitpick_Orefl_H(c_Transitive__Closure_Otrancl(X0,X1),X1) )
| ~ spl0_480
| ~ spl0_558 ),
inference(resolution,[],[f7386,f5762]) ).
fof(f5762,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_480 ),
inference(avatar_component_clause,[],[f5761]) ).
fof(f8036,plain,
( spl0_601
| ~ spl0_201
| ~ spl0_579 ),
inference(avatar_split_clause,[],[f7716,f7713,f2344,f8034]) ).
fof(f8034,plain,
( spl0_601
<=> ! [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_601])]) ).
fof(f7713,plain,
( spl0_579
<=> ! [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_579])]) ).
fof(f7716,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_201
| ~ spl0_579 ),
inference(forward_demodulation,[],[f7714,f2346]) ).
fof(f7714,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_579 ),
inference(avatar_component_clause,[],[f7713]) ).
fof(f8009,plain,
( spl0_600
| ~ spl0_178
| ~ spl0_481 ),
inference(avatar_split_clause,[],[f6391,f5765,f2218,f8007]) ).
fof(f8007,plain,
( spl0_600
<=> ! [X11] : ~ c_Wellfounded_Owf(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X11,X11),tc_bool)),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f6391,plain,
( ! [X11] : ~ c_Wellfounded_Owf(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X11,X11),tc_bool)),X11)
| ~ spl0_178
| ~ spl0_481 ),
inference(resolution,[],[f5766,f2219]) ).
fof(f7951,plain,
( spl0_599
| ~ spl0_201
| ~ spl0_570 ),
inference(avatar_split_clause,[],[f7678,f7675,f2344,f7949]) ).
fof(f7949,plain,
( spl0_599
<=> ! [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_599])]) ).
fof(f7675,plain,
( spl0_570
<=> ! [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_570])]) ).
fof(f7678,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_201
| ~ spl0_570 ),
inference(forward_demodulation,[],[f7676,f2346]) ).
fof(f7676,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_570 ),
inference(avatar_component_clause,[],[f7675]) ).
fof(f7865,plain,
( spl0_598
| ~ spl0_177
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f6378,f5761,f2214,f7863]) ).
fof(f7863,plain,
( spl0_598
<=> ! [X2] : ~ c_Nitpick_Orefl_H(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f6378,plain,
( ! [X2] : ~ c_Nitpick_Orefl_H(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2)
| ~ spl0_177
| ~ spl0_480 ),
inference(resolution,[],[f5762,f2215]) ).
fof(f7788,plain,
spl0_597,
inference(avatar_split_clause,[],[f1346,f7786]) ).
fof(f7786,plain,
( spl0_597
<=> ! [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_597])]) ).
fof(f1346,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__nonneg__eq__0__iff_2) ).
fof(f7784,plain,
spl0_596,
inference(avatar_split_clause,[],[f1251,f7782]) ).
fof(f7782,plain,
( spl0_596
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X3 = X4
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f1251,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X3 = X4
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X4))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X4),X3)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_linorder__neqE__ordered__idom_0) ).
fof(f7780,plain,
spl0_595,
inference(avatar_split_clause,[],[f1244,f7778]) ).
fof(f7778,plain,
( spl0_595
<=> ! [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_595])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_linorder__antisym__conv3_0) ).
fof(f7776,plain,
spl0_594,
inference(avatar_split_clause,[],[f958,f7774]) ).
fof(f7774,plain,
( spl0_594
<=> ! [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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_trancl__unfold_0) ).
fof(f7772,plain,
spl0_593,
inference(avatar_split_clause,[],[f953,f7770]) ).
fof(f7770,plain,
( spl0_593
<=> ! [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_593])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc_Oinduct_2) ).
fof(f7768,plain,
spl0_592,
inference(avatar_split_clause,[],[f949,f7766]) ).
fof(f7766,plain,
( spl0_592
<=> ! [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_592])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc_Oinducts_2) ).
fof(f7764,plain,
spl0_591,
inference(avatar_split_clause,[],[f849,f7762]) ).
fof(f7762,plain,
( spl0_591
<=> ! [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_591])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__supI2_0) ).
fof(f7760,plain,
spl0_590,
inference(avatar_split_clause,[],[f848,f7758]) ).
fof(f7758,plain,
( spl0_590
<=> ! [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_590])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__supI1_0) ).
fof(f7756,plain,
( spl0_589
| ~ spl0_178
| ~ spl0_478 ),
inference(avatar_split_clause,[],[f6375,f5753,f2218,f7754]) ).
fof(f7754,plain,
( spl0_589
<=> ! [X9] : ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X9,X9),tc_bool)),X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f5753,plain,
( spl0_478
<=> ! [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_478])]) ).
fof(f6375,plain,
( ! [X9] : ~ c_Relation_Oirrefl(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X9,X9),tc_bool)),X9)
| ~ spl0_178
| ~ spl0_478 ),
inference(resolution,[],[f5754,f2219]) ).
fof(f5754,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_478 ),
inference(avatar_component_clause,[],[f5753]) ).
fof(f7752,plain,
spl0_588,
inference(avatar_split_clause,[],[f833,f7750]) ).
fof(f7750,plain,
( spl0_588
<=> ! [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_588])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__infI2_0) ).
fof(f7748,plain,
spl0_587,
inference(avatar_split_clause,[],[f832,f7746]) ).
fof(f7746,plain,
( spl0_587
<=> ! [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_587])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__infI1_0) ).
fof(f7744,plain,
spl0_586,
inference(avatar_split_clause,[],[f806,f7742]) ).
fof(f7742,plain,
( spl0_586
<=> ! [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_586])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_IntE_0) ).
fof(f7740,plain,
spl0_585,
inference(avatar_split_clause,[],[f805,f7738]) ).
fof(f7738,plain,
( spl0_585
<=> ! [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_585])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_IntE_1) ).
fof(f7736,plain,
spl0_584,
inference(avatar_split_clause,[],[f801,f7734]) ).
fof(f7734,plain,
( spl0_584
<=> ! [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_584])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_ComplD_0) ).
fof(f7732,plain,
spl0_583,
inference(avatar_split_clause,[],[f800,f7730]) ).
fof(f7730,plain,
( spl0_583
<=> ! [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_583])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_ComplI_0) ).
fof(f7728,plain,
spl0_582,
inference(avatar_split_clause,[],[f792,f7726]) ).
fof(f7726,plain,
( spl0_582
<=> ! [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_582])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_UnCI_0) ).
fof(f7724,plain,
spl0_581,
inference(avatar_split_clause,[],[f791,f7722]) ).
fof(f7722,plain,
( spl0_581
<=> ! [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_581])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_UnCI_1) ).
fof(f7720,plain,
spl0_580,
inference(avatar_split_clause,[],[f717,f7718]) ).
fof(f7718,plain,
( spl0_580
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f717,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X5)),X5) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__eq__eq_4) ).
fof(f7715,plain,
spl0_579,
inference(avatar_split_clause,[],[f621,f7713]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_card__gt__0__iff_2) ).
fof(f7710,plain,
spl0_578,
inference(avatar_split_clause,[],[f600,f7708]) ).
fof(f7708,plain,
( spl0_578
<=> ! [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_578])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__add_0) ).
fof(f7706,plain,
spl0_577,
inference(avatar_split_clause,[],[f494,f7704]) ).
fof(f7704,plain,
( spl0_577
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Ozero__class_Ozero(X0)))
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Oone__class_Oone(X0)) = c_HOL_Osgn__class_Osgn(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f494,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Ozero__class_Ozero(X0)))
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Oone__class_Oone(X0)) = c_HOL_Osgn__class_Osgn(X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn__neg_0) ).
fof(f7702,plain,
spl0_576,
inference(avatar_split_clause,[],[f493,f7700]) ).
fof(f7700,plain,
( spl0_576
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Ozero__class_Ozero(X0)))
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Oone__class_Oone(X0)) != c_HOL_Osgn__class_Osgn(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f493,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X2),c_HOL_Ozero__class_Ozero(X0)))
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Oone__class_Oone(X0)) != c_HOL_Osgn__class_Osgn(X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn__1__neg_0) ).
fof(f7698,plain,
spl0_575,
inference(avatar_split_clause,[],[f364,f7696]) ).
fof(f7696,plain,
( spl0_575
<=> ! [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_575])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__eq__0__iff_0) ).
fof(f7694,plain,
spl0_574,
inference(avatar_split_clause,[],[f351,f7692]) ).
fof(f7692,plain,
( spl0_574
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),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_574])]) ).
fof(f351,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__eq__neg_0) ).
fof(f7690,plain,
spl0_573,
inference(avatar_split_clause,[],[f350,f7688]) ).
fof(f7688,plain,
( spl0_573
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),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_573])]) ).
fof(f350,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__eq__neg_1) ).
fof(f7686,plain,
spl0_572,
inference(avatar_split_clause,[],[f294,f7684]) ).
fof(f7684,plain,
( spl0_572
<=> ! [X5,X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X5) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f294,axiom,
! [X2,X0,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X5)),X5) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_eq__divide__imp_0) ).
fof(f7682,plain,
spl0_571,
inference(avatar_split_clause,[],[f169,f7680]) ).
fof(f7680,plain,
( spl0_571
<=> ! [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_571])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wfE__pf_0) ).
fof(f7677,plain,
spl0_570,
inference(avatar_split_clause,[],[f142,f7675]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_finite__UNIV__card__ge__0_0) ).
fof(f7673,plain,
spl0_569,
inference(avatar_split_clause,[],[f123,f7671]) ).
fof(f7671,plain,
( spl0_569
<=> ! [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_569])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_no__zero__divisors_0) ).
fof(f7668,plain,
spl0_568,
inference(avatar_split_clause,[],[f122,f7666]) ).
fof(f7666,plain,
( spl0_568
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring__no__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_568])]) ).
fof(f122,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring__no__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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__eq__0__iff_0) ).
fof(f7664,plain,
spl0_567,
inference(avatar_split_clause,[],[f95,f7662]) ).
fof(f7662,plain,
( spl0_567
<=> ! [X4,X0,X23,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X23,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X4),X23),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f95,axiom,
! [X3,X0,X4,X23] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X23,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X4),X23),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__diff_0) ).
fof(f7660,plain,
spl0_566,
inference(avatar_split_clause,[],[f56,f7658]) ).
fof(f7658,plain,
( spl0_566
<=> ! [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_566])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__insert__left_0) ).
fof(f7656,plain,
spl0_565,
inference(avatar_split_clause,[],[f55,f7654]) ).
fof(f7654,plain,
( spl0_565
<=> ! [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_565])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__insert__right_0) ).
fof(f7652,plain,
spl0_564,
inference(avatar_split_clause,[],[f34,f7650]) ).
fof(f7650,plain,
( spl0_564
<=> ! [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_564])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__singleton__eq_1) ).
fof(f7623,plain,
( spl0_563
| ~ spl0_480
| ~ spl0_532 ),
inference(avatar_split_clause,[],[f7283,f6638,f5761,f7621]) ).
fof(f7621,plain,
( spl0_563
<=> ! [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_563])]) ).
fof(f6638,plain,
( spl0_532
<=> ! [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_532])]) ).
fof(f7283,plain,
( ! [X0,X1] : ~ c_Nitpick_Orefl_H(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X0),X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_480
| ~ spl0_532 ),
inference(resolution,[],[f6639,f5762]) ).
fof(f6639,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_532 ),
inference(avatar_component_clause,[],[f6638]) ).
fof(f7427,plain,
( spl0_562
| ~ spl0_480
| ~ spl0_530 ),
inference(avatar_split_clause,[],[f7215,f6630,f5761,f7425]) ).
fof(f7425,plain,
( spl0_562
<=> ! [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_562])]) ).
fof(f6630,plain,
( spl0_530
<=> ! [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_530])]) ).
fof(f7215,plain,
( ! [X0,X1] : ~ c_Nitpick_Orefl_H(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X0),X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_480
| ~ spl0_530 ),
inference(resolution,[],[f6631,f5762]) ).
fof(f6631,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_530 ),
inference(avatar_component_clause,[],[f6630]) ).
fof(f7399,plain,
spl0_561,
inference(avatar_split_clause,[],[f1202,f7397]) ).
fof(f7397,plain,
( spl0_561
<=> ! [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_561])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_complete__Lin_1) ).
fof(f7395,plain,
spl0_560,
inference(avatar_split_clause,[],[f1186,f7393]) ).
fof(f7393,plain,
( spl0_560
<=> ! [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_560])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Id__on__iff_0) ).
fof(f7391,plain,
spl0_559,
inference(avatar_split_clause,[],[f1143,f7389]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_comp__equivI_0) ).
fof(f7387,plain,
spl0_558,
inference(avatar_split_clause,[],[f1012,f7385]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acyclic__def_0) ).
fof(f7383,plain,
spl0_557,
inference(avatar_split_clause,[],[f919,f7381]) ).
fof(f7381,plain,
( spl0_557
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f919,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),X1) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_right__inverse__eq_0) ).
fof(f7379,plain,
spl0_556,
inference(avatar_split_clause,[],[f772,f7377]) ).
fof(f7377,plain,
( spl0_556
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X1),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f772,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X1),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__diff__eq_0) ).
fof(f7375,plain,
spl0_555,
inference(avatar_split_clause,[],[f698,f7373]) ).
fof(f7373,plain,
( spl0_555
<=> ! [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_555])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__mono_0) ).
fof(f7371,plain,
spl0_554,
inference(avatar_split_clause,[],[f626,f7369]) ).
fof(f7369,plain,
( spl0_554
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f626,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_diff__minus__eq__add_0) ).
fof(f7367,plain,
spl0_553,
inference(avatar_split_clause,[],[f602,f7365]) ).
fof(f7365,plain,
( spl0_553
<=> ! [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_553])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__left__absorb_0) ).
fof(f7363,plain,
spl0_552,
inference(avatar_split_clause,[],[f601,f7361]) ).
fof(f7361,plain,
( spl0_552
<=> ! [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_552])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc__subset_0) ).
fof(f7359,plain,
spl0_551,
inference(avatar_split_clause,[],[f576,f7357]) ).
fof(f7357,plain,
( spl0_551
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f576,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_diff__minus_0) ).
fof(f7355,plain,
spl0_550,
inference(avatar_split_clause,[],[f575,f7353]) ).
fof(f7353,plain,
( spl0_550
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f575,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_diff__def_0) ).
fof(f7351,plain,
spl0_549,
inference(avatar_split_clause,[],[f574,f7349]) ).
fof(f7349,plain,
( spl0_549
<=> ! [X4,X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f574,axiom,
! [X3,X0,X4] :
( ~ class_Int_Onumber__ring(X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__ring_Osub__add_0) ).
fof(f7347,plain,
spl0_548,
inference(avatar_split_clause,[],[f567,f7345]) ).
fof(f7345,plain,
( spl0_548
<=> ! [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_548])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_subset__trans_0) ).
fof(f7343,plain,
spl0_547,
inference(avatar_split_clause,[],[f518,f7341]) ).
fof(f7341,plain,
( spl0_547
<=> ! [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_547])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__left__absorb_0) ).
fof(f7339,plain,
spl0_546,
inference(avatar_split_clause,[],[f502,f7337]) ).
fof(f7337,plain,
( spl0_546
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f502,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),X1)) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__minus__cancel_0) ).
fof(f7335,plain,
spl0_545,
inference(avatar_split_clause,[],[f439,f7333]) ).
fof(f7333,plain,
( spl0_545
<=> ! [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_545])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__right__cancel_0) ).
fof(f7331,plain,
spl0_544,
inference(avatar_split_clause,[],[f438,f7329]) ).
fof(f7329,plain,
( spl0_544
<=> ! [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_544])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__left__cancel_0) ).
fof(f7327,plain,
spl0_543,
inference(avatar_split_clause,[],[f437,f7325]) ).
fof(f7325,plain,
( spl0_543
<=> ! [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_543])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__imp__eq_0) ).
fof(f7323,plain,
spl0_542,
inference(avatar_split_clause,[],[f405,f7321]) ).
fof(f7321,plain,
( spl0_542
<=> ! [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_542])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_singleton__inject_0) ).
fof(f7319,plain,
( spl0_541
| ~ spl0_480
| ~ spl0_481 ),
inference(avatar_split_clause,[],[f6388,f5765,f5761,f7317]) ).
fof(f7317,plain,
( spl0_541
<=> ! [X4,X3] :
( ~ c_Wellfounded_Owf(X3,X4)
| ~ c_Nitpick_Orefl_H(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f6388,plain,
( ! [X3,X4] :
( ~ c_Wellfounded_Owf(X3,X4)
| ~ c_Nitpick_Orefl_H(X3,X4) )
| ~ spl0_480
| ~ spl0_481 ),
inference(resolution,[],[f5766,f5762]) ).
fof(f7315,plain,
spl0_540,
inference(avatar_split_clause,[],[f338,f7313]) ).
fof(f7313,plain,
( spl0_540
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f338,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X1),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__mult__cancel__left_1) ).
fof(f7311,plain,
spl0_539,
inference(avatar_split_clause,[],[f337,f7309]) ).
fof(f7309,plain,
( spl0_539
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ozero__class_Ozero(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f337,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),c_HOL_Ozero__class_Ozero(X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),c_HOL_Ozero__class_Ozero(X0)),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__mult__cancel__right_1) ).
fof(f7307,plain,
spl0_538,
inference(avatar_split_clause,[],[f326,f7305]) ).
fof(f7305,plain,
( spl0_538
<=> ! [X4,X0,X23] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X23)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f326,axiom,
! [X0,X4,X23] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X23)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X4),X23)) = X4 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__cancel__end_1) ).
fof(f7303,plain,
spl0_537,
inference(avatar_split_clause,[],[f325,f7301]) ).
fof(f7301,plain,
( spl0_537
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f325,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__add__cancel_0) ).
