TSTP Solution File: SWV693-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV693-1 : 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 : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 2 13:57:39 EDT 2023
% Result : Unsatisfiable 30.47s 4.91s
% Output : Refutation 30.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2704
% Syntax : Number of formulae : 5118 (1409 unt; 0 def)
% Number of atoms : 14125 (2093 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 16208 (7201 ~;7459 |; 0 &)
% (1548 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of predicates : 1634 (1632 usr;1549 prp; 0-5 aty)
% Number of functors : 44 ( 44 usr; 8 con; 0-5 aty)
% Number of variables : 8975 (;8975 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f54078,plain,
$false,
inference(avatar_sat_refutation,[],[f1504,f1509,f1514,f1519,f1524,f1529,f1534,f1539,f1544,f1549,f1554,f1559,f1564,f1569,f1574,f1579,f1584,f1589,f1594,f1599,f1604,f1609,f1614,f1619,f1624,f1629,f1634,f1639,f1644,f1649,f1654,f1659,f1664,f1669,f1674,f1679,f1684,f1689,f1694,f1699,f1704,f1709,f1714,f1719,f1724,f1729,f1734,f1739,f1744,f1749,f1754,f1759,f1764,f1769,f1774,f1779,f1784,f1789,f1794,f1799,f1804,f1809,f1814,f1819,f1824,f1829,f1834,f1839,f1844,f1849,f1854,f1859,f1864,f1869,f1874,f1879,f1884,f1889,f1894,f1899,f1904,f1909,f1914,f1919,f1924,f1929,f1934,f1939,f1944,f1949,f1954,f1959,f1964,f1969,f1974,f1979,f1984,f1989,f1994,f1999,f2004,f2009,f2014,f2019,f2024,f2029,f2034,f2039,f2044,f2049,f2054,f2059,f2064,f2069,f2074,f2079,f2084,f2089,f2094,f2099,f2104,f2109,f2114,f2119,f2124,f2129,f2134,f2139,f2144,f2149,f2154,f2159,f2164,f2169,f2174,f2179,f2184,f2189,f2194,f2199,f2204,f2209,f2214,f2219,f2224,f2228,f2232,f2236,f2240,f2244,f2248,f2253,f2258,f2262,f2266,f2270,f2274,f2278,f2282,f2286,f2290,f2294,f2300,f2304,f2308,f2312,f2316,f2320,f2324,f2329,f2333,f2337,f2341,f2345,f2349,f2353,f2357,f2361,f2365,f2369,f2382,f2386,f2390,f2394,f2398,f2402,f2406,f2410,f2414,f2419,f2423,f2427,f2431,f2435,f2439,f2443,f2456,f2462,f2466,f2470,f2474,f2478,f2482,f2486,f2490,f2494,f2498,f2502,f2506,f2510,f2514,f2518,f2522,f2526,f2530,f2534,f2538,f2546,f2555,f2559,f2563,f2567,f2571,f2575,f2579,f2583,f2587,f2591,f2595,f2599,f2603,f2607,f2611,f2615,f2619,f2623,f2627,f2631,f2635,f2639,f2643,f2647,f2651,f2655,f2659,f2663,f2667,f2671,f2675,f2679,f2683,f2687,f2691,f2695,f2699,f2703,f2707,f2711,f2715,f2719,f2723,f2727,f2731,f2735,f2739,f2743,f2747,f2751,f2786,f2816,f2860,f2898,f2928,f2932,f2936,f2940,f2944,f2948,f2952,f2956,f2960,f2964,f2968,f2974,f2978,f2982,f2986,f2990,f2994,f2998,f3002,f3006,f3010,f3016,f3049,f3084,f3088,f3092,f3096,f3100,f3104,f3108,f3112,f3117,f3121,f3125,f3129,f3133,f3137,f3141,f3145,f3149,f3155,f3161,f3188,f3192,f3196,f3201,f3206,f3210,f3214,f3218,f3222,f3226,f3231,f3306,f3310,f3340,f3408,f3412,f3416,f3420,f3424,f3428,f3432,f3436,f3440,f3445,f3450,f3454,f3458,f3462,f3466,f3470,f3474,f3478,f3482,f3486,f3496,f3500,f3504,f3508,f3512,f3516,f3520,f3524,f3528,f3532,f3537,f3541,f3545,f3549,f3553,f3557,f3561,f3565,f3569,f3573,f3577,f3582,f3587,f3591,f3595,f3599,f3603,f3607,f3611,f3615,f3619,f3623,f3716,f3850,f3940,f4041,f4046,f4193,f4197,f4201,f4205,f4209,f4213,f4217,f4221,f4225,f4229,f4237,f4241,f4245,f4249,f4254,f4259,f4263,f4268,f4273,f4277,f4281,f4285,f4289,f4414,f4425,f4429,f4435,f4439,f4532,f4536,f4541,f4545,f4549,f4553,f4557,f4561,f4565