fof(f7299,plain,
spl0_536,
inference(avatar_split_clause,[],[f256,f7297]) ).
fof(f7297,plain,
( spl0_536
<=> ! [X37,X4,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X4 = X37
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X37),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f256,axiom,
! [X3,X0,X37,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X4 = X37
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X3) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X37),X4) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_eq__eqI_1) ).
fof(f7211,plain,
( spl0_535
| ~ spl0_478
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f6377,f5761,f5753,f7209]) ).
fof(f7209,plain,
( spl0_535
<=> ! [X0,X1] :
( ~ c_Nitpick_Orefl_H(X0,X1)
| ~ c_Relation_Oirrefl(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f6377,plain,
( ! [X0,X1] :
( ~ c_Nitpick_Orefl_H(X0,X1)
| ~ c_Relation_Oirrefl(X0,X1) )
| ~ spl0_478
| ~ spl0_480 ),
inference(resolution,[],[f5762,f5754]) ).
fof(f7049,plain,
( spl0_534
| ~ spl0_201
| ~ spl0_518 ),
inference(avatar_split_clause,[],[f6584,f6581,f2344,f7047]) ).
fof(f7047,plain,
( spl0_534
<=> ! [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_534])]) ).
fof(f6581,plain,
( spl0_518
<=> ! [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_518])]) ).
fof(f6584,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_201
| ~ spl0_518 ),
inference(forward_demodulation,[],[f6582,f2346]) ).
fof(f6582,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_518 ),
inference(avatar_component_clause,[],[f6581]) ).
fof(f6670,plain,
( spl0_533
| ~ spl0_438
| ~ spl0_481 ),
inference(avatar_split_clause,[],[f6387,f5765,f5103,f6668]) ).
fof(f6387,plain,
( ! [X2,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ spl0_438
| ~ spl0_481 ),
inference(resolution,[],[f5766,f5104]) ).
fof(f6640,plain,
spl0_532,
inference(avatar_split_clause,[],[f1260,f6638]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__mkbot_0) ).
fof(f6636,plain,
spl0_531,
inference(avatar_split_clause,[],[f1249,f6634]) ).
fof(f6634,plain,
( spl0_531
<=> ! [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_531])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_nat__neq__iff_0) ).
fof(f6632,plain,
spl0_530,
inference(avatar_split_clause,[],[f1243,f6630]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_in__mktop_0) ).
fof(f6628,plain,
spl0_529,
inference(avatar_split_clause,[],[f1188,f6626]) ).
fof(f6626,plain,
( spl0_529
<=> ! [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_529])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_pair__in__Id__conv_0) ).
fof(f6624,plain,
spl0_528,
inference(avatar_split_clause,[],[f1139,f6622]) ).
fof(f6622,plain,
( spl0_528
<=> ! [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_528])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__inv__image_0) ).
fof(f6620,plain,
( spl0_527
| ~ spl0_438
| ~ spl0_478 ),
inference(avatar_split_clause,[],[f6372,f5753,f5103,f6618]) ).
fof(f6372,plain,
( ! [X2,X1] : ~ c_Relation_Oirrefl(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ spl0_438
| ~ spl0_478 ),
inference(resolution,[],[f5754,f5104]) ).
fof(f6616,plain,
spl0_526,
inference(avatar_split_clause,[],[f975,f6614]) ).
fof(f6614,plain,
( spl0_526
<=> ! [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_526])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__less__two_0) ).
fof(f6612,plain,
spl0_525,
inference(avatar_split_clause,[],[f835,f6610]) ).
fof(f6610,plain,
( spl0_525
<=> ! [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_525])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__le__not__le_2) ).
fof(f6608,plain,
spl0_524,
inference(avatar_split_clause,[],[f785,f6606]) ).
fof(f6606,plain,
( spl0_524
<=> ! [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_524])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__iff_2) ).
fof(f6604,plain,
spl0_523,
inference(avatar_split_clause,[],[f715,f6602]) ).
fof(f6602,plain,
( spl0_523
<=> ! [X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Oone__class_Oone(X0))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f715,axiom,
! [X3,X0] :
( ~ class_Int_Onumber__ring(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Oone__class_Oone(X0))),X3) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__ring_Oneg__mul_0) ).
fof(f6600,plain,
spl0_522,
inference(avatar_split_clause,[],[f692,f6598]) ).
fof(f6598,plain,
( spl0_522
<=> ! [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_522])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf1I_0) ).
fof(f6596,plain,
spl0_521,
inference(avatar_split_clause,[],[f686,f6594]) ).
fof(f6594,plain,
( spl0_521
<=> ! [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_521])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_subset__Compl__self__eq_0) ).
fof(f6592,plain,
spl0_520,
inference(avatar_split_clause,[],[f608,f6590]) ).
fof(f6590,plain,
( spl0_520
<=> ! [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_520])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_card__mono_0) ).
fof(f6588,plain,
spl0_519,
inference(avatar_split_clause,[],[f599,f6586]) ).
fof(f6586,plain,
( spl0_519
<=> ! [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_519])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__is__Un_0) ).
fof(f6583,plain,
spl0_518,
inference(avatar_split_clause,[],[f557,f6581]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__power_0) ).
fof(f6579,plain,
spl0_517,
inference(avatar_split_clause,[],[f556,f6577]) ).
fof(f6577,plain,
( spl0_517
<=> ! [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_517])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__subset__iff_1) ).
fof(f6575,plain,
spl0_516,
inference(avatar_split_clause,[],[f555,f6573]) ).
fof(f6573,plain,
( spl0_516
<=> ! [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_516])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__subset__iff_0) ).
fof(f6571,plain,
spl0_515,
inference(avatar_split_clause,[],[f520,f6569]) ).
fof(f6569,plain,
( spl0_515
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f520,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f6567,plain,
spl0_514,
inference(avatar_split_clause,[],[f519,f6565]) ).
fof(f6565,plain,
( spl0_514
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f519,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f6563,plain,
spl0_513,
inference(avatar_split_clause,[],[f482,f6561]) ).
fof(f6561,plain,
( spl0_513
<=> ! [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_513])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__greatest_0) ).
fof(f6559,plain,
spl0_512,
inference(avatar_split_clause,[],[f462,f6557]) ).
fof(f6557,plain,
( spl0_512
<=> ! [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_512])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__subset__iff_0) ).
fof(f6555,plain,
spl0_511,
inference(avatar_split_clause,[],[f461,f6553]) ).
fof(f6553,plain,
( spl0_511
<=> ! [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_511])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__subset__iff_1) ).
fof(f6551,plain,
spl0_510,
inference(avatar_split_clause,[],[f455,f6549]) ).
fof(f6549,plain,
( spl0_510
<=> ! [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_510])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__empty_0) ).
fof(f6547,plain,
spl0_509,
inference(avatar_split_clause,[],[f454,f6545]) ).
fof(f6545,plain,
( spl0_509
<=> ! [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_509])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__empty_1) ).
fof(f6543,plain,
spl0_508,
inference(avatar_split_clause,[],[f389,f6541]) ).
fof(f6541,plain,
( spl0_508
<=> ! [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_508])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__sup__iff_2) ).
fof(f6539,plain,
spl0_507,
inference(avatar_split_clause,[],[f374,f6537]) ).
fof(f6537,plain,
( spl0_507
<=> ! [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_507])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__aci_I6_J_0) ).
fof(f6535,plain,
spl0_506,
inference(avatar_split_clause,[],[f373,f6533]) ).
fof(f6533,plain,
( spl0_506
<=> ! [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_506])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__aci_I7_J_0) ).
fof(f6531,plain,
spl0_505,
inference(avatar_split_clause,[],[f372,f6529]) ).
fof(f6529,plain,
( spl0_505
<=> ! [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_505])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__left__commute_0) ).
fof(f6527,plain,
spl0_504,
inference(avatar_split_clause,[],[f354,f6525]) ).
fof(f6525,plain,
( spl0_504
<=> ! [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_504])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_finite__compl_0) ).
fof(f6523,plain,
spl0_503,
inference(avatar_split_clause,[],[f271,f6521]) ).
fof(f6521,plain,
( spl0_503
<=> ! [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_503])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__assoc_0) ).
fof(f6519,plain,
spl0_502,
inference(avatar_split_clause,[],[f198,f6517]) ).
fof(f6517,plain,
( spl0_502
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f198,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f6515,plain,
spl0_501,
inference(avatar_split_clause,[],[f197,f6513]) ).
fof(f6513,plain,
( spl0_501
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f197,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f6511,plain,
spl0_500,
inference(avatar_split_clause,[],[f139,f6509]) ).
fof(f6509,plain,
( spl0_500
<=> ! [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_500])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__assoc_0) ).
fof(f6507,plain,
spl0_499,
inference(avatar_split_clause,[],[f138,f6505]) ).
fof(f6505,plain,
( spl0_499
<=> ! [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_499])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__left__commute_0) ).
fof(f6503,plain,
spl0_498,
inference(avatar_split_clause,[],[f137,f6501]) ).
fof(f6501,plain,
( spl0_498
<=> ! [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_498])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__aci_I3_J_0) ).
fof(f6499,plain,
spl0_497,
inference(avatar_split_clause,[],[f136,f6497]) ).
fof(f6497,plain,
( spl0_497
<=> ! [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_497])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__aci_I2_J_0) ).
fof(f6495,plain,
( spl0_496
| ~ spl0_397
| ~ spl0_481 ),
inference(avatar_split_clause,[],[f6386,f5765,f4107,f6493]) ).
fof(f6493,plain,
( spl0_496
<=> ! [X0] : ~ c_Wellfounded_Owf(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f6386,plain,
( ! [X0] : ~ c_Wellfounded_Owf(c_Relation_OId(X0),X0)
| ~ spl0_397
| ~ spl0_481 ),
inference(resolution,[],[f5766,f4108]) ).
fof(f6491,plain,
spl0_495,
inference(avatar_split_clause,[],[f134,f6489]) ).
fof(f6489,plain,
( spl0_495
<=> ! [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_495])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_single__valued__rel__comp_0) ).
fof(f6487,plain,
spl0_494,
inference(avatar_split_clause,[],[f133,f6485]) ).
fof(f6485,plain,
( spl0_494
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2) = X1
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f133,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2) = X1
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__unique_0) ).
fof(f6483,plain,
spl0_493,
inference(avatar_split_clause,[],[f132,f6481]) ).
fof(f6481,plain,
( spl0_493
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1) = X2
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f132,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1) = X2
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_eq__neg__iff__add__eq__0_1) ).
fof(f6479,plain,
spl0_492,
inference(avatar_split_clause,[],[f128,f6477]) ).
fof(f6477,plain,
( spl0_492
<=> ! [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_492])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup1E_0) ).
fof(f6396,plain,
( spl0_491
| ~ spl0_397
| ~ spl0_478 ),
inference(avatar_split_clause,[],[f6371,f5753,f4107,f6394]) ).
fof(f6394,plain,
( spl0_491
<=> ! [X0] : ~ c_Relation_Oirrefl(c_Relation_OId(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f6371,plain,
( ! [X0] : ~ c_Relation_Oirrefl(c_Relation_OId(X0),X0)
| ~ spl0_397
| ~ spl0_478 ),
inference(resolution,[],[f5754,f4108]) ).
fof(f6197,plain,
( spl0_490
| ~ spl0_36
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2619,f2385,f1537,f6195]) ).
fof(f2619,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_211 ),
inference(resolution,[],[f2386,f1539]) ).
fof(f1539,plain,
( class_Lattices_Olattice(tc_nat)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1537]) ).
fof(f6151,plain,
( spl0_489
| ~ spl0_201
| ~ spl0_469 ),
inference(avatar_split_clause,[],[f5719,f5716,f2344,f6149]) ).
fof(f6149,plain,
( spl0_489
<=> ! [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_489])]) ).
fof(f5716,plain,
( spl0_469
<=> ! [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_469])]) ).
fof(f5719,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_201
| ~ spl0_469 ),
inference(forward_demodulation,[],[f5717,f2346]) ).
fof(f5717,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_469 ),
inference(avatar_component_clause,[],[f5716]) ).
fof(f6011,plain,
( spl0_488
| ~ spl0_48
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2595,f2377,f1597,f6009]) ).
fof(f2377,plain,
( spl0_209
<=> ! [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_209])]) ).
fof(f2595,plain,
( ! [X2,X3] : c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,tc_bool),tc_bool) = X2
| ~ spl0_48
| ~ spl0_209 ),
inference(resolution,[],[f2378,f1599]) ).
fof(f2378,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_209 ),
inference(avatar_component_clause,[],[f2377]) ).
fof(f6005,plain,
( spl0_487
| ~ spl0_201
| ~ spl0_458 ),
inference(avatar_split_clause,[],[f5674,f5671,f2344,f6003]) ).
fof(f6003,plain,
( spl0_487
<=> ! [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_487])]) ).
fof(f5671,plain,
( spl0_458
<=> ! [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_458])]) ).
fof(f5674,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_201
| ~ spl0_458 ),
inference(forward_demodulation,[],[f5672,f2346]) ).
fof(f5672,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_458 ),
inference(avatar_component_clause,[],[f5671]) ).
fof(f5869,plain,
( spl0_486
| ~ spl0_36
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2594,f2377,f1537,f5867]) ).
fof(f2594,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_209 ),
inference(resolution,[],[f2378,f1539]) ).
fof(f5783,plain,
spl0_485,
inference(avatar_split_clause,[],[f1341,f5781]) ).
fof(f5781,plain,
( spl0_485
<=> ! [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_485])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_ATP__Linkup_OCOMBS__def_0) ).
fof(f5779,plain,
spl0_484,
inference(avatar_split_clause,[],[f1235,f5777]) ).
fof(f5777,plain,
( spl0_484
<=> ! [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_484])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_xt1_I9_J_0) ).
fof(f5775,plain,
spl0_483,
inference(avatar_split_clause,[],[f1234,f5773]) ).
fof(f5773,plain,
( spl0_483
<=> ! [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_483])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_not__less__iff__gr__or__eq_1) ).
fof(f5771,plain,
spl0_482,
inference(avatar_split_clause,[],[f1232,f5769]) ).
fof(f5769,plain,
( spl0_482
<=> ! [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_482])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_order__less__asym_H_0) ).
fof(f5767,plain,
spl0_481,
inference(avatar_split_clause,[],[f1190,f5765]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__irrefl_0) ).
fof(f5763,plain,
spl0_480,
inference(avatar_split_clause,[],[f1189,f5761]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Nitpick_Orefl_H__def_0) ).
fof(f5759,plain,
( spl0_479
| ~ spl0_28
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2580,f2349,f1497,f5757]) ).
fof(f1497,plain,
( spl0_28
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f2349,plain,
( spl0_202
<=> ! [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_202])]) ).
fof(f2580,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)) = X0
| ~ spl0_28
| ~ spl0_202 ),
inference(resolution,[],[f2350,f1499]) ).
fof(f1499,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f1497]) ).
fof(f2350,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_202 ),
inference(avatar_component_clause,[],[f2349]) ).
fof(f5755,plain,
spl0_478,
inference(avatar_split_clause,[],[f1173,f5753]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_irrefl__def_0) ).
fof(f5751,plain,
spl0_477,
inference(avatar_split_clause,[],[f869,f5749]) ).
fof(f5749,plain,
( spl0_477
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Osgn__class_Osgn(X2,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f869,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Osgn__class_Osgn(X2,X0)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn__1__pos_0) ).
fof(f5747,plain,
spl0_476,
inference(avatar_split_clause,[],[f868,f5745]) ).
fof(f5745,plain,
( spl0_476
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f868,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X2,X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),c_HOL_Ozero__class_Ozero(X0)),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn__pos_0) ).
fof(f5743,plain,
spl0_475,
inference(avatar_split_clause,[],[f814,f5741]) ).
fof(f5741,plain,
( spl0_475
<=> ! [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_475])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_order__less__le_2) ).
fof(f5739,plain,
spl0_474,
inference(avatar_split_clause,[],[f810,f5737]) ).
fof(f5737,plain,
( spl0_474
<=> ! [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_474])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_linorder__antisym__conv2_0) ).
fof(f5735,plain,
spl0_473,
inference(avatar_split_clause,[],[f781,f5733]) ).
fof(f5733,plain,
( spl0_473
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X1,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f781,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X1,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__le__iff_0) ).
fof(f5731,plain,
spl0_472,
inference(avatar_split_clause,[],[f779,f5729]) ).
fof(f5729,plain,
( spl0_472
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0)
| c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f779,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0)
| c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__minus__iff_0) ).
fof(f5727,plain,
spl0_471,
inference(avatar_split_clause,[],[f778,f5725]) ).
fof(f5725,plain,
( spl0_471
<=> ! [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_471])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__funD_0) ).
fof(f5723,plain,
spl0_470,
inference(avatar_split_clause,[],[f677,f5721]) ).
fof(f5721,plain,
( spl0_470
<=> ! [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_470])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_single__valued__subset_0) ).
fof(f5718,plain,
spl0_469,
inference(avatar_split_clause,[],[f478,f5716]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__0__left_1) ).
fof(f5714,plain,
( spl0_468
| ~ spl0_14
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2577,f2332,f1427,f5712]) ).
fof(f2332,plain,
( spl0_198
<=> ! [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_198])]) ).
fof(f2577,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) = X0
| ~ spl0_14
| ~ spl0_198 ),
inference(resolution,[],[f2333,f1429]) ).
fof(f2333,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_198 ),
inference(avatar_component_clause,[],[f2332]) ).
fof(f5710,plain,
spl0_467,
inference(avatar_split_clause,[],[f453,f5708]) ).
fof(f5708,plain,
( spl0_467
<=> ! [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_467])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__power__same_0) ).
fof(f5706,plain,
spl0_466,
inference(avatar_split_clause,[],[f433,f5704]) ).
fof(f5704,plain,
( spl0_466
<=> ! [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_466])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__subset_0) ).
fof(f5702,plain,
spl0_465,
inference(avatar_split_clause,[],[f415,f5700]) ).
fof(f5700,plain,
( spl0_465
<=> ! [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_465])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Compl__partition_0) ).
fof(f5698,plain,
spl0_464,
inference(avatar_split_clause,[],[f414,f5696]) ).
fof(f5696,plain,
( spl0_464
<=> ! [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_464])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Compl__partition2_0) ).
fof(f5694,plain,
spl0_463,
inference(avatar_split_clause,[],[f409,f5692]) ).
fof(f5692,plain,
( spl0_463
<=> ! [X4,X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f409,axiom,
! [X3,X0,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X4) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__ringb_Osubr0__iff_0) ).
fof(f5690,plain,
spl0_462,
inference(avatar_split_clause,[],[f316,f5688]) ).
fof(f5688,plain,
( spl0_462
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f316,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__iff__diff__le__0_0) ).
fof(f5686,plain,
spl0_461,
inference(avatar_split_clause,[],[f315,f5684]) ).
fof(f5684,plain,
( spl0_461
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X2,X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f315,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X2,X1,X0)
| ~ c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__iff__diff__le__0_1) ).
fof(f5682,plain,
spl0_460,
inference(avatar_split_clause,[],[f303,f5680]) ).
fof(f5680,plain,
( spl0_460
<=> ! [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_460])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Compl__eq__Compl__iff_0) ).
fof(f5678,plain,
spl0_459,
inference(avatar_split_clause,[],[f258,f5676]) ).
fof(f5676,plain,
( spl0_459
<=> ! [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_459])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_diff__eq_0) ).
fof(f5673,plain,
spl0_458,
inference(avatar_split_clause,[],[f234,f5671]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__eq__0__iff_1) ).
fof(f5669,plain,
( spl0_457
| ~ spl0_64
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f2130,f2029,f1666,f5667]) ).
fof(f5667,plain,
( spl0_457
<=> ! [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_457])]) ).
fof(f2130,plain,
( ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Wellfounded_Omlex__prod(X2,X0,X1),X1) )
| ~ spl0_64
| ~ spl0_152 ),
inference(resolution,[],[f2030,f1667]) ).
fof(f5665,plain,
spl0_456,
inference(avatar_split_clause,[],[f202,f5663]) ).
fof(f5663,plain,
( spl0_456
<=> ! [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_456])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_singletonE_0) ).
fof(f5661,plain,
spl0_455,
inference(avatar_split_clause,[],[f199,f5659]) ).
fof(f5659,plain,
( spl0_455
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Olower__semilattice__class_Oinf(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f199,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Olower__semilattice__class_Oinf(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__0__imp__0_0) ).
fof(f5657,plain,
spl0_454,
inference(avatar_split_clause,[],[f190,f5655]) ).
fof(f5655,plain,
( spl0_454
<=> ! [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_454])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_of__nat__le__iff_1) ).
fof(f5653,plain,
spl0_453,
inference(avatar_split_clause,[],[f189,f5651]) ).
fof(f5651,plain,
( spl0_453
<=> ! [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_453])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_of__nat__le__iff_0) ).
fof(f5649,plain,
spl0_452,
inference(avatar_split_clause,[],[f173,f5647]) ).
fof(f5647,plain,
( spl0_452
<=> ! [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_452])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Compl__disjoint_0) ).
fof(f5645,plain,
spl0_451,
inference(avatar_split_clause,[],[f172,f5643]) ).
fof(f5643,plain,
( spl0_451
<=> ! [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_451])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Compl__disjoint2_0) ).
fof(f5641,plain,
spl0_450,
inference(avatar_split_clause,[],[f161,f5639]) ).
fof(f5639,plain,
( spl0_450
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f161,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__0__imp__0_0) ).
fof(f5637,plain,
spl0_449,
inference(avatar_split_clause,[],[f78,f5635]) ).
fof(f5635,plain,
( spl0_449
<=> ! [X2,X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X2) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f78,axiom,
! [X2,X3,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X2) != X3 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f5633,plain,
spl0_448,
inference(avatar_split_clause,[],[f51,f5631]) ).
fof(f5631,plain,
( spl0_448
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X2,X1,X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f51,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X2,X1,X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__le__iff__le_0) ).
fof(f5629,plain,
spl0_447,
inference(avatar_split_clause,[],[f50,f5627]) ).
fof(f5627,plain,
( spl0_447
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f50,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__imp__neg__le_0) ).
fof(f5622,plain,
spl0_446,
inference(avatar_split_clause,[],[f30,f5620]) ).
fof(f5620,plain,
( spl0_446
<=> ! [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_446])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__imp__power__dvd_0) ).
fof(f5618,plain,
spl0_445,
inference(avatar_split_clause,[],[f16,f5616]) ).
fof(f5616,plain,
( spl0_445
<=> ! [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_445])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sym__Un_0) ).
fof(f5463,plain,
( spl0_444
| ~ spl0_201
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f5057,f5054,f2344,f5461]) ).
fof(f5461,plain,
( spl0_444
<=> ! [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_444])]) ).
fof(f5054,plain,
( spl0_426
<=> ! [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_426])]) ).
fof(f5057,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_201
| ~ spl0_426 ),
inference(forward_demodulation,[],[f5055,f2346]) ).
fof(f5055,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_426 ),
inference(avatar_component_clause,[],[f5054]) ).
fof(f5441,plain,
( ~ spl0_442
| spl0_443
| ~ spl0_57
| ~ spl0_201
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f5273,f5009,f2344,f1638,f5439,f5435]) ).
fof(f5435,plain,
( spl0_442
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f5439,plain,
( spl0_443
<=> ! [X2] : c_lessequals(X2,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f5009,plain,
( spl0_415
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f5273,plain,
( ! [X2] :
( c_lessequals(X2,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_57
| ~ spl0_201
| ~ spl0_415 ),
inference(forward_demodulation,[],[f5262,f2346]) ).
fof(f5262,plain,
( ! [X2] :
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_57
| ~ spl0_415 ),
inference(resolution,[],[f5010,f1639]) ).
fof(f5010,plain,
( ! [X2,X0] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_415 ),
inference(avatar_component_clause,[],[f5009]) ).
fof(f5118,plain,
spl0_441,
inference(avatar_split_clause,[],[f1351,f5116]) ).
fof(f5116,plain,
( spl0_441
<=> ! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),c_Transitive__Closure_Otrancl(X8,X0),tc_fun(tc_prod(X0,X0),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f1351,plain,
! [X0,X8] : c_Transitive__Closure_Ortrancl(X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(X0),c_Transitive__Closure_Otrancl(X8,X0),tc_fun(tc_prod(X0,X0),tc_bool)),
inference(forward_demodulation,[],[f1032,f1162]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__unfold_0) ).
fof(f5114,plain,
( ~ spl0_13
| ~ spl0_440
| ~ spl0_101
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2392,f2344,f1815,f5111,f1422]) ).
fof(f1422,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f5111,plain,
( spl0_440
<=> 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_440])]) ).
fof(f1815,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(f2392,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_201 ),
inference(superposition,[],[f1816,f2346]) ).
fof(f1816,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,[],[f1815]) ).
fof(f5109,plain,
spl0_439,
inference(avatar_split_clause,[],[f1268,f5107]) ).
fof(f5107,plain,
( spl0_439
<=> ! [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_439])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_COMBC__def_0) ).
fof(f5105,plain,
spl0_438,
inference(avatar_split_clause,[],[f1180,f5103]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl_Ortrancl__refl_0) ).
fof(f5101,plain,
spl0_437,
inference(avatar_split_clause,[],[f1153,f5099]) ).
fof(f5099,plain,
( spl0_437
<=> ! [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_437])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_equiv__comp__eq_0) ).
fof(f5097,plain,
spl0_436,
inference(avatar_split_clause,[],[f1151,f5095]) ).
fof(f5095,plain,
( spl0_436
<=> ! [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_436])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__def_1) ).
fof(f5093,plain,
spl0_435,
inference(avatar_split_clause,[],[f1030,f5091]) ).
fof(f5091,plain,
( spl0_435
<=> ! [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) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_trancl__reflcl_0) ).
fof(f5089,plain,
spl0_434,
inference(avatar_split_clause,[],[f1029,f5087]) ).
fof(f5087,plain,
( spl0_434
<=> ! [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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_reflcl__trancl_0) ).
fof(f5085,plain,
spl0_433,
inference(avatar_split_clause,[],[f961,f5083]) ).
fof(f5083,plain,
( spl0_433
<=> ! [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_433])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__reflcl_0) ).
fof(f5081,plain,
spl0_432,
inference(avatar_split_clause,[],[f960,f5079]) ).
fof(f5079,plain,
( spl0_432
<=> ! [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_432])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__reflcl__absorb_0) ).
fof(f5077,plain,
spl0_431,
inference(avatar_split_clause,[],[f926,f5075]) ).
fof(f5075,plain,
( spl0_431
<=> ! [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_431])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setsum__empty_0) ).
fof(f5073,plain,
spl0_430,
inference(avatar_split_clause,[],[f921,f5071]) ).
fof(f5071,plain,
( spl0_430
<=> ! [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_430])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__add__one_0) ).
fof(f5069,plain,
( spl0_429
| ~ spl0_99
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2389,f2344,f1807,f5067]) ).
fof(f5067,plain,
( spl0_429
<=> ! [X1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Orderings_Obot__class_Obot(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f1807,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(f2389,plain,
( ! [X1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),c_Orderings_Obot__class_Obot(tc_nat)))
| ~ spl0_99
| ~ spl0_201 ),
inference(superposition,[],[f1808,f2346]) ).
fof(f1808,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,[],[f1807]) ).
fof(f5065,plain,
spl0_428,
inference(avatar_split_clause,[],[f914,f5063]) ).
fof(f5063,plain,
( spl0_428
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f914,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oone__class_Oone(X0) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X3),X3) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_right__inverse__eq_1) ).
fof(f5061,plain,
spl0_427,
inference(avatar_split_clause,[],[f876,f5059]) ).
fof(f5059,plain,
( spl0_427
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2)),c_HOL_Ozero__class_Ozero(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f876,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2)),c_HOL_Ozero__class_Ozero(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_not__square__less__zero_0) ).
fof(f5056,plain,
spl0_426,
inference(avatar_split_clause,[],[f679,f5054]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_card__eq__0__iff_0) ).
fof(f5052,plain,
spl0_425,
inference(avatar_split_clause,[],[f656,f5050]) ).
fof(f5050,plain,
( spl0_425
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f656,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X1)),X1) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__diff__cancel_0) ).
fof(f5048,plain,
spl0_424,
inference(avatar_split_clause,[],[f513,f5046]) ).
fof(f5046,plain,
( spl0_424
<=> ! [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_424])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__mult_0) ).
fof(f5044,plain,
spl0_423,
inference(avatar_split_clause,[],[f512,f5042]) ).
fof(f5042,plain,
( spl0_423
<=> ! [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_423])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__mult2_0) ).
fof(f5040,plain,
spl0_422,
inference(avatar_split_clause,[],[f511,f5038]) ).
fof(f5038,plain,
( spl0_422
<=> ! [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_422])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__mult__left_0) ).
fof(f5036,plain,
spl0_421,
inference(avatar_split_clause,[],[f510,f5034]) ).
fof(f5034,plain,
( spl0_421
<=> ! [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_421])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__mult__right_0) ).
fof(f5032,plain,
spl0_420,
inference(avatar_split_clause,[],[f366,f5030]) ).
fof(f5030,plain,
( spl0_420
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f366,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__le__0__iff__le_0) ).
fof(f5028,plain,
spl0_419,
inference(avatar_split_clause,[],[f365,f5026]) ).
fof(f5026,plain,
( spl0_419
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f365,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__le__0__iff__le_1) ).
fof(f5023,plain,
spl0_418,
inference(avatar_split_clause,[],[f356,f5021]) ).
fof(f5021,plain,
( spl0_418
<=> ! [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_418])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_subset__empty_0) ).
fof(f5019,plain,
spl0_417,
inference(avatar_split_clause,[],[f308,f5017]) ).
fof(f5017,plain,
( spl0_417
<=> ! [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_417])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_equalityI_0) ).
fof(f5015,plain,
spl0_416,
inference(avatar_split_clause,[],[f242,f5013]) ).
fof(f5013,plain,
( spl0_416
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f242,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__0__le__iff__le_1) ).
fof(f5011,plain,
spl0_415,
inference(avatar_split_clause,[],[f241,f5009]) ).
fof(f241,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__0__le__iff__le_0) ).
fof(f5007,plain,
spl0_414,
inference(avatar_split_clause,[],[f238,f5005]) ).
fof(f5005,plain,
( spl0_414
<=> ! [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_414])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__commute_0) ).
fof(f5003,plain,
spl0_413,
inference(avatar_split_clause,[],[f211,f5001]) ).
fof(f5001,plain,
( spl0_413
<=> ! [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_413])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f4999,plain,
spl0_412,
inference(avatar_split_clause,[],[f201,f4997]) ).
fof(f4997,plain,
( spl0_412
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f201,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1)),X1) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_diff__add__cancel_0) ).
fof(f4995,plain,
spl0_411,
inference(avatar_split_clause,[],[f196,f4993]) ).
fof(f4993,plain,
( spl0_411
<=> ! [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_411])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__subset_1) ).
fof(f4991,plain,
spl0_410,
inference(avatar_split_clause,[],[f195,f4989]) ).
fof(f4989,plain,
( spl0_410
<=> ! [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_410])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_subset__insertI2_0) ).
fof(f4987,plain,
spl0_409,
inference(avatar_split_clause,[],[f156,f4985]) ).
fof(f4985,plain,
( spl0_409
<=> ! [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_409])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_refl__reflcl_0) ).
fof(f4979,plain,
spl0_408,
inference(avatar_split_clause,[],[f114,f4977]) ).
fof(f4977,plain,
( spl0_408
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f114,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_double__eq__0__iff_0) ).
fof(f4975,plain,
spl0_407,
inference(avatar_split_clause,[],[f71,f4973]) ).
fof(f4973,plain,
( spl0_407
<=> ! [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_407])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__power_0) ).
fof(f4971,plain,
spl0_406,
inference(avatar_split_clause,[],[f53,f4969]) ).
fof(f4969,plain,
( spl0_406
<=> ! [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_406])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_one__le__power_0) ).
fof(f4967,plain,
spl0_405,
inference(avatar_split_clause,[],[f6,f4965]) ).
fof(f4965,plain,
( spl0_405
<=> ! [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_405])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_comm__monoid__add_Omult__commute_0) ).
fof(f4963,plain,
spl0_404,
inference(avatar_split_clause,[],[f5,f4961]) ).
fof(f4961,plain,
( spl0_404
<=> ! [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_404])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Oadd__c_0) ).
fof(f4863,plain,
( spl0_403
| ~ spl0_329
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4211,f3844,f3318,f4861]) ).
fof(f4861,plain,
( spl0_403
<=> ! [X47] : c_Relation_Osym(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X47,X47),tc_bool)),X47) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f3318,plain,
( spl0_329
<=> ! [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_329])]) ).
fof(f3844,plain,
( spl0_344
<=> ! [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_344])]) ).
fof(f4211,plain,
( ! [X47] : c_Relation_Osym(c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X47,X47),tc_bool)),X47)
| ~ spl0_329
| ~ spl0_344 ),
inference(superposition,[],[f3319,f3845]) ).
fof(f3845,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_344 ),
inference(avatar_component_clause,[],[f3844]) ).
fof(f3319,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_329 ),
inference(avatar_component_clause,[],[f3318]) ).
fof(f4652,plain,
( spl0_402
| ~ spl0_201
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f3792,f3788,f2344,f4649]) ).
fof(f4649,plain,
( spl0_402
<=> 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_402])]) ).
fof(f3788,plain,
( spl0_339
<=> 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_339])]) ).
fof(f3792,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_201
| ~ spl0_339 ),
inference(forward_demodulation,[],[f3790,f2346]) ).
fof(f3790,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_339 ),
inference(avatar_component_clause,[],[f3788]) ).
fof(f4363,plain,
( spl0_401
| ~ spl0_201
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f3582,f3579,f2344,f4361]) ).
fof(f4361,plain,
( spl0_401
<=> ! [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_401])]) ).
fof(f3579,plain,
( spl0_337
<=> ! [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_337])]) ).
fof(f3582,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_201
| ~ spl0_337 ),
inference(forward_demodulation,[],[f3580,f2346]) ).
fof(f3580,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_337 ),
inference(avatar_component_clause,[],[f3579]) ).
fof(f4121,plain,
spl0_400,
inference(avatar_split_clause,[],[f1267,f4119]) ).
fof(f4119,plain,
( spl0_400
<=> ! [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_400])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_COMBB__def_0) ).
fof(f4117,plain,
spl0_399,
inference(avatar_split_clause,[],[f1239,f4115]) ).
fof(f4115,plain,
( spl0_399
<=> ! [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_399])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Pair__eq_0) ).
fof(f4113,plain,
spl0_398,
inference(avatar_split_clause,[],[f1238,f4111]) ).
fof(f4111,plain,
( spl0_398
<=> ! [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_398])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Pair__eq_1) ).
fof(f4109,plain,
spl0_397,
inference(avatar_split_clause,[],[f1199,f4107]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_IdI_0) ).
fof(f4105,plain,
spl0_396,
inference(avatar_split_clause,[],[f1168,f4103]) ).
fof(f4103,plain,
( spl0_396
<=> ! [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_396])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__code_1) ).
fof(f4100,plain,
spl0_395,
inference(avatar_split_clause,[],[f1167,f4098]) ).