,f4569,f4573,f4577,f4581,f4589,f4593,f4597,f4601,f4823,f4827,f4831,f4835,f4839,f4843,f4847,f4851,f4855,f4859,f4867,f4871,f4875,f4879,f4883,f4887,f4891,f4895,f4899,f4905,f4915,f4919,f4923,f4927,f4931,f4935,f4939,f4943,f4947,f4951,f4956,f4960,f4964,f4969,f4974,f4978,f4982,f4986,f4993,f4997,f5001,f5006,f5010,f5014,f5018,f5022,f5026,f5030,f5034,f5038,f5042,f5046,f5050,f5054,f5058,f5062,f5066,f5070,f5074,f5078,f5082,f5120,f5357,f5512,f5516,f5565,f5788,f5793,f5890,f6037,f6376,f6380,f6384,f6388,f6392,f6396,f6400,f6404,f6408,f6412,f6417,f6423,f6427,f6431,f6435,f6439,f6443,f6447,f6451,f6455,f6459,f6463,f6476,f6481,f6485,f6490,f6495,f6499,f6503,f6547,f6679,f6683,f6762,f6766,f6774,f6778,f6910,f6914,f6918,f6925,f6931,f6937,f6941,f6945,f6949,f6953,f6964,f6968,f6972,f6976,f6980,f6984,f6988,f6992,f6996,f7000,f7043,f7047,f7051,f7482,f7486,f7490,f7494,f7498,f7502,f7506,f7510,f7514,f7518,f7522,f7526,f7530,f7534,f7538,f7542,f7546,f7570,f7575,f7579,f7583,f7587,f7591,f7595,f7600,f7605,f7611,f7647,f7651,f7655,f7659,f7663,f7667,f7783,f8267,f8271,f8394,f8402,f8406,f8410,f8736,f8740,f8744,f8748,f8752,f8756,f8760,f8764,f8768,f8772,f8776,f8780,f8784,f8788,f8792,f8796,f8800,f8822,f8826,f8830,f8834,f8841,f8845,f8849,f8853,f8857,f8864,f8872,f8876,f8880,f8884,f8888,f8892,f8896,f8900,f8904,f8908,f8912,f8928,f8932,f8938,f9063,f9300,f9392,f9396,f9408,f9619,f9623,f9698,f9702,f9706,f9710,f9714,f9718,f9722,f9726,f9730,f9734,f9738,f9742,f9746,f9750,f9754,f9758,f9762,f9766,f9770,f9774,f9778,f9782,f9786,f9790,f9794,f9798,f9802,f9806,f9810,f9814,f10073,f10442,f10586,f10590,f10598,f10602,f10606,f10610,f10614,f10618,f10622,f10629,f10633,f10637,f10641,f10645,f10650,f10655,f10659,f10663,f10667,f10673,f10679,f10684,f10689,f10693,f10698,f10702,f10706,f10710,f10714,f10718,f10722,f10726,f10730,f10734,f10738,f10742,f11141,f11217,f11510,f11514,f11870,f11874,f11878,f11882,f11886,f11890,f12241,f12710,f12739,f12743,f12747,f12751,f12755,f12759,f12763,f12767,f12771,f12776,f12780,f12784,f12788,f12792,f12796,f12800,f12804,f12808,f12812,f12816,f12820,f12824,f12828,f12832,f12836,f12840,f12845,f12849,f12853,f12857,f12861,f12865,f12869,f12873,f12877,f13265,f13468,f13789,f13796,f13856,f13860,f13864,f13868,f13872,f13876,f13880,f13884,f13888,f13892,f13896,f13900,f13905,f13909,f13913,f13917,f13921,f13925,f13929,f13933,f13937,f13941,f13945,f13949,f13953,f13959,f13963,f13967,f13971,f13975,f13979,f13983,f13987,f14035,f14087,f14123,f14208,f14215,f14385,f14389,f14396,f14400,f14404,f14408,f14415,f14419,f14423,f14427,f14431,f14435,f14439,f14443,f14447,f14451,f14455,f14459,f14463,f14467,f14471,f14475,f14479,f14483,f14488,f14492,f14542,f14548,f14610,f14656,f14718,f14722,f14726,f14730,f14734,f14738,f14742,f14746,f14750,f14754,f14758,f14762,f14766,f14770,f14774,f14798,f14802,f14806,f14811,f14815,f14819,f14913,f15269,f15386,f15390,f15394,f15398,f15402,f15406,f15410,f15414,f15418,f15422,f15426,f15430,f15434,f15438,f15442,f15446,f15450,f15454,f15458,f15462,f15466,f15470,f15474,f15478,f15482,f15486,f15490,f15494,f15499,f15503,f15507,f15511,f15515,f15519,f15523,f15539,f15543,f15547,f15551,f15555,f15559,f15563,f15567,f15571,f15575,f15619,f15623,f15627,f15631,f15635,f15639,f15643,f15647,f15651,f15655,f15707,f15711,f15715,f15719,f15723,f15727,f15731,f15735,f15739,f15743,f15787,f15791,f15795,f15799,f15803,f15807,f15811,f15815,f15819,f15823,f15888,f15892,f15896,f15900,f17