fof(f4098,plain,
( spl0_395
<=> ! [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_395])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__code_0) ).
fof(f4096,plain,
spl0_394,
inference(avatar_split_clause,[],[f1154,f4094]) ).
fof(f4094,plain,
( spl0_394
<=> ! [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_394])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__idemp__self__comp_0) ).
fof(f4092,plain,
spl0_393,
inference(avatar_split_clause,[],[f1141,f4090]) ).
fof(f4090,plain,
( spl0_393
<=> ! [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_393])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_of__nat__eq__iff_0) ).
fof(f4088,plain,
spl0_392,
inference(avatar_split_clause,[],[f1115,f4086]) ).
fof(f4086,plain,
( spl0_392
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__converse__trancl_0) ).
fof(f4084,plain,
spl0_391,
inference(avatar_split_clause,[],[f1024,f4082]) ).
fof(f4082,plain,
( spl0_391
<=> ! [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_391])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc__wfI_0) ).
fof(f4080,plain,
spl0_390,
inference(avatar_split_clause,[],[f1023,f4078]) ).
fof(f4078,plain,
( spl0_390
<=> ! [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_390])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__acc__iff_1) ).
fof(f4076,plain,
spl0_389,
inference(avatar_split_clause,[],[f971,f4074]) ).
fof(f4074,plain,
( spl0_389
<=> ! [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_389])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_antisym__reflcl_1) ).
fof(f4072,plain,
spl0_388,
inference(avatar_split_clause,[],[f970,f4070]) ).
fof(f4070,plain,
( spl0_388
<=> ! [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_388])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_antisym__reflcl_0) ).
fof(f4068,plain,
spl0_387,
inference(avatar_split_clause,[],[f969,f4066]) ).
fof(f4066,plain,
( spl0_387
<=> ! [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_387])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Image__Id__on_0) ).
fof(f4064,plain,
spl0_386,
inference(avatar_split_clause,[],[f856,f4062]) ).
fof(f4062,plain,
( spl0_386
<=> ! [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_386])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_nat__less__le_2) ).
fof(f4047,plain,
spl0_385,
inference(avatar_split_clause,[],[f675,f4045]) ).
fof(f4045,plain,
( spl0_385
<=> ! [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_385])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acyclic__subset_0) ).
fof(f4043,plain,
spl0_384,
inference(avatar_split_clause,[],[f672,f4041]) ).
fof(f4041,plain,
( spl0_384
<=> ! [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_384])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_antisym__subset_0) ).
fof(f4039,plain,
spl0_383,
inference(avatar_split_clause,[],[f613,f4037]) ).
fof(f4037,plain,
( spl0_383
<=> ! [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_383])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__induct__rule_1) ).
fof(f4035,plain,
spl0_382,
inference(avatar_split_clause,[],[f604,f4033]) ).
fof(f4033,plain,
( spl0_382
<=> ! [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_382])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__aci_I8_J_0) ).
fof(f4031,plain,
spl0_381,
inference(avatar_split_clause,[],[f603,f4029]) ).
fof(f4029,plain,
( spl0_381
<=> ! [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_381])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__left__idem_0) ).
fof(f4027,plain,
spl0_380,
inference(avatar_split_clause,[],[f592,f4025]) ).
fof(f4025,plain,
( spl0_380
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f592,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),c_HOL_Ozero__class_Ozero(X0)),X2) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_group__add__class_Odiff__0_0) ).
fof(f4023,plain,
spl0_379,
inference(avatar_split_clause,[],[f569,f4021]) ).
fof(f4021,plain,
( spl0_379
<=> ! [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_379])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__subset_0) ).
fof(f4019,plain,
spl0_378,
inference(avatar_split_clause,[],[f568,f4017]) ).
fof(f4017,plain,
( spl0_378
<=> ! [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_378])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_predicate1D_0) ).
fof(f4015,plain,
spl0_377,
inference(avatar_split_clause,[],[f561,f4013]) ).
fof(f4013,plain,
( spl0_377
<=> ! [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_377])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_order__trans_0) ).
fof(f4011,plain,
spl0_376,
inference(avatar_split_clause,[],[f558,f4009]) ).
fof(f4009,plain,
( spl0_376
<=> ! [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_376])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_xt1_I6_J_0) ).
fof(f3995,plain,
spl0_375,
inference(avatar_split_clause,[],[f517,f3993]) ).
fof(f3993,plain,
( spl0_375
<=> ! [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_375])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__left__idem_0) ).
fof(f3991,plain,
spl0_374,
inference(avatar_split_clause,[],[f516,f3989]) ).
fof(f3989,plain,
( spl0_374
<=> ! [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_374])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__aci_I4_J_0) ).
fof(f3987,plain,
spl0_373,
inference(avatar_split_clause,[],[f515,f3985]) ).
fof(f3985,plain,
( spl0_373
<=> ! [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_373])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Compl__empty__eq_0) ).
fof(f3983,plain,
spl0_372,
inference(avatar_split_clause,[],[f418,f3981]) ).
fof(f3981,plain,
( spl0_372
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f418,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X1),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__eq__eq_1) ).
fof(f3979,plain,
spl0_371,
inference(avatar_split_clause,[],[f411,f3977]) ).
fof(f3977,plain,
( spl0_371
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f411,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_eq__iff__diff__eq__0_1) ).
fof(f3975,plain,
spl0_370,
inference(avatar_split_clause,[],[f410,f3973]) ).
fof(f3973,plain,
( spl0_370
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f410,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),X1) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_right__minus__eq_0) ).
fof(f3971,plain,
spl0_369,
inference(avatar_split_clause,[],[f402,f3969]) ).
fof(f3969,plain,
( spl0_369
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f402,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),X2) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_ab__left__minus_0) ).
fof(f3967,plain,
spl0_368,
inference(avatar_split_clause,[],[f401,f3965]) ).
fof(f3965,plain,
( spl0_368
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f401,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_right__minus_0) ).
fof(f3963,plain,
spl0_367,
inference(avatar_split_clause,[],[f400,f3961]) ).
fof(f3961,plain,
( spl0_367
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f400,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)),X2) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_left__minus_0) ).
fof(f3959,plain,
spl0_366,
inference(avatar_split_clause,[],[f377,f3957]) ).
fof(f3957,plain,
( spl0_366
<=> ! [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_366])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__absorb1_0) ).
fof(f3944,plain,
spl0_365,
inference(avatar_split_clause,[],[f376,f3942]) ).
fof(f3942,plain,
( spl0_365
<=> ! [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_365])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__absorb2_0) ).
fof(f3940,plain,
spl0_364,
inference(avatar_split_clause,[],[f327,f3938]) ).
fof(f3938,plain,
( spl0_364
<=> ! [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_364])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__trans_0) ).
fof(f3936,plain,
spl0_363,
inference(avatar_split_clause,[],[f324,f3934]) ).
fof(f3934,plain,
( spl0_363
<=> ! [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_363])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_subset__Un__eq_1) ).
fof(f3932,plain,
spl0_362,
inference(avatar_split_clause,[],[f323,f3930]) ).
fof(f3930,plain,
( spl0_362
<=> ! [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_362])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__absorb2_0) ).
fof(f3928,plain,
spl0_361,
inference(avatar_split_clause,[],[f322,f3926]) ).
fof(f3926,plain,
( spl0_361
<=> ! [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_361])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__absorb1_0) ).
fof(f3924,plain,
spl0_360,
inference(avatar_split_clause,[],[f302,f3922]) ).
fof(f3922,plain,
( spl0_360
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f302,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__equal__iff__equal_0) ).
fof(f3920,plain,
spl0_359,
inference(avatar_split_clause,[],[f301,f3918]) ).
fof(f3918,plain,
( spl0_359
<=> ! [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_359])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_compl__eq__compl__iff_0) ).
fof(f3916,plain,
spl0_358,
inference(avatar_split_clause,[],[f293,f3914]) ).
fof(f3914,plain,
( spl0_358
<=> ! [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_358])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__def_1) ).
fof(f3912,plain,
spl0_357,
inference(avatar_split_clause,[],[f279,f3910]) ).
fof(f3910,plain,
( spl0_357
<=> ! [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_357])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Compl__UNIV__eq_0) ).
fof(f3908,plain,
spl0_356,
inference(avatar_split_clause,[],[f233,f3906]) ).
fof(f3906,plain,
( spl0_356
<=> ! [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_356])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_tfl__wf__induct_1) ).
fof(f3892,plain,
spl0_355,
inference(avatar_split_clause,[],[f186,f3890]) ).
fof(f3890,plain,
( spl0_355
<=> ! [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_355])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__induct_1) ).
fof(f3888,plain,
spl0_354,
inference(avatar_split_clause,[],[f115,f3886]) ).
fof(f3886,plain,
( spl0_354
<=> ! [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_354])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_card__insert__le_0) ).
fof(f3884,plain,
spl0_353,
inference(avatar_split_clause,[],[f96,f3882]) ).
fof(f3882,plain,
( spl0_353
<=> ! [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_353])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_finite__Un_2) ).
fof(f3880,plain,
spl0_352,
inference(avatar_split_clause,[],[f70,f3878]) ).
fof(f3878,plain,
( spl0_352
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f70,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__less__eq__nonneg_1) ).
fof(f3876,plain,
spl0_351,
inference(avatar_split_clause,[],[f69,f3874]) ).
fof(f3874,plain,
( spl0_351
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f69,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__less__eq__nonneg_0) ).
fof(f3872,plain,
spl0_350,
inference(avatar_split_clause,[],[f68,f3870]) ).
fof(f3870,plain,
( spl0_350
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f68,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__eq__neg__nonpos_1) ).
fof(f3868,plain,
spl0_349,
inference(avatar_split_clause,[],[f67,f3866]) ).
fof(f3866,plain,
( spl0_349
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f67,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__eq__neg__nonpos_0) ).
fof(f3864,plain,
spl0_348,
inference(avatar_split_clause,[],[f66,f3862]) ).
fof(f3862,plain,
( spl0_348
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f66,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__le__self__iff_1) ).
fof(f3860,plain,
spl0_347,
inference(avatar_split_clause,[],[f65,f3858]) ).
fof(f3858,plain,
( spl0_347
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f65,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__le__self__iff_0) ).
fof(f3856,plain,
spl0_346,
inference(avatar_split_clause,[],[f64,f3854]) ).
fof(f3854,plain,
( spl0_346
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f64,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__minus__self__iff_1) ).
fof(f3850,plain,
spl0_345,
inference(avatar_split_clause,[],[f63,f3848]) ).
fof(f3848,plain,
( spl0_345
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f63,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__minus__self__iff_0) ).
fof(f3846,plain,
spl0_344,
inference(avatar_split_clause,[],[f37,f3844]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__UNIV__left_0) ).
fof(f3842,plain,
spl0_343,
inference(avatar_split_clause,[],[f36,f3840]) ).
fof(f3840,plain,
( spl0_343
<=> ! [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_343])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__UNIV__right_0) ).
fof(f3838,plain,
spl0_342,
inference(avatar_split_clause,[],[f19,f3836]) ).
fof(f3836,plain,
( spl0_342
<=> ! [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_342])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__code_0) ).
fof(f3834,plain,
spl0_341,
inference(avatar_split_clause,[],[f9,f3832]) ).
fof(f3832,plain,
( spl0_341
<=> ! [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_341])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__empty__left_0) ).
fof(f3830,plain,
spl0_340,
inference(avatar_split_clause,[],[f8,f3828]) ).
fof(f3828,plain,
( spl0_340
<=> ! [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_340])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__empty__right_0) ).
fof(f3791,plain,
( spl0_339
| ~ spl0_23
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f2289,f2230,f1472,f3788]) ).
fof(f1472,plain,
( spl0_23
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f2230,plain,
( spl0_181
<=> ! [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_181])]) ).
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_181 ),
inference(resolution,[],[f2231,f1474]) ).
fof(f1474,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f1472]) ).
fof(f2231,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_181 ),
inference(avatar_component_clause,[],[f2230]) ).
fof(f3750,plain,
( spl0_338
| ~ spl0_45
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f2278,f2202,f1582,f3747]) ).
fof(f3747,plain,
( spl0_338
<=> 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_338])]) ).
fof(f2202,plain,
( spl0_174
<=> ! [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_174])]) ).
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_174 ),
inference(resolution,[],[f2203,f1584]) ).
fof(f2203,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_174 ),
inference(avatar_component_clause,[],[f2202]) ).
fof(f3581,plain,
( spl0_337
| ~ spl0_39
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f2276,f2182,f1552,f3579]) ).
fof(f1552,plain,
( spl0_39
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f2182,plain,
( spl0_169
<=> ! [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_169])]) ).
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_169 ),
inference(resolution,[],[f2183,f1554]) ).
fof(f1554,plain,
( class_Power_Opower(tc_nat)
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f1552]) ).
fof(f2183,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_169 ),
inference(avatar_component_clause,[],[f2182]) ).
fof(f3404,plain,
( spl0_336
| ~ spl0_45
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2274,f2178,f1582,f3401]) ).
fof(f3401,plain,
( spl0_336
<=> 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_336])]) ).
fof(f2178,plain,
( spl0_168
<=> ! [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_168])]) ).
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_168 ),
inference(resolution,[],[f2179,f1584]) ).
fof(f2179,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_168 ),
inference(avatar_component_clause,[],[f2178]) ).
fof(f3364,plain,
( spl0_335
| ~ spl0_201
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f3184,f3181,f2344,f3362]) ).
fof(f3181,plain,
( spl0_295
<=> ! [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_295])]) ).
fof(f3184,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_201
| ~ spl0_295 ),
inference(forward_demodulation,[],[f3182,f2346]) ).
fof(f3182,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_295 ),
inference(avatar_component_clause,[],[f3181]) ).
fof(f3340,plain,
( spl0_334
| ~ spl0_28
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f2273,f2174,f1497,f3338]) ).
fof(f3338,plain,
( spl0_334
<=> ! [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_334])]) ).
fof(f2174,plain,
( spl0_167
<=> ! [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_167])]) ).
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_167 ),
inference(resolution,[],[f2175,f1499]) ).
fof(f2175,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_167 ),
inference(avatar_component_clause,[],[f2174]) ).
fof(f3336,plain,
spl0_333,
inference(avatar_split_clause,[],[f1159,f3334]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__converse_0) ).
fof(f3332,plain,
spl0_332,
inference(avatar_split_clause,[],[f1140,f3330]) ).
fof(f3330,plain,
( spl0_332
<=> ! [X0,X8] : c_Relation_Oconverse(c_Transitive__Closure_Otrancl(X8,X0),X0,X0) = c_Transitive__Closure_Otrancl(c_Relation_Oconverse(X8,X0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_trancl__converse_0) ).
fof(f3328,plain,
spl0_331,
inference(avatar_split_clause,[],[f1127,f3326]) ).
fof(f3326,plain,
( spl0_331
<=> ! [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_331])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__def_1) ).
fof(f3324,plain,
spl0_330,
inference(avatar_split_clause,[],[f1110,f3322]) ).
fof(f3322,plain,
( spl0_330
<=> ! [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_330])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_of__nat__less__0__iff_0) ).
fof(f3320,plain,
spl0_329,
inference(avatar_split_clause,[],[f965,f3318]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sym__Un__converse_0) ).
fof(f3316,plain,
spl0_328,
inference(avatar_split_clause,[],[f944,f3314]) ).
fof(f3314,plain,
( spl0_328
<=> ! [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_328])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_setprod__empty_0) ).
fof(f3312,plain,
spl0_327,
inference(avatar_split_clause,[],[f845,f3310]) ).
fof(f3310,plain,
( spl0_327
<=> ! [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_327])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__le__not__le_1) ).
fof(f3308,plain,
spl0_326,
inference(avatar_split_clause,[],[f843,f3306]) ).
fof(f3306,plain,
( spl0_326
<=> ! [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_326])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_linorder__not__le_1) ).
fof(f3304,plain,
( spl0_325
| ~ spl0_44
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2267,f2170,f1577,f3302]) ).
fof(f3302,plain,
( spl0_325
<=> ! [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_325])]) ).
fof(f1577,plain,
( spl0_44
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f2170,plain,
( spl0_166
<=> ! [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_166])]) ).
fof(f2267,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_166 ),
inference(resolution,[],[f2171,f1579]) ).
fof(f1579,plain,
( class_Lattices_Obounded__lattice(tc_bool)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f1577]) ).
fof(f2171,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_166 ),
inference(avatar_component_clause,[],[f2170]) ).
fof(f3300,plain,
spl0_324,
inference(avatar_split_clause,[],[f838,f3298]) ).
fof(f3298,plain,
( spl0_324
<=> ! [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_324])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_not__leE_0) ).
fof(f3296,plain,
spl0_323,
inference(avatar_split_clause,[],[f831,f3294]) ).
fof(f3294,plain,
( spl0_323
<=> ! [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_323])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_order__le__less_1) ).
fof(f3292,plain,
spl0_322,
inference(avatar_split_clause,[],[f830,f3290]) ).
fof(f3290,plain,
( spl0_322
<=> ! [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_322])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_order__less__imp__le_0) ).
fof(f3288,plain,
spl0_321,
inference(avatar_split_clause,[],[f809,f3286]) ).
fof(f3286,plain,
( spl0_321
<=> ! [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_321])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__absorb_0) ).
fof(f3284,plain,
spl0_320,
inference(avatar_split_clause,[],[f714,f3282]) ).
fof(f3282,plain,
( spl0_320
<=> ! [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_320])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__empty_0) ).
fof(f3280,plain,
spl0_319,
inference(avatar_split_clause,[],[f665,f3278]) ).
fof(f3278,plain,
( spl0_319
<=> ! [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_319])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_double__complement_0) ).
fof(f3276,plain,
spl0_318,
inference(avatar_split_clause,[],[f638,f3274]) ).