382,f20223,f20227,f20231,f20235,f20240,f20245,f20250,f20255,f20259,f20332,f20336,f20342,f20348,f20352,f20356,f20360,f20364,f20368,f20372,f20376,f20380,f20452,f20456,f20460,f20464,f21128,f21132,f21161,f21212,f21479,f21483,f21487,f21491,f21495,f21500,f21504,f21508,f21512,f21516,f21520,f21524,f21528,f21532,f21536,f21540,f21544,f21548,f21552,f21556,f21560,f21590,f21594,f21598,f21602,f21606,f21610,f21614,f21618,f21622,f21626,f21664,f21668,f21672,f21676,f21680,f21684,f21688,f21692,f21696,f21700,f21734,f21738,f21742,f21746,f21750,f21754,f21758,f21762,f21766,f21909,f23111,f23133,f23137,f23141,f23145,f23149,f23153,f23157,f23161,f23165,f23169,f23191,f23195,f23199,f23203,f23207,f23211,f23215,f23219,f23223,f23227,f23285,f23289,f23293,f23297,f23301,f23305,f23309,f23313,f23317,f23321,f23379,f23383,f23387,f23391,f23395,f23399,f23403,f23407,f23411,f23415,f23465,f23469,f23473,f23477,f23481,f23485,f23489,f23493,f23497,f23501,f23505,f23509,f23513,f23518,f23522,f23526,f26207,f26593,f26597,f26669,f26673,f26680,f26684,f26691,f26696,f26700,f26704,f26708,f26712,f26716,f26720,f26724,f26728,f26732,f26736,f26740,f26744,f26748,f26757,f26837,f26841,f27027,f27042,f27232,f27236,f27240,f27244,f27248,f27252,f27256,f27260,f27265,f27269,f27273,f27277,f27281,f27285,f27289,f27293,f28390,f28401,f28405,f28409,f28413,f28417,f28421,f28425,f28429,f28433,f28437,f28441,f28445,f28449,f28453,f28457,f28461,f28465,f28614,f28883,f28965,f28969,f28973,f28977,f28981,f28985,f28989,f28993,f28997,f29001,f29005,f29126,f29485,f29489,f29493,f29497,f29501,f29505,f29509,f29513,f29517,f29521,f29525,f29529,f29533,f29537,f29541,f29545,f30592,f30636,f30640,f30644,f30648,f30652,f30841,f30845,f30849,f30853,f30857,f30886,f31008,f31012,f31016,f31020,f31024,f31029,f31033,f31037,f31041,f31046,f31050,f31054,f31058,f31062,f31066,f31747,f31852,f31856,f31861,f31865,f31908,f32003,f32011,f32369,f32373,f32378,f32382,f32386,f32390,f32394,f32398,f32402,f32406,f32410,f32414,f32418,f32452,f32456,f32460,f32464,f32468,f32472,f32476,f32480,f32484,f32488,f32529,f32533,f34112,f34117,f34122,f34126,f34183,f34190,f34234,f34238,f34242,f34351,f34359,f34363,f34367,f34371,f34375,f34379,f34383,f34396,f34400,f34404,f35033,f35037,f35041,f35045,f35049,f35053,f35057,f35061,f35065,f35069,f35073,f35077,f35081,f35085,f35089,f35093,f35097,f35101,f35105,f35891,f36488,f36493,f36497,f36501,f36505,f36509,f36513,f36518,f36618,f36622,f36626,f36672,f36678,f36682,f36769,f36773,f36777,f36781,f36785,f36789,f36793,f36797,f36801,f36805,f36809,f36951,f38399,f38403,f38788,f38792,f38796,f38800,f38804,f38808,f38812,f38816,f38820,f38824,f38828,f38832,f38836,f38841,f38847,f39205,f40131,f40136,f40142,f40146,f40150,f40865,f40869,f40874,f41008,f41142,f41201,f41206,f41211,f41215,f41216,f41225,f41230,f41237,f41244,f41464,f41469,f41474,f41696,f41701,f41707,f41714,f41719,f41723,f41730,f41735,f41742,f41747,f41754,f41761,f41786,f41790,f41794,f41798,f41802,f41807,f41812,f41817,f41821,f41825,f41829,f41833,f41837,f41841,f41845,f41849,f41853,f41857,f41866,f41882,f41899,f42281,f42285,f42289,f43763,f44001,f44005,f44079,f44083,f44087,f44091,f44095,f44099,f44103,f44116,f44120,f44124,f44128,f44132,f44136,f44167,f44171,f44175,f44179,f44230,f45654,f45658,f45662,f45666,f45670,f45674,f45678,f45682,f45686,f45690,f45694,f45808,f45812,f45816,f45820,f45964,f45968,f45972,f45976,f45980,f47240,f47244,f47271,f47275,f47279,f47284,f47288