fof(f3274,plain,
( spl0_318
<=> ! [X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),c_HOL_Ozero__class_Ozero(X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f638,axiom,
! [X3,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),c_HOL_Ozero__class_Ozero(X0)) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f3272,plain,
spl0_317,
inference(avatar_split_clause,[],[f628,f3270]) ).
fof(f3270,plain,
( spl0_317
<=> ! [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_317])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf1E_0) ).
fof(f3268,plain,
spl0_316,
inference(avatar_split_clause,[],[f627,f3266]) ).
fof(f3266,plain,
( spl0_316
<=> ! [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_316])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf1E_1) ).
fof(f3264,plain,
spl0_315,
inference(avatar_split_clause,[],[f584,f3262]) ).
fof(f3260,plain,
( spl0_314
| ~ spl0_44
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f2265,f2166,f1577,f3258]) ).
fof(f3258,plain,
( spl0_314
<=> ! [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_314])]) ).
fof(f2166,plain,
( spl0_165
<=> ! [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_165])]) ).
fof(f2265,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_165 ),
inference(resolution,[],[f2167,f1579]) ).
fof(f2167,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_165 ),
inference(avatar_component_clause,[],[f2166]) ).
fof(f3256,plain,
spl0_313,
inference(avatar_split_clause,[],[f572,f3254]) ).
fof(f3254,plain,
( spl0_313
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f572,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),X4,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__dvd__iff_1) ).
fof(f3252,plain,
spl0_312,
inference(avatar_split_clause,[],[f553,f3250]) ).
fof(f3250,plain,
( spl0_312
<=> ! [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_312])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__supE_1) ).
fof(f3248,plain,
spl0_311,
inference(avatar_split_clause,[],[f552,f3246]) ).
fof(f3246,plain,
( spl0_311
<=> ! [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_311])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__supI1_0) ).
fof(f3244,plain,
spl0_310,
inference(avatar_split_clause,[],[f551,f3242]) ).
fof(f3242,plain,
( spl0_310
<=> ! [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_310])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__supI2_0) ).
fof(f3240,plain,
spl0_309,
inference(avatar_split_clause,[],[f550,f3238]) ).
fof(f3238,plain,
( spl0_309
<=> ! [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_309])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__sup__iff_0) ).
fof(f3236,plain,
spl0_308,
inference(avatar_split_clause,[],[f471,f3234]) ).
fof(f3234,plain,
( spl0_308
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f471,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3),X4,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__dvd__iff_0) ).
fof(f3232,plain,
spl0_307,
inference(avatar_split_clause,[],[f470,f3230]) ).
fof(f3230,plain,
( spl0_307
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f470,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__minus__iff_1) ).
fof(f3228,plain,
spl0_306,
inference(avatar_split_clause,[],[f469,f3226]) ).
fof(f469,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X4),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__minus__iff_0) ).
fof(f3224,plain,
spl0_305,
inference(avatar_split_clause,[],[f467,f3222]) ).
fof(f3222,plain,
( spl0_305
<=> ! [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_305])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__inf__iff_0) ).
fof(f3220,plain,
spl0_304,
inference(avatar_split_clause,[],[f466,f3218]) ).
fof(f3218,plain,
( spl0_304
<=> ! [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_304])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__infI2_0) ).
fof(f3216,plain,
( spl0_303
| ~ spl0_44
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2263,f2162,f1577,f3214]) ).
fof(f3214,plain,
( spl0_303
<=> ! [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_303])]) ).
fof(f2162,plain,
( spl0_164
<=> ! [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_164])]) ).
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_164 ),
inference(resolution,[],[f2163,f1579]) ).
fof(f2163,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_164 ),
inference(avatar_component_clause,[],[f2162]) ).
fof(f3212,plain,
spl0_302,
inference(avatar_split_clause,[],[f465,f3210]) ).
fof(f3210,plain,
( spl0_302
<=> ! [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_302])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__infI1_0) ).
fof(f3208,plain,
spl0_301,
inference(avatar_split_clause,[],[f464,f3206]) ).
fof(f3206,plain,
( spl0_301
<=> ! [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_301])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__infE_1) ).
fof(f3204,plain,
spl0_300,
inference(avatar_split_clause,[],[f457,f3202]) ).
fof(f3202,plain,
( spl0_300
<=> ! [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_300])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__eq__bot__eq2_0) ).
fof(f3200,plain,
spl0_299,
inference(avatar_split_clause,[],[f456,f3198]) ).
fof(f3198,plain,
( spl0_299
<=> ! [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_299])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__eq__bot__eq1_0) ).
fof(f3196,plain,
spl0_298,
inference(avatar_split_clause,[],[f392,f3194]) ).
fof(f3192,plain,
spl0_297,
inference(avatar_split_clause,[],[f363,f3190]) ).
fof(f3190,plain,
( spl0_297
<=> ! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oring__1__no__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_297])]) ).
fof(f363,axiom,
! [X2,X0,X14] :
( ~ class_Ring__and__Field_Oring__1__no__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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_field__power__not__zero_0) ).
fof(f3188,plain,
spl0_296,
inference(avatar_split_clause,[],[f313,f3186]) ).
fof(f3186,plain,
( spl0_296
<=> ! [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_296])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_order__antisym__conv_0) ).
fof(f3183,plain,
spl0_295,
inference(avatar_split_clause,[],[f253,f3181]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_card__gt__0__iff_1) ).
fof(f3179,plain,
spl0_294,
inference(avatar_split_clause,[],[f209,f3177]) ).
fof(f3177,plain,
( spl0_294
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(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_294])]) ).
fof(f209,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_double__eq__0__iff_1) ).
fof(f3175,plain,
spl0_293,
inference(avatar_split_clause,[],[f162,f3173]) ).
fof(f3173,plain,
( spl0_293
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f162,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__equal__0__iff__equal_0) ).
fof(f3171,plain,
( spl0_292
| ~ spl0_44
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f2261,f2158,f1577,f3169]) ).
fof(f3169,plain,
( spl0_292
<=> ! [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_292])]) ).
fof(f2158,plain,
( spl0_163
<=> ! [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_163])]) ).
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_163 ),
inference(resolution,[],[f2159,f1579]) ).
fof(f2159,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_163 ),
inference(avatar_component_clause,[],[f2158]) ).
fof(f3167,plain,
spl0_291,
inference(avatar_split_clause,[],[f159,f3165]) ).
fof(f3165,plain,
( spl0_291
<=> ! [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_291])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__eq__top__eq1_0) ).
fof(f3163,plain,
spl0_290,
inference(avatar_split_clause,[],[f158,f3161]) ).
fof(f3161,plain,
( spl0_290
<=> ! [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_290])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__eq__top__eq2_0) ).
fof(f3159,plain,
spl0_289,
inference(avatar_split_clause,[],[f130,f3157]) ).
fof(f3157,plain,
( spl0_289
<=> ! [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_289])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup1CI_1) ).
fof(f3155,plain,
spl0_288,
inference(avatar_split_clause,[],[f129,f3153]) ).
fof(f3153,plain,
( spl0_288
<=> ! [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_288])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup1CI_0) ).
fof(f3151,plain,
spl0_287,
inference(avatar_split_clause,[],[f94,f3149]) ).
fof(f3149,plain,
( spl0_287
<=> ! [X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f94,axiom,
! [X3,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X3) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__ringb_Osubr0__iff_1) ).
fof(f3147,plain,
spl0_286,
inference(avatar_split_clause,[],[f40,f3145]) ).
fof(f3145,plain,
( spl0_286
<=> ! [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_286])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_vimage__UNIV_0) ).
fof(f3143,plain,
spl0_285,
inference(avatar_split_clause,[],[f29,f3141]) ).
fof(f3141,plain,
( spl0_285
<=> ! [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_285])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Image__empty_0) ).
fof(f3123,plain,
( spl0_284
| ~ spl0_64
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1883,f1847,f1666,f3121]) ).
fof(f3121,plain,
( spl0_284
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f1883,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X0,X1)
| c_Wellfounded_Oacyclic(c_Transitive__Closure_Otrancl(X0,X1),X1) )
| ~ spl0_64
| ~ spl0_109 ),
inference(resolution,[],[f1848,f1667]) ).
fof(f3108,plain,
( spl0_283
| ~ spl0_201
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f2823,f2819,f2344,f3106]) ).
fof(f2819,plain,
( spl0_276
<=> ! [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_276])]) ).
fof(f2823,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_201
| ~ spl0_276 ),
inference(forward_demodulation,[],[f2822,f2346]) ).
fof(f2822,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_201
| ~ spl0_276 ),
inference(forward_demodulation,[],[f2820,f2346]) ).
fof(f2820,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_276 ),
inference(avatar_component_clause,[],[f2819]) ).
fof(f2863,plain,
( ~ spl0_42
| spl0_282
| ~ spl0_140
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f2583,f2234,f1981,f2861,f1567]) ).
fof(f2861,plain,
( spl0_282
<=> ! [X1] : c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2234,plain,
( spl0_182
<=> ! [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_182])]) ).
fof(f2583,plain,
( ! [X1] :
( c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_bool),tc_bool)
| ~ class_Lattices_Olower__semilattice(tc_bool) )
| ~ spl0_140
| ~ spl0_182 ),
inference(superposition,[],[f1982,f2235]) ).
fof(f2235,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = X0
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f2234]) ).
fof(f2843,plain,
spl0_281,
inference(avatar_split_clause,[],[f1164,f2841]) ).
fof(f2841,plain,
( spl0_281
<=> ! [X0,X8,X10] : c_Relation_ORange(X8,X10,X0) = c_Relation_ODomain(c_Relation_Oconverse(X8,X10,X0),X0,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Range__def_0) ).
fof(f2839,plain,
spl0_280,
inference(avatar_split_clause,[],[f1163,f2837]) ).
fof(f2837,plain,
( spl0_280
<=> ! [X0,X8] : c_Transitive__Closure_Otrancl(X8,X0) = c_Relation_Orel__comp(X8,c_Transitive__Closure_Ortrancl(X8,X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_trancl__unfold__left_0) ).
fof(f2835,plain,
spl0_279,
inference(avatar_split_clause,[],[f1162,f2833]) ).
fof(f2831,plain,
spl0_278,
inference(avatar_split_clause,[],[f1146,f2829]) ).
fof(f2829,plain,
( spl0_278
<=> ! [X0,X8,X10] : c_Relation_ODomain(X8,X0,X10) = c_Relation_ORange(c_Relation_Oconverse(X8,X0,X10),X10,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Range__converse_0) ).
fof(f2827,plain,
spl0_277,
inference(avatar_split_clause,[],[f1102,f2825]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acc__wfD_0) ).
fof(f2821,plain,
spl0_276,
inference(avatar_split_clause,[],[f858,f2819]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_gr0I_0) ).
fof(f2817,plain,
spl0_275,
inference(avatar_split_clause,[],[f710,f2815]) ).
fof(f2815,plain,
( spl0_275
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f710,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X2),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__square_0) ).
fof(f2813,plain,
spl0_274,
inference(avatar_split_clause,[],[f673,f2811]) ).
fof(f2811,plain,
( spl0_274
<=> ! [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_274])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_finite__subset_0) ).
fof(f2809,plain,
spl0_273,
inference(avatar_split_clause,[],[f651,f2807]) ).
fof(f2807,plain,
( spl0_273
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f651,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2) != X2 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__equal__zero_0) ).
fof(f2805,plain,
spl0_272,
inference(avatar_split_clause,[],[f593,f2803]) ).
fof(f2803,plain,
( spl0_272
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f593,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X2,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn__0__0_0) ).
fof(f2801,plain,
spl0_271,
inference(avatar_split_clause,[],[f563,f2799]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__trans_0) ).
fof(f2797,plain,
spl0_270,
inference(avatar_split_clause,[],[f420,f2795]) ).
fof(f2795,plain,
( spl0_270
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_HOL_Ozero__class_Ozero(X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f420,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),c_HOL_Ozero__class_Ozero(X0)),X2) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__zero__left_0) ).
fof(f2793,plain,
spl0_269,
inference(avatar_split_clause,[],[f417,f2791]) ).
fof(f2791,plain,
( spl0_269
<=> ! [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_269])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__compl__top_0) ).
fof(f2789,plain,
( ~ spl0_48
| spl0_268
| ~ spl0_136
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f2522,f2154,f1965,f2787,f1597]) ).
fof(f2787,plain,
( spl0_268
<=> ! [X1] : c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f1965,plain,
( spl0_136
<=> ! [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_136])]) ).
fof(f2154,plain,
( spl0_162
<=> ! [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_162])]) ).
fof(f2522,plain,
( ! [X1] :
( c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool)
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_136
| ~ spl0_162 ),
inference(superposition,[],[f1966,f2155]) ).
fof(f2155,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f2154]) ).
fof(f1966,plain,
( ! [X3,X0,X4] :
( c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1965]) ).
fof(f2785,plain,
spl0_267,
inference(avatar_split_clause,[],[f416,f2783]) ).
fof(f2783,plain,
( spl0_267
<=> ! [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_267])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_compl__sup__top_0) ).
fof(f2781,plain,
spl0_266,
inference(avatar_split_clause,[],[f380,f2779]) ).
fof(f2779,plain,
( spl0_266
<=> ! [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_266])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__absorb2_0) ).
fof(f2777,plain,
spl0_265,
inference(avatar_split_clause,[],[f379,f2775]) ).
fof(f2775,plain,
( spl0_265
<=> ! [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_265])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__iff__inf_1) ).
fof(f2773,plain,
spl0_264,
inference(avatar_split_clause,[],[f378,f2771]) ).
fof(f2771,plain,
( spl0_264
<=> ! [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_264])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__iff__inf_0) ).
fof(f2769,plain,
spl0_263,
inference(avatar_split_clause,[],[f321,f2767]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__iff__sup_0) ).
fof(f2765,plain,
spl0_262,
inference(avatar_split_clause,[],[f320,f2763]) ).
fof(f2763,plain,
( spl0_262
<=> ! [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_262])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__iff__sup_1) ).
fof(f2761,plain,
spl0_261,
inference(avatar_split_clause,[],[f319,f2759]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__absorb1_0) ).
fof(f2757,plain,
spl0_260,
inference(avatar_split_clause,[],[f275,f2755]) ).
fof(f2755,plain,
( spl0_260
<=> ! [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_260])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__zero__left_0) ).
fof(f2753,plain,
spl0_259,
inference(avatar_split_clause,[],[f274,f2751]) ).
fof(f2751,plain,
( spl0_259
<=> ! [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_259])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__zero__right_0) ).
fof(f2749,plain,
spl0_258,
inference(avatar_split_clause,[],[f273,f2747]) ).
fof(f2747,plain,
( spl0_258
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f273,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),c_HOL_Ozero__class_Ozero(X0)),X1) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__eq__0__iff_1) ).
fof(f2744,plain,
spl0_257,
inference(avatar_split_clause,[],[f272,f2742]) ).
fof(f2742,plain,
( spl0_257
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(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_257])]) ).
fof(f272,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__eq__0__iff_2) ).
fof(f2740,plain,
spl0_256,
inference(avatar_split_clause,[],[f175,f2738]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__compl__bot_0) ).
fof(f2736,plain,
spl0_255,
inference(avatar_split_clause,[],[f174,f2734]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_compl__inf__bot_0) ).
fof(f2732,plain,
spl0_254,
inference(avatar_split_clause,[],[f171,f2730]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f2728,plain,
spl0_253,
inference(avatar_split_clause,[],[f170,f2726]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f2724,plain,
spl0_252,
inference(avatar_split_clause,[],[f27,f2722]) ).
fof(f2722,plain,
( spl0_252
<=> ! [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_252])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__absorb2_0) ).
fof(f2708,plain,
( ~ spl0_14
| spl0_251
| ~ spl0_83
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2395,f2344,f1743,f2706,f1427]) ).
fof(f2706,plain,
( spl0_251
<=> ! [X4] : c_Ring__and__Field_Odvd__class_Odvd(X4,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f1743,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(f2395,plain,
( ! [X4] :
( c_Ring__and__Field_Odvd__class_Odvd(X4,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat) )
| ~ spl0_83
| ~ spl0_201 ),
inference(superposition,[],[f1744,f2346]) ).
fof(f1744,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,[],[f1743]) ).
fof(f2666,plain,
( ~ spl0_20
| ~ spl0_250
| ~ spl0_90
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2394,f2344,f1771,f2663,f1457]) ).
fof(f1457,plain,
( spl0_20
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f2663,plain,
( spl0_250
<=> c_HOL_Oone__class_Oone(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f1771,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(f2394,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_201 ),
inference(superposition,[],[f1772,f2346]) ).
fof(f1772,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,[],[f1771]) ).
fof(f2552,plain,
spl0_249,
inference(avatar_split_clause,[],[f1266,f2550]) ).
fof(f1266,axiom,
! [X3,X0,X22] :
( hBOOL(hAPP(X22,X3))
| ~ hBOOL(hAPP(hAPP(c_in(X0),X3),X22)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mem__def_0) ).
fof(f2548,plain,
spl0_248,
inference(avatar_split_clause,[],[f1265,f2546]) ).
fof(f2546,plain,
( spl0_248
<=> ! [X22,X0,X3] :
( ~ hBOOL(hAPP(X22,X3))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f1265,axiom,
! [X3,X0,X22] :
( ~ hBOOL(hAPP(X22,X3))
| hBOOL(hAPP(hAPP(c_in(X0),X3),X22)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mem__def_1) ).
fof(f2544,plain,
spl0_247,
inference(avatar_split_clause,[],[f1166,f2542]) ).
fof(f2542,plain,
( spl0_247
<=> ! [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_247])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_total__on__converse_1) ).
fof(f2540,plain,
spl0_246,
inference(avatar_split_clause,[],[f1165,f2538]) ).