,f47292,f47296,f47358,f47362,f47389,f47393,f47397,f47401,f47405,f47409,f47445,f47492,f47496,f47500,f47504,f47508,f47512,f47544,f47596,f47600,f47604,f47610,f47614,f47618,f47622,f47626,f47630,f47634,f47638,f47642,f47646,f47651,f47655,f47659,f47663,f47667,f47671,f47675,f47679,f47683,f47687,f47691,f47696,f47704,f47708,f47712,f47716,f47720,f47724,f47728,f47732,f47736,f47741,f47745,f47749,f47753,f47757,f47761,f47765,f47769,f47805,f47809,f47844,f47848,f47852,f47857,f47958,f47962,f47966,f47970,f47974,f47986,f48576,f48635,f49724,f51878,f52499,f52503,f52508,f52512,f52516,f52520,f52705,f52709,f52713,f52896,f52900,f52904,f52909,f52913,f52917,f52921,f53108,f53112,f53116,f53297,f53301,f53338,f53342,f53455,f53459,f53564,f53637,f53710,f53714,f53798,f53802,f53806,f53810,f53814,f53818,f53822,f53826,f53830,f53834,f53838,f53842,f53846,f53850,f53854,f53858,f53862,f53903,f53968,f54012,f54056,f54062,f54077]) ).
fof(f54077,plain,
( spl0_1239
| ~ spl0_1548 ),
inference(avatar_contradiction_clause,[],[f54076]) ).
fof(f54076,plain,
( $false
| spl0_1239
| ~ spl0_1548 ),
inference(trivial_inequality_removal,[],[f54063]) ).
fof(f54063,plain,
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) != hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat))
| spl0_1239
| ~ spl0_1548 ),
inference(superposition,[],[f34358,f54061]) ).
fof(f54061,plain,
( c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat) = c_Set_Oinsert(v_i,c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_nat)
| ~ spl0_1548 ),
inference(avatar_component_clause,[],[f54059]) ).
fof(f54059,plain,
( spl0_1548
<=> c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat) = c_Set_Oinsert(v_i,c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1548])]) ).
fof(f34358,plain,
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) != hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Set_Oinsert(v_i,c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_nat))
| spl0_1239 ),
inference(avatar_component_clause,[],[f34356]) ).
fof(f34356,plain,
( spl0_1239
<=> hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Set_Oinsert(v_i,c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f54062,plain,
( spl0_1548
| ~ spl0_35
| ~ spl0_153
| ~ spl0_594 ),
inference(avatar_split_clause,[],[f8520,f7665,f2255,f1671,f54059]) ).
fof(f1671,plain,
( spl0_35
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f2255,plain,
( spl0_153
<=> hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f7665,plain,
( spl0_594
<=> ! [X29,X5,X28] :
( c_SetInterval_Oord__class_OatLeastLessThan(X29,X28,X5) = c_Set_Oinsert(X29,c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X28,X5),X5)
| ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X29,X5),X28)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f8520,plain,
( ~ class_Orderings_Olinorder(tc_nat)
| c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat) = c_Set_Oinsert(v_i,c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_nat)
| ~ spl0_153
| ~ spl0_594 ),
inference(resolution,[],[f7666,f2257]) ).
fof(f2257,plain,
( hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n))
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f2255]) ).
fof(f7666,plain,
( ! [X28,X29,X5] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X29,X5),X28))
| ~ class_Orderings_Olinorder(X5)
| c_SetInterval_Oord__class_OatLeastLessThan(X