fof(f2538,plain,
( spl0_246
<=> ! [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_246])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_total__on__converse_0) ).
fof(f2536,plain,
spl0_245,
inference(avatar_split_clause,[],[f1158,f2534]) ).
fof(f2534,plain,
( spl0_245
<=> ! [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_245])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__less__one_0) ).
fof(f2532,plain,
spl0_244,
inference(avatar_split_clause,[],[f1148,f2530]) ).
fof(f2530,plain,
( spl0_244
<=> ! [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_244])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_not__one__less__zero_0) ).
fof(f2528,plain,
spl0_243,
inference(avatar_split_clause,[],[f1126,f2526]) ).
fof(f2526,plain,
( spl0_243
<=> ! [X0,X8] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X8,X0),X0,X0) = c_Relation_ORange(X8,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_trancl__range_0) ).
fof(f2520,plain,
spl0_242,
inference(avatar_split_clause,[],[f1120,f2518]) ).
fof(f2518,plain,
( spl0_242
<=> ! [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_242])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__comp__self_1) ).
fof(f2516,plain,
spl0_241,
inference(avatar_split_clause,[],[f1119,f2514]) ).
fof(f2514,plain,
( spl0_241
<=> ! [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_241])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__comp__self_0) ).
fof(f2512,plain,
spl0_240,
inference(avatar_split_clause,[],[f1117,f2510]) ).
fof(f2510,plain,
( spl0_240
<=> ! [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_240])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_refl__on__converse_1) ).
fof(f2508,plain,
spl0_239,
inference(avatar_split_clause,[],[f1116,f2506]) ).
fof(f2506,plain,
( spl0_239
<=> ! [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_239])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_refl__on__converse_0) ).
fof(f2504,plain,
spl0_238,
inference(avatar_split_clause,[],[f1107,f2502]) ).
fof(f2502,plain,
( spl0_238
<=> ! [X0,X8] : c_Relation_ODomain(X8,X0,X0) = c_Relation_ODomain(c_Transitive__Closure_Otrancl(X8,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_trancl__domain_0) ).
fof(f2500,plain,
spl0_237,
inference(avatar_split_clause,[],[f963,f2498]) ).
fof(f2498,plain,
( spl0_237
<=> ! [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_237])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Range__rtrancl_0) ).
fof(f2496,plain,
spl0_236,
inference(avatar_split_clause,[],[f959,f2494]) ).
fof(f2494,plain,
( spl0_236
<=> ! [X0,X15] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X15,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Domain__rtrancl_0) ).
fof(f2492,plain,
spl0_235,
inference(avatar_split_clause,[],[f859,f2490]) ).
fof(f2490,plain,
( spl0_235
<=> ! [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_235])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_nat__less__le_0) ).
fof(f2488,plain,
spl0_234,
inference(avatar_split_clause,[],[f777,f2486]) ).
fof(f2486,plain,
( spl0_234
<=> ! [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_234])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_finite__Int_0) ).
fof(f2484,plain,
spl0_233,
inference(avatar_split_clause,[],[f776,f2482]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_finite__Int_1) ).
fof(f2479,plain,
spl0_232,
inference(avatar_split_clause,[],[f668,f2477]) ).
fof(f2477,plain,
( spl0_232
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f668,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_equation__minus__iff_0) ).
fof(f2475,plain,
spl0_231,
inference(avatar_split_clause,[],[f667,f2473]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_double__compl_0) ).
fof(f2471,plain,
spl0_230,
inference(avatar_split_clause,[],[f643,f2469]) ).
fof(f2469,plain,
( spl0_230
<=> ! [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_230])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f2467,plain,
spl0_229,
inference(avatar_split_clause,[],[f642,f2465]) ).
fof(f2465,plain,
( spl0_229
<=> ! [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_229])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f2463,plain,
spl0_228,
inference(avatar_split_clause,[],[f641,f2461]) ).
fof(f2461,plain,
( spl0_228
<=> ! [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_228])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f2459,plain,
spl0_227,
inference(avatar_split_clause,[],[f640,f2457]) ).
fof(f2457,plain,
( spl0_227
<=> ! [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_227])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_add__0__left_0) ).
fof(f2455,plain,
spl0_226,
inference(avatar_split_clause,[],[f639,f2453]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f2451,plain,
spl0_225,
inference(avatar_split_clause,[],[f637,f2449]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_comm__monoid__add_Omult__1_0) ).
fof(f2447,plain,
spl0_224,
inference(avatar_split_clause,[],[f620,f2445]) ).
fof(f2445,plain,
( spl0_224
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(X2,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f620,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(X2,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X2,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn__sgn_0) ).
fof(f2443,plain,
spl0_223,
inference(avatar_split_clause,[],[f586,f2441]) ).
fof(f2441,plain,
( spl0_223
<=> ! [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_223])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__aci_I5_J_0) ).
fof(f2439,plain,
( spl0_222
| ~ spl0_57
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2390,f2344,f1638,f2437]) ).
fof(f2437,plain,
( spl0_222
<=> ! [X2] : c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f2390,plain,
( ! [X2] : c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)
| ~ spl0_57
| ~ spl0_201 ),
inference(superposition,[],[f1639,f2346]) ).
fof(f2435,plain,
spl0_221,
inference(avatar_split_clause,[],[f585,f2433]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__commute_0) ).
fof(f2431,plain,
spl0_220,
inference(avatar_split_clause,[],[f488,f2429]) ).
fof(f2429,plain,
( spl0_220
<=> ! [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_220])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__lower2_0) ).
fof(f2427,plain,
spl0_219,
inference(avatar_split_clause,[],[f487,f2425]) ).
fof(f2425,plain,
( spl0_219
<=> ! [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_219])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__lower1_0) ).
fof(f2423,plain,
spl0_218,
inference(avatar_split_clause,[],[f446,f2421]) ).
fof(f2421,plain,
( spl0_218
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),c_HOL_Oone__class_Oone(X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f446,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X0),X2),c_HOL_Oone__class_Oone(X0)) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_divide__1_0) ).
fof(f2419,plain,
spl0_217,
inference(avatar_split_clause,[],[f435,f2417]) ).
fof(f2417,plain,
( spl0_217
<=> ! [X6,X4,X0,X3] :
( ~ hBOOL(hAPP(X6,X3))
| hBOOL(hAPP(c_Set_Oinsert(X4,X6,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f435,axiom,
! [X3,X0,X6,X4] :
( ~ hBOOL(hAPP(X6,X3))
| hBOOL(hAPP(c_Set_Oinsert(X4,X6,X0),X3)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__code_2) ).
fof(f2415,plain,
spl0_216,
inference(avatar_split_clause,[],[f407,f2413]) ).
fof(f2413,plain,
( spl0_216
<=> ! [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_216])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__0__left_0) ).
fof(f2411,plain,
spl0_215,
inference(avatar_split_clause,[],[f394,f2409]) ).
fof(f2409,plain,
( spl0_215
<=> ! [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_215])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__aci_I1_J_0) ).
fof(f2407,plain,
spl0_214,
inference(avatar_split_clause,[],[f393,f2405]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__commute_0) ).
fof(f2403,plain,
spl0_213,
inference(avatar_split_clause,[],[f383,f2401]) ).
fof(f2401,plain,
( spl0_213
<=> ! [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_213])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__upper1_0) ).
fof(f2399,plain,
spl0_212,
inference(avatar_split_clause,[],[f382,f2397]) ).
fof(f2397,plain,
( spl0_212
<=> ! [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_212])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__upper2_0) ).
fof(f2387,plain,
spl0_211,
inference(avatar_split_clause,[],[f318,f2385]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__absorb_0) ).
fof(f2383,plain,
spl0_210,
inference(avatar_split_clause,[],[f309,f2381]) ).
fof(f2381,plain,
( spl0_210
<=> ! [X16,X14] :
( X14 = X16
| ~ c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(X14,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f309,axiom,
! [X16,X14] :
( X14 = X16
| ~ c_lessequals(X16,X14,tc_nat)
| ~ c_lessequals(X14,X16,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__antisym_0) ).
fof(f2379,plain,
spl0_209,
inference(avatar_split_clause,[],[f292,f2377]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__inf__absorb_0) ).
fof(f2375,plain,
spl0_208,
inference(avatar_split_clause,[],[f288,f2373]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__UNIV__right_0) ).
fof(f2371,plain,
spl0_207,
inference(avatar_split_clause,[],[f287,f2369]) ).
fof(f2369,plain,
( spl0_207
<=> ! [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_207])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__UNIV__left_0) ).
fof(f2367,plain,
spl0_206,
inference(avatar_split_clause,[],[f185,f2365]) ).
fof(f2365,plain,
( spl0_206
<=> ! [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_206])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__triv__right_0) ).
fof(f2363,plain,
spl0_205,
inference(avatar_split_clause,[],[f184,f2361]) ).
fof(f2361,plain,
( spl0_205
<=> ! [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_205])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__triv__left_0) ).
fof(f2359,plain,
spl0_204,
inference(avatar_split_clause,[],[f183,f2357]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvdI_0) ).
fof(f2355,plain,
spl0_203,
inference(avatar_split_clause,[],[f180,f2353]) ).
fof(f2353,plain,
( spl0_203
<=> ! [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_203])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(f2351,plain,
spl0_202,
inference(avatar_split_clause,[],[f179,f2349]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__1__right_0) ).
fof(f2347,plain,
( ~ spl0_38
| spl0_201
| ~ spl0_82
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f2078,f1929,f1739,f2344,f1547]) ).
fof(f1547,plain,
( spl0_38
<=> class_Orderings_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1739,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(f2078,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ class_Orderings_Obot(tc_nat)
| ~ spl0_82
| ~ spl0_127 ),
inference(resolution,[],[f1930,f1740]) ).
fof(f1740,plain,
( ! [X3,X0] :
( c_lessequals(c_Orderings_Obot__class_Obot(X0),X3,X0)
| ~ class_Orderings_Obot(X0) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f1739]) ).
fof(f2342,plain,
spl0_200,
inference(avatar_split_clause,[],[f178,f2340]) ).
fof(f2340,plain,
( spl0_200
<=> ! [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_200])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__1__left_0) ).
fof(f2338,plain,
spl0_199,
inference(avatar_split_clause,[],[f177,f2336]) ).
fof(f2336,plain,
( spl0_199
<=> ! [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_199])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__1_0) ).
fof(f2334,plain,
spl0_198,
inference(avatar_split_clause,[],[f176,f2332]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Omul__1_0) ).
fof(f2330,plain,
spl0_197,
inference(avatar_split_clause,[],[f153,f2328]) ).
fof(f2328,plain,
( spl0_197
<=> ! [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_197])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__empty__right_0) ).
fof(f2326,plain,
spl0_196,
inference(avatar_split_clause,[],[f152,f2324]) ).
fof(f2324,plain,
( spl0_196
<=> ! [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_196])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__empty__left_0) ).
fof(f2322,plain,
spl0_195,
inference(avatar_split_clause,[],[f149,f2320]) ).
fof(f2320,plain,
( spl0_195
<=> ! [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_195])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_finite__Un_1) ).
fof(f2318,plain,
spl0_194,
inference(avatar_split_clause,[],[f148,f2316]) ).
fof(f2316,plain,
( spl0_194
<=> ! [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_194])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_finite__Un_0) ).
fof(f2314,plain,
spl0_193,
inference(avatar_split_clause,[],[f92,f2312]) ).
fof(f2312,plain,
( spl0_193
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f92,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X2),c_HOL_Ozero__class_Ozero(X0)) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_diff__0__right_0) ).
fof(f2310,plain,
spl0_192,
inference(avatar_split_clause,[],[f91,f2308]) ).
fof(f2308,plain,
( spl0_192
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f91,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X3) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_right__minus__eq_1) ).
fof(f2306,plain,
spl0_191,
inference(avatar_split_clause,[],[f90,f2304]) ).
fof(f2304,plain,
( spl0_191
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f90,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X0),X3),X3) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_eq__iff__diff__eq__0_0) ).
fof(f2288,plain,
( spl0_190
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f2284,f2210,f2286]) ).
fof(f2286,plain,
( spl0_190
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f2210,plain,
( spl0_176
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X4,X0)
| c_lessequals(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f2284,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_176 ),
inference(factoring,[],[f2211]) ).
fof(f2211,plain,
( ! [X3,X0,X4] :
( c_lessequals(X4,X3,X0)
| c_lessequals(X3,X4,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f2210]) ).
fof(f2272,plain,
( spl0_189
| ~ spl0_44
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f2072,f1925,f1577,f2270]) ).
fof(f2270,plain,
( spl0_189
<=> ! [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_189])]) ).
fof(f1925,plain,
( spl0_126
<=> ! [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_126])]) ).
fof(f2072,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_bool),X0,tc_bool) = X0
| ~ spl0_44
| ~ spl0_126 ),
inference(resolution,[],[f1926,f1579]) ).
fof(f1926,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(X0),X3,X0) = X3 )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f1925]) ).
fof(f2260,plain,
spl0_188,
inference(avatar_split_clause,[],[f1345,f2258]) ).
fof(f2258,plain,
( spl0_188
<=> ! [X70,X0,X71] :
( X70 = X71
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X70),X71)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1345,axiom,
! [X70,X0,X71] :
( X70 = X71
| ~ hBOOL(hAPP(hAPP(c_fequal(X0),X70),X71)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f2256,plain,
spl0_187,
inference(avatar_split_clause,[],[f1142,f2254]) ).
fof(f2254,plain,
( spl0_187
<=> ! [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_187])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__Id__on_0) ).
fof(f2252,plain,
spl0_186,
inference(avatar_split_clause,[],[f1134,f2250]) ).
fof(f2250,plain,
( spl0_186
<=> ! [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_186])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sym__inv__image_0) ).
fof(f2248,plain,
spl0_185,
inference(avatar_split_clause,[],[f1132,f2246]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__inv__image_0) ).
fof(f2244,plain,
spl0_184,
inference(avatar_split_clause,[],[f967,f2242]) ).
fof(f2242,plain,
( spl0_184
<=> ! [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_184])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Range__Id_0) ).
fof(f2240,plain,
spl0_183,
inference(avatar_split_clause,[],[f966,f2238]) ).
fof(f966,axiom,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Relation_ODomain(c_Relation_OId(X0),X0,X0),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Domain__Id_0) ).
fof(f2236,plain,
( spl0_182
| ~ spl0_44
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f2070,f1921,f1577,f2234]) ).
fof(f1921,plain,
( spl0_125
<=> ! [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_125])]) ).
fof(f2070,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Otop__class_Otop(tc_bool),tc_bool) = X0
| ~ spl0_44
| ~ spl0_125 ),
inference(resolution,[],[f1922,f1579]) ).
fof(f1922,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Orderings_Otop__class_Otop(X0),X0) = X3 )
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1921]) ).
fof(f2232,plain,
spl0_181,
inference(avatar_split_clause,[],[f931,f2230]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_of__nat__0_0) ).
fof(f2228,plain,
spl0_180,
inference(avatar_split_clause,[],[f929,f2226]) ).
fof(f2226,plain,
( spl0_180
<=> ! [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_180])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__imp__of__nat_0) ).
fof(f2224,plain,
spl0_179,
inference(avatar_split_clause,[],[f804,f2222]) ).
fof(f2222,plain,
( spl0_179
<=> ! [X0,X7,X3] : hBOOL(hAPP(hAPP(c_in(X0),X3),c_Set_Oinsert(X3,X7,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f804,axiom,
! [X3,X0,X7] : hBOOL(hAPP(hAPP(c_in(X0),X3),c_Set_Oinsert(X3,X7,X0))),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insertCI_1) ).
fof(f2220,plain,
spl0_178,
inference(avatar_split_clause,[],[f799,f2218]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_UNIV__I_0) ).
fof(f2216,plain,
spl0_177,
inference(avatar_split_clause,[],[f795,f2214]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_empty__iff_0) ).
fof(f2212,plain,
spl0_176,
inference(avatar_split_clause,[],[f731,f2210]) ).
fof(f731,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X4,X0)
| c_lessequals(X4,X3,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_linorder__linear_0) ).
fof(f2208,plain,
spl0_175,
inference(avatar_split_clause,[],[f683,f2206]) ).
fof(f2206,plain,
( spl0_175
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f683,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X0)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X3),X3) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_mult__idem_0) ).
fof(f2204,plain,
spl0_174,
inference(avatar_split_clause,[],[f514,f2202]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_compl__bot__eq_0) ).
fof(f2200,plain,
spl0_173,
inference(avatar_split_clause,[],[f503,f2198]) ).
fof(f2198,plain,
( spl0_173
<=> ! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f503,axiom,
! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_minus__zero_0) ).
fof(f2196,plain,
spl0_172,
inference(avatar_split_clause,[],[f501,f2194]) ).
fof(f2194,plain,
( spl0_172
<=> ! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f501,axiom,
! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_neg__equal__zero_1) ).
fof(f2192,plain,
( spl0_171
| ~ spl0_44
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f2068,f1913,f1577,f2190]) ).
fof(f2190,plain,
( spl0_171
<=> ! [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_171])]) ).
fof(f1913,plain,
( spl0_123
<=> ! [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_123])]) ).
fof(f2068,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0
| ~ spl0_44
| ~ spl0_123 ),
inference(resolution,[],[f1914,f1579]) ).
fof(f1914,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X0),X3,X0) = X3 )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1913]) ).
fof(f2188,plain,
spl0_170,
inference(avatar_split_clause,[],[f473,f2186]) ).
fof(f2186,plain,
( spl0_170
<=> ! [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_170])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_class__semiring_Opwr__0_0) ).
fof(f2184,plain,
spl0_169,
inference(avatar_split_clause,[],[f472,f2182]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__0_0) ).
fof(f2180,plain,
spl0_168,
inference(avatar_split_clause,[],[f278,f2178]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_compl__top__eq_0) ).
fof(f2176,plain,
spl0_167,
inference(avatar_split_clause,[],[f239,f2174]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_power__one_0) ).
fof(f2172,plain,
spl0_166,
inference(avatar_split_clause,[],[f39,f2170]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__top__right_0) ).
fof(f2168,plain,
spl0_165,
inference(avatar_split_clause,[],[f38,f2166]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__top__left_0) ).
fof(f2164,plain,
spl0_164,
inference(avatar_split_clause,[],[f11,f2162]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__bot__right_0) ).
fof(f2160,plain,
spl0_163,
inference(avatar_split_clause,[],[f10,f2158]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__bot__left_0) ).
fof(f2156,plain,
( spl0_162
| ~ spl0_44
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f2066,f1909,f1577,f2154]) ).
fof(f1909,plain,
( spl0_122
<=> ! [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_122])]) ).
fof(f2066,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
| ~ spl0_44
| ~ spl0_122 ),
inference(resolution,[],[f1910,f1579]) ).
fof(f1910,plain,
( ! [X3,X0] :
( ~ class_Lattices_Obounded__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Orderings_Obot__class_Obot(X0),X0) = X3 )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1909]) ).
fof(f2104,plain,
( ~ spl0_41
| spl0_161
| ~ spl0_115
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f2087,f1957,f1880,f2102,f1562]) ).
fof(f2102,plain,
( spl0_161
<=> ! [X3] : c_lessequals(X3,X3,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1880,plain,
( spl0_115
<=> ! [X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_bool) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1957,plain,
( spl0_134
<=> ! [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_134])]) ).
fof(f2087,plain,
( ! [X3] :
( c_lessequals(X3,X3,tc_bool)
| ~ class_Lattices_Oupper__semilattice(tc_bool) )
| ~ spl0_115
| ~ spl0_134 ),
inference(superposition,[],[f1958,f1881]) ).
fof(f1881,plain,
( ! [X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_bool) = X1
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1880]) ).
fof(f1958,plain,
( ! [X3,X0,X4] :
( c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1957]) ).
fof(f2063,plain,
spl0_160,
inference(avatar_split_clause,[],[f1255,f2061]) ).
fof(f2061,plain,
( spl0_160
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1255,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_order__less__le_1) ).
fof(f2059,plain,
spl0_159,
inference(avatar_split_clause,[],[f1254,f2057]) ).
fof(f2057,plain,
( spl0_159
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1254,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_linorder__neq__iff_1) ).
fof(f2055,plain,
spl0_158,
inference(avatar_split_clause,[],[f1253,f2053]) ).
fof(f2053,plain,
( spl0_158
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1253,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_order__less__irrefl_0) ).
fof(f2051,plain,
spl0_157,
inference(avatar_split_clause,[],[f1171,f2049]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__idemp_0) ).
fof(f2047,plain,
spl0_156,
inference(avatar_split_clause,[],[f1170,f2045]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_trancl__rtrancl__absorb_0) ).
fof(f2043,plain,
spl0_155,
inference(avatar_split_clause,[],[f1156,f2041]) ).
fof(f2041,plain,
( spl0_155
<=> ! [X0,X8] :
( ~ c_Relation_Oantisym(X8,X0)
| c_Relation_Oantisym(c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1156,axiom,
! [X0,X8] :
( ~ c_Relation_Oantisym(X8,X0)
| c_Relation_Oantisym(c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_antisym__converse_1) ).
fof(f2039,plain,
spl0_154,
inference(avatar_split_clause,[],[f1155,f2037]) ).
fof(f2037,plain,
( spl0_154
<=> ! [X0,X8] :
( c_Relation_Oantisym(X8,X0)
| ~ c_Relation_Oantisym(c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1155,axiom,
! [X0,X8] :
( c_Relation_Oantisym(X8,X0)
| ~ c_Relation_Oantisym(c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_antisym__converse_0) ).
fof(f2035,plain,
spl0_153,
inference(avatar_split_clause,[],[f1149,f2033]) ).
fof(f2033,plain,
( spl0_153
<=> ! [X0,X8,X10] : c_Relation_Oconverse(c_Relation_Oconverse(X8,X0,X10),X10,X0) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1149,axiom,
! [X10,X0,X8] : c_Relation_Oconverse(c_Relation_Oconverse(X8,X0,X10),X10,X0) = X8,
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__converse_0) ).
fof(f2031,plain,
spl0_152,
inference(avatar_split_clause,[],[f1145,f2029]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__mlex_0) ).
fof(f2027,plain,
spl0_151,
inference(avatar_split_clause,[],[f1135,f2025]) ).
fof(f2025,plain,
( spl0_151
<=> ! [X0,X15] : c_Transitive__Closure_Ortrancl(X15,X0) = c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X15,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_rtrancl__trancl__absorb_0) ).
fof(f2023,plain,
spl0_150,
inference(avatar_split_clause,[],[f1125,f2021]) ).
fof(f2021,plain,
( spl0_150
<=> ! [X0,X8] :
( c_Relation_Osym(X8,X0)
| c_Relation_Oconverse(X8,X0,X0) != X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1125,axiom,
! [X0,X8] :
( c_Relation_Osym(X8,X0)
| c_Relation_Oconverse(X8,X0,X0) != X8 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sym__conv__converse__eq_1) ).
fof(f2019,plain,
spl0_149,
inference(avatar_split_clause,[],[f1124,f2017]) ).
fof(f2017,plain,
( spl0_149
<=> ! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Oconverse(X8,X0,X0) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1124,axiom,
! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Oconverse(X8,X0,X0) = X8 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sym__conv__converse__eq_0) ).
fof(f2015,plain,
spl0_148,
inference(avatar_split_clause,[],[f1113,f2013]) ).
fof(f1113,axiom,
! [X10,X0,X15] : c_Relation_Orel__comp(X15,c_Relation_OId(X10),X0,X10,X10) = X15,
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_R__O__Id_0) ).
fof(f2011,plain,
spl0_147,
inference(avatar_split_clause,[],[f1112,f2009]) ).
fof(f2009,plain,
( spl0_147
<=> ! [X10,X0,X15] : c_Relation_Orel__comp(c_Relation_OId(X0),X15,X0,X0,X10) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1112,axiom,
! [X10,X0,X15] : c_Relation_Orel__comp(c_Relation_OId(X0),X15,X0,X0,X10) = X15,
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Id__O__R_0) ).
fof(f2007,plain,
spl0_146,
inference(avatar_split_clause,[],[f1106,f2005]) ).
fof(f2005,plain,
( spl0_146
<=> ! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1106,axiom,
! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sym__converse_1) ).
fof(f2003,plain,
spl0_145,
inference(avatar_split_clause,[],[f1105,f2001]) ).
fof(f2001,plain,
( spl0_145
<=> ! [X0,X8] :
( c_Relation_Osym(X8,X0)
| ~ c_Relation_Osym(c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1105,axiom,
! [X0,X8] :
( c_Relation_Osym(X8,X0)
| ~ c_Relation_Osym(c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sym__converse_0) ).
fof(f1999,plain,
spl0_144,
inference(avatar_split_clause,[],[f962,f1997]) ).
fof(f1997,plain,
( spl0_144
<=> ! [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_144])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_refl__rtrancl_0) ).
fof(f1995,plain,
spl0_143,
inference(avatar_split_clause,[],[f619,f1993]) ).
fof(f1993,plain,
( spl0_143
<=> ! [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_143])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_card__empty_0) ).
fof(f1991,plain,
spl0_142,
inference(avatar_split_clause,[],[f491,f1989]) ).
fof(f1989,plain,
( spl0_142
<=> ! [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_142])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_subset__UNIV_0) ).
fof(f1987,plain,
spl0_141,
inference(avatar_split_clause,[],[f486,f1985]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__le1_0) ).
fof(f1983,plain,
spl0_140,
inference(avatar_split_clause,[],[f485,f1981]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__le2_0) ).
fof(f1979,plain,
spl0_139,
inference(avatar_split_clause,[],[f481,f1977]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__ord_I2_J_0) ).
fof(f1975,plain,
spl0_138,
inference(avatar_split_clause,[],[f480,f1973]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__ord_I1_J_0) ).
fof(f1971,plain,
spl0_137,
inference(avatar_split_clause,[],[f391,f1969]) ).
fof(f1969,plain,
( spl0_137
<=> ! [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_137])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__ord_I3_J_0) ).
fof(f1967,plain,
spl0_136,
inference(avatar_split_clause,[],[f390,f1965]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__sup__ord_I4_J_0) ).
fof(f1963,plain,
spl0_135,
inference(avatar_split_clause,[],[f387,f1961]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__ge2_0) ).
fof(f1959,plain,
spl0_134,
inference(avatar_split_clause,[],[f386,f1957]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__ge1_0) ).
fof(f1955,plain,
spl0_133,
inference(avatar_split_clause,[],[f358,f1953]) ).
fof(f1953,plain,
( spl0_133
<=> ! [X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f358,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn0_0) ).
fof(f1951,plain,
spl0_132,
inference(avatar_split_clause,[],[f357,f1949]) ).
fof(f1949,plain,
( spl0_132
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f357,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sgn__0__0_1) ).
fof(f1947,plain,
( spl0_131
| ~ spl0_42
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1870,f1795,f1567,f1945]) ).
fof(f1945,plain,
( spl0_131
<=> ! [X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_bool) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1870,plain,
( ! [X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_bool) = X1
| ~ spl0_42
| ~ spl0_96 ),
inference(resolution,[],[f1796,f1569]) ).
fof(f1943,plain,
spl0_130,
inference(avatar_split_clause,[],[f307,f1941]) ).
fof(f1941,plain,
( spl0_130
<=> ! [X0,X8] :
( ~ c_Wellfounded_Oacyclic(X8,X0)
| c_Wellfounded_Oacyclic(c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f307,axiom,
! [X0,X8] :
( ~ c_Wellfounded_Oacyclic(X8,X0)
| c_Wellfounded_Oacyclic(c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acyclic__converse_1) ).
fof(f1939,plain,
spl0_129,
inference(avatar_split_clause,[],[f306,f1937]) ).
fof(f1937,plain,
( spl0_129
<=> ! [X0,X8] :
( c_Wellfounded_Oacyclic(X8,X0)
| ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X8,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f306,axiom,
! [X0,X8] :
( c_Wellfounded_Oacyclic(X8,X0)
| ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X8,X0,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acyclic__converse_0) ).
fof(f1935,plain,
spl0_128,
inference(avatar_split_clause,[],[f300,f1933]) ).
fof(f1933,plain,
( spl0_128
<=> ! [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_128])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_card__eq__0__iff_2) ).
fof(f1931,plain,
spl0_127,
inference(avatar_split_clause,[],[f298,f1929]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__0__eq_0) ).
fof(f1927,plain,
spl0_126,
inference(avatar_split_clause,[],[f286,f1925]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__top__left_0) ).
fof(f1923,plain,
spl0_125,
inference(avatar_split_clause,[],[f285,f1921]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__top__right_0) ).
fof(f1919,plain,
spl0_124,
inference(avatar_split_clause,[],[f283,f1917]) ).
fof(f1917,plain,
( spl0_124
<=> ! [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_124])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_UNIV__not__empty_0) ).
fof(f1915,plain,
spl0_123,
inference(avatar_split_clause,[],[f151,f1913]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__bot__left_0) ).
fof(f1911,plain,
spl0_122,
inference(avatar_split_clause,[],[f150,f1909]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__bot__right_0) ).
fof(f1907,plain,
spl0_121,
inference(avatar_split_clause,[],[f76,f1905]) ).
fof(f1905,plain,
( spl0_121
<=> ! [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_121])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_finite__insert_1) ).
fof(f1903,plain,
( spl0_120
| ~ spl0_22
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1869,f1795,f1467,f1901]) ).
fof(f1901,plain,
( spl0_120
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1869,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0
| ~ spl0_22
| ~ spl0_96 ),
inference(resolution,[],[f1796,f1469]) ).
fof(f1899,plain,
spl0_119,
inference(avatar_split_clause,[],[f75,f1897]) ).
fof(f1897,plain,
( spl0_119
<=> ! [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_119])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_finite__insert_0) ).
fof(f1895,plain,
spl0_118,
inference(avatar_split_clause,[],[f72,f1893]) ).
fof(f1893,plain,
( spl0_118
<=> ! [X2,X0,X7] : c_lessequals(X7,c_Set_Oinsert(X2,X7,X0),tc_fun(X0,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f72,axiom,
! [X2,X0,X7] : c_lessequals(X7,c_Set_Oinsert(X2,X7,X0),tc_fun(X0,tc_bool)),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_subset__insertI_0) ).
fof(f1891,plain,
spl0_117,
inference(avatar_split_clause,[],[f42,f1889]) ).
fof(f1889,plain,
( spl0_117
<=> ! [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_117])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_empty__subsetI_0) ).
fof(f1887,plain,
spl0_116,
inference(avatar_split_clause,[],[f35,f1885]) ).
fof(f1885,plain,
( spl0_116
<=> ! [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_116])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__not__empty_0) ).
fof(f1882,plain,
( spl0_115
| ~ spl0_41
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1867,f1791,f1562,f1880]) ).
fof(f1867,plain,
( ! [X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_bool) = X1
| ~ spl0_41
| ~ spl0_95 ),
inference(resolution,[],[f1792,f1564]) ).
fof(f1875,plain,
( spl0_114
| ~ spl0_21
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f1866,f1791,f1462,f1873]) ).
fof(f1873,plain,
( spl0_114
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1866,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0
| ~ spl0_21
| ~ spl0_95 ),
inference(resolution,[],[f1792,f1464]) ).
fof(f1865,plain,
spl0_113,
inference(avatar_split_clause,[],[f1282,f1863]) ).
fof(f1863,plain,
( spl0_113
<=> ! [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_113])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(f1861,plain,
spl0_112,
inference(avatar_split_clause,[],[f1276,f1859]) ).
fof(f1859,plain,
( spl0_112
<=> ! [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_112])]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_prod__Finite__Set_Ofinite_Ofinite) ).
fof(f1857,plain,
spl0_111,
inference(avatar_split_clause,[],[f1157,f1855]) ).
fof(f1855,plain,
( spl0_111
<=> ! [X6,X0,X8] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| c_Relation_Orefl__on(X6,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1157,axiom,
! [X0,X8,X6] :
( ~ c_Equiv__Relations_Oequiv(X6,X8,X0)
| c_Relation_Orefl__on(X6,X8,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_equiv_Orefl__on_0) ).
fof(f1853,plain,
spl0_110,
inference(avatar_split_clause,[],[f1147,f1851]) ).
fof(f1851,plain,
( spl0_110
<=> ! [X6,X0] : c_Relation_ORange(c_Relation_OId__on(X6,X0),X0,X0) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1147,axiom,
! [X0,X6] : c_Relation_ORange(c_Relation_OId__on(X6,X0),X0,X0) = X6,
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Range__Id__on_0) ).
fof(f1849,plain,
spl0_109,
inference(avatar_split_clause,[],[f1137,f1847]) ).
fof(f1137,axiom,
! [X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X8,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__trancl_0) ).
fof(f1845,plain,
spl0_108,
inference(avatar_split_clause,[],[f1136,f1843]) ).
fof(f1136,axiom,
! [X0] : c_Relation_OId(X0) = c_Relation_Oconverse(c_Relation_OId(X0),X0,X0),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_converse__Id_0) ).
fof(f1841,plain,
spl0_107,
inference(avatar_split_clause,[],[f1123,f1839]) ).
fof(f1839,plain,
( spl0_107
<=> ! [X6,X0] : c_Relation_ODomain(c_Relation_OId__on(X6,X0),X0,X0) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1123,axiom,
! [X0,X6] : c_Relation_ODomain(c_Relation_OId__on(X6,X0),X0,X0) = X6,
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Domain__Id__on_0) ).
fof(f1837,plain,
spl0_106,
inference(avatar_split_clause,[],[f1121,f1835]) ).
fof(f1835,plain,
( spl0_106
<=> ! [X6,X0] : c_Relation_OImage(c_Relation_OId(X0),X6,X0,X0) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1121,axiom,
! [X0,X6] : c_Relation_OImage(c_Relation_OId(X0),X6,X0,X0) = X6,
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Image__Id_0) ).
fof(f1833,plain,
spl0_105,
inference(avatar_split_clause,[],[f1118,f1831]) ).
fof(f1118,axiom,
! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Transitive__Closure_Ortrancl(X8,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sym__rtrancl_0) ).
fof(f1829,plain,
spl0_104,
inference(avatar_split_clause,[],[f1103,f1827]) ).
fof(f1827,plain,
( spl0_104
<=> ! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1103,axiom,
! [X0,X8] :
( ~ c_Relation_Osym(X8,X0)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(X8,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sym__trancl_0) ).
fof(f1825,plain,
spl0_103,
inference(avatar_split_clause,[],[f968,f1823]) ).
fof(f1823,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_refl__Id_0) ).
fof(f1821,plain,
spl0_102,
inference(avatar_split_clause,[],[f964,f1819]) ).
fof(f964,axiom,
! [X0,X8] :
( ~ c_Wellfounded_Oacyclic(X8,X0)
| c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X8,X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_acyclic__impl__antisym__rtrancl_0) ).
fof(f1817,plain,
spl0_101,
inference(avatar_split_clause,[],[f918,f1815]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_not__one__le__zero_0) ).
fof(f1813,plain,
spl0_100,
inference(avatar_split_clause,[],[f917,f1811]) ).
fof(f1811,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__le__one_0) ).
fof(f1809,plain,
spl0_99,
inference(avatar_split_clause,[],[f861,f1807]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_gr__implies__not0_0) ).
fof(f1805,plain,
spl0_98,
inference(avatar_split_clause,[],[f730,f1803]) ).
fof(f1803,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_nat__le__linear_0) ).
fof(f1801,plain,
spl0_97,
inference(avatar_split_clause,[],[f542,f1799]) ).
fof(f1799,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Int__absorb_0) ).
fof(f1797,plain,
spl0_96,
inference(avatar_split_clause,[],[f541,f1795]) ).
fof(f541,axiom,
! [X3,X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X3,X0) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_inf__idem_0) ).
fof(f1793,plain,
spl0_95,
inference(avatar_split_clause,[],[f218,f1791]) ).
fof(f218,axiom,
! [X3,X0] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X3,X0) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sup__idem_0) ).
fof(f1789,plain,
spl0_94,
inference(avatar_split_clause,[],[f217,f1787]) ).
fof(f1787,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_Un__absorb_0) ).
fof(f1785,plain,
spl0_93,
inference(avatar_split_clause,[],[f1344,f1783]) ).
fof(f1783,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f1781,plain,
spl0_92,
inference(avatar_split_clause,[],[f1256,f1779]) ).
fof(f1779,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_less__not__refl_0) ).
fof(f1777,plain,
spl0_91,
inference(avatar_split_clause,[],[f1160,f1775]) ).
fof(f1775,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_equiv_Osym_0) ).
fof(f1773,plain,
spl0_90,
inference(avatar_split_clause,[],[f1122,f1771]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_zero__neq__one_0) ).
fof(f1769,plain,
spl0_89,
inference(avatar_split_clause,[],[f508,f1767]) ).
fof(f1767,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_insert__code_1) ).
fof(f1765,plain,
spl0_88,
inference(avatar_split_clause,[],[f492,f1763]) ).
fof(f1763,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_top__greatest_0) ).
fof(f1761,plain,
spl0_87,
inference(avatar_split_clause,[],[f474,f1759]) ).
fof(f1759,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_total__on__empty_0) ).
fof(f1757,plain,
spl0_86,
inference(avatar_split_clause,[],[f369,f1755]) ).
fof(f1755,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_one__dvd_0) ).
fof(f1753,plain,
spl0_85,
inference(avatar_split_clause,[],[f299,f1751]) ).
fof(f1751,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_top1I_0) ).
fof(f1749,plain,
spl0_84,
inference(avatar_split_clause,[],[f282,f1747]) ).
fof(f1747,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_bot1E_0) ).
fof(f1745,plain,
spl0_83,
inference(avatar_split_clause,[],[f160,f1743]) ).
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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__0__right_0) ).
fof(f1741,plain,
spl0_82,
inference(avatar_split_clause,[],[f41,f1739]) ).
fof(f41,axiom,
! [X3,X0] :
( ~ class_Orderings_Obot(X0)
| c_lessequals(c_Orderings_Obot__class_Obot(X0),X3,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_bot__least_0) ).
fof(f1737,plain,
( spl0_81
| ~ spl0_61
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f1733,f1666,f1654,f1735]) ).
fof(f1735,plain,
( spl0_81
<=> ! [X0,X1] : c_Wellfounded_Oacyclic(c_Wellfounded_Omeasure(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1733,plain,
( ! [X0,X1] : c_Wellfounded_Oacyclic(c_Wellfounded_Omeasure(X0,X1),X1)
| ~ spl0_61
| ~ spl0_64 ),
inference(resolution,[],[f1667,f1655]) ).
fof(f1732,plain,
spl0_80,
inference(avatar_split_clause,[],[f1288,f1730]) ).
fof(f1730,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_fun__HOL_Oord) ).
fof(f1728,plain,
spl0_79,
inference(avatar_split_clause,[],[f1287,f1726]) ).
fof(f1726,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_fun__Orderings_Obot) ).
fof(f1724,plain,
spl0_78,
inference(avatar_split_clause,[],[f1286,f1722]) ).
fof(f1722,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_fun__Orderings_Otop) ).
fof(f1720,plain,
spl0_77,
inference(avatar_split_clause,[],[f1285,f1718]) ).
fof(f1718,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_fun__Orderings_Oorder) ).
fof(f1716,plain,
spl0_76,
inference(avatar_split_clause,[],[f1284,f1714]) ).
fof(f1714,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_fun__Lattices_Olattice) ).
fof(f1712,plain,
spl0_75,
inference(avatar_split_clause,[],[f1283,f1710]) ).
fof(f1710,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_fun__Orderings_Opreorder) ).
fof(f1708,plain,
spl0_74,
inference(avatar_split_clause,[],[f1281,f1706]) ).
fof(f1706,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_fun__Lattices_Oboolean__algebra) ).
fof(f1704,plain,
spl0_73,
inference(avatar_split_clause,[],[f1280,f1702]) ).
fof(f1702,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f1700,plain,
spl0_72,
inference(avatar_split_clause,[],[f1279,f1698]) ).
fof(f1698,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(f1696,plain,
spl0_71,
inference(avatar_split_clause,[],[f1278,f1694]) ).
fof(f1278,axiom,
! [X68,X69] :
( ~ class_Lattices_Olattice(X69)
| class_Lattices_Olower__semilattice(tc_fun(X68,X69)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f1692,plain,
spl0_70,
inference(avatar_split_clause,[],[f1277,f1690]) ).
fof(f1277,axiom,
! [X68,X69] :
( ~ class_Lattices_Olattice(X69)
| class_Lattices_Oupper__semilattice(tc_fun(X68,X69)) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(f1688,plain,
spl0_69,
inference(avatar_split_clause,[],[f1131,f1686]) ).
fof(f1686,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_refl__on__Id__on_0) ).
fof(f1684,plain,
spl0_68,
inference(avatar_split_clause,[],[f661,f1682]) ).
fof(f1682,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_single__valued__Id__on_0) ).
fof(f1680,plain,
spl0_67,
inference(avatar_split_clause,[],[f571,f1678]) ).
fof(f1678,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_order__eq__refl_0) ).
fof(f1676,plain,
spl0_66,
inference(avatar_split_clause,[],[f570,f1674]) ).
fof(f1674,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_order__eq__iff_0) ).
fof(f1672,plain,
spl0_65,
inference(avatar_split_clause,[],[f566,f1670]) ).
fof(f1670,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_subset__refl_0) ).
fof(f1668,plain,
spl0_64,
inference(avatar_split_clause,[],[f395,f1666]) ).
fof(f395,axiom,
! [X0,X8] :
( ~ c_Wellfounded_Owf(X8,X0)
| c_Wellfounded_Oacyclic(X8,X0) ),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__acyclic_0) ).
fof(f1664,plain,
spl0_63,
inference(avatar_split_clause,[],[f328,f1662]) ).
fof(f1662,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_dvd__refl_0) ).
fof(f1660,plain,
spl0_62,
inference(avatar_split_clause,[],[f77,f1658]) ).
fof(f1658,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_finite_OemptyI_0) ).
fof(f1656,plain,
spl0_61,
inference(avatar_split_clause,[],[f1169,f1654]) ).
fof(f1169,axiom,
! [X0,X18] : c_Wellfounded_Owf(c_Wellfounded_Omeasure(X18,X0),X0),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_wf__measure_0) ).
fof(f1652,plain,
spl0_60,
inference(avatar_split_clause,[],[f1130,f1650]) ).
fof(f1650,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sym__Id__on_0) ).
fof(f1648,plain,
spl0_59,
inference(avatar_split_clause,[],[f1114,f1646]) ).
fof(f1646,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_antisym__Id__on_0) ).
fof(f1644,plain,
spl0_58,
inference(avatar_split_clause,[],[f1104,f1642]) ).
fof(f1642,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_finite_0) ).
fof(f1640,plain,
spl0_57,
inference(avatar_split_clause,[],[f422,f1638]) ).
fof(f422,axiom,
! [X14] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X14,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le0_0) ).
fof(f1636,plain,
spl0_56,
inference(avatar_split_clause,[],[f240,f1634]) ).
fof(f1634,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_single__valued__Id_0) ).
fof(f1632,plain,
spl0_55,
inference(avatar_split_clause,[],[f1144,f1630]) ).
fof(f1630,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_antisym__Id_0) ).
fof(f1628,plain,
spl0_54,
inference(avatar_split_clause,[],[f1111,f1626]) ).
fof(f1626,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_sym__Id_0) ).
fof(f1624,plain,
spl0_53,
inference(avatar_split_clause,[],[f562,f1622]) ).
fof(f562,axiom,
! [X14] : c_lessequals(X14,X14,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',cls_le__refl_0) ).
fof(f1620,plain,
spl0_52,
inference(avatar_split_clause,[],[f1340,f1617]) ).
fof(f1617,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_bool__HOL_Oord) ).
fof(f1615,plain,
spl0_51,
inference(avatar_split_clause,[],[f1339,f1612]) ).
fof(f1612,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_bool__Orderings_Obot) ).
fof(f1610,plain,
spl0_50,
inference(avatar_split_clause,[],[f1338,f1607]) ).
fof(f1607,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_bool__Orderings_Otop) ).
fof(f1605,plain,
spl0_49,
inference(avatar_split_clause,[],[f1337,f1602]) ).
fof(f1602,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_bool__Orderings_Oorder) ).
fof(f1600,plain,
spl0_48,
inference(avatar_split_clause,[],[f1336,f1597]) ).
fof(f1336,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_bool__Lattices_Olattice) ).
fof(f1595,plain,
spl0_47,
inference(avatar_split_clause,[],[f1335,f1592]) ).
fof(f1592,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_bool__Orderings_Opreorder) ).
fof(f1590,plain,
spl0_46,
inference(avatar_split_clause,[],[f1334,f1587]) ).
fof(f1587,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
fof(f1585,plain,
spl0_45,
inference(avatar_split_clause,[],[f1333,f1582]) ).
fof(f1333,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_bool__Lattices_Oboolean__algebra) ).
fof(f1580,plain,
spl0_44,
inference(avatar_split_clause,[],[f1332,f1577]) ).
fof(f1332,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f1575,plain,
spl0_43,
inference(avatar_split_clause,[],[f1331,f1572]) ).
fof(f1572,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(f1570,plain,
spl0_42,
inference(avatar_split_clause,[],[f1330,f1567]) ).
fof(f1330,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f1565,plain,
spl0_41,
inference(avatar_split_clause,[],[f1329,f1562]) ).
fof(f1329,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(f1560,plain,
spl0_40,
inference(avatar_split_clause,[],[f1328,f1557]) ).
fof(f1557,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__HOL_Oord) ).
fof(f1555,plain,
spl0_39,
inference(avatar_split_clause,[],[f1327,f1552]) ).
fof(f1327,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Power_Opower) ).
fof(f1550,plain,
spl0_38,
inference(avatar_split_clause,[],[f1326,f1547]) ).
fof(f1326,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Orderings_Obot) ).
fof(f1545,plain,
spl0_37,
inference(avatar_split_clause,[],[f1325,f1542]) ).
fof(f1542,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Orderings_Oorder) ).
fof(f1540,plain,
spl0_36,
inference(avatar_split_clause,[],[f1324,f1537]) ).
fof(f1324,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Lattices_Olattice) ).
fof(f1535,plain,
spl0_35,
inference(avatar_split_clause,[],[f1323,f1532]) ).
fof(f1532,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Orderings_Olinorder) ).
fof(f1530,plain,
spl0_34,
inference(avatar_split_clause,[],[f1322,f1527]) ).
fof(f1527,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Orderings_Opreorder) ).
fof(f1525,plain,
spl0_33,
inference(avatar_split_clause,[],[f1321,f1522]) ).
fof(f1321,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Odvd) ).
fof(f1520,plain,
spl0_32,
inference(avatar_split_clause,[],[f1320,f1517]) ).
fof(f1517,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f1515,plain,
spl0_31,
inference(avatar_split_clause,[],[f1319,f1512]) ).
fof(f1512,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f1510,plain,
spl0_30,
inference(avatar_split_clause,[],[f1318,f1507]) ).
fof(f1507,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f1505,plain,
spl0_29,
inference(avatar_split_clause,[],[f1317,f1502]) ).
fof(f1502,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Lattices_Odistrib__lattice) ).
fof(f1500,plain,
spl0_28,
inference(avatar_split_clause,[],[f1316,f1497]) ).
fof(f1316,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f1495,plain,
spl0_27,
inference(avatar_split_clause,[],[f1315,f1492]) ).
fof(f1492,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f1490,plain,
spl0_26,
inference(avatar_split_clause,[],[f1314,f1487]) ).
fof(f1487,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f1485,plain,
spl0_25,
inference(avatar_split_clause,[],[f1313,f1482]) ).
fof(f1482,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f1480,plain,
spl0_24,
inference(avatar_split_clause,[],[f1312,f1477]) ).
fof(f1477,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f1475,plain,
spl0_23,
inference(avatar_split_clause,[],[f1311,f1472]) ).
fof(f1311,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f1470,plain,
spl0_22,
inference(avatar_split_clause,[],[f1310,f1467]) ).
fof(f1310,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Lattices_Olower__semilattice) ).
fof(f1465,plain,
spl0_21,
inference(avatar_split_clause,[],[f1309,f1462]) ).
fof(f1309,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Lattices_Oupper__semilattice) ).
fof(f1460,plain,
spl0_20,
inference(avatar_split_clause,[],[f1308,f1457]) ).
fof(f1308,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f1455,plain,
spl0_19,
inference(avatar_split_clause,[],[f1307,f1452]) ).
fof(f1307,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1450,plain,
spl0_18,
inference(avatar_split_clause,[],[f1306,f1447]) ).
fof(f1447,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f1445,plain,
spl0_17,
inference(avatar_split_clause,[],[f1305,f1442]) ).
fof(f1442,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1440,plain,
spl0_16,
inference(avatar_split_clause,[],[f1304,f1437]) ).
fof(f1437,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1435,plain,
spl0_15,
inference(avatar_split_clause,[],[f1303,f1432]) ).
fof(f1432,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f1430,plain,
spl0_14,
inference(avatar_split_clause,[],[f1302,f1427]) ).
fof(f1302,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1425,plain,
spl0_13,
inference(avatar_split_clause,[],[f1301,f1422]) ).
fof(f1301,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f1420,plain,
spl0_12,
inference(avatar_split_clause,[],[f1300,f1417]) ).
fof(f1417,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f1415,plain,
spl0_11,
inference(avatar_split_clause,[],[f1299,f1412]) ).
fof(f1412,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f1410,plain,
spl0_10,
inference(avatar_split_clause,[],[f1298,f1407]) ).
fof(f1407,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f1405,plain,
spl0_9,
inference(avatar_split_clause,[],[f1297,f1402]) ).
fof(f1402,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1400,plain,
spl0_8,
inference(avatar_split_clause,[],[f1296,f1397]) ).
fof(f1397,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1395,plain,
spl0_7,
inference(avatar_split_clause,[],[f1295,f1392]) ).
fof(f1392,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1390,plain,
spl0_6,
inference(avatar_split_clause,[],[f1294,f1387]) ).
fof(f1387,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1385,plain,
spl0_5,
inference(avatar_split_clause,[],[f1293,f1382]) ).
fof(f1382,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1380,plain,
spl0_4,
inference(avatar_split_clause,[],[f1292,f1377]) ).
fof(f1377,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1375,plain,
spl0_3,
inference(avatar_split_clause,[],[f1291,f1372]) ).
fof(f1372,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1370,plain,
spl0_2,
inference(avatar_split_clause,[],[f1290,f1367]) ).
fof(f1367,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1365,plain,
spl0_1,
inference(avatar_split_clause,[],[f1289,f1362]) ).
fof(f1362,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/tmp/tmp.UhcjaVgq9Z/Vampire---4.8_28338',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.22 % Problem : SCT097-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.24 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.24/0.45 % Computer : n013.cluster.edu
% 0.24/0.45 % Model : x86_64 x86_64
% 0.24/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.45 % Memory : 8042.1875MB
% 0.24/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.24/0.45 % CPULimit : 300
% 0.24/0.45 % WCLimit : 300
% 0.24/0.45 % DateTime : Wed Aug 30 14:35:31 EDT 2023
% 0.24/0.45 % CPUTime :
% 0.24/0.49 % (28683)Running in auto input_syntax mode. Trying TPTP
% 0.30/0.55 % (28690)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.30/0.55 % (28691)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.30/0.55 % (28696)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.30/0.55 % (28693)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 Vampire---4 for (569ds/0Mi)
% 0.30/0.55 % (28698)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 Vampire---4 for (531ds/0Mi)
% 0.30/0.55 % (28699)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 Vampire---4 for (522ds/0Mi)
% 0.30/0.55 % (28703)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 Vampire---4 for (497ds/0Mi)
% 2.85/0.93 TRYING [1]
% 3.40/1.02 TRYING [2]
% 9.20/1.89 TRYING [1]
% 9.68/1.89 TRYING [3]
% 9.68/1.94 TRYING [2]
% 10.28/2.00 TRYING [1]
% 11.55/2.15 TRYING [2]
% 15.41/2.73 TRYING [3]
% 17.55/3.07 % (28698)First to succeed.
% 17.55/3.11 % (28698)Refutation found. Thanks to Tanya!
% 17.55/3.11 % SZS status Unsatisfiable for Vampire---4
% 17.55/3.11 % SZS output start Proof for Vampire---4
% See solution above
% 17.55/3.13 % (28698)------------------------------
% 17.55/3.13 % (28698)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 17.55/3.13 % (28698)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 17.55/3.13 % (28698)Termination reason: Refutation
% 17.55/3.13
% 17.55/3.13 % (28698)Memory used [KB]: 50788
% 17.55/3.13 % (28698)Time elapsed: 2.553 s
% 17.55/3.13 % (28698)------------------------------
% 17.55/3.13 % (28698)------------------------------
% 17.55/3.13 % (28683)Success in time 2.652 s
% 17.55/3.13 % Vampire---4.8 exiting
%------------------------------------------------------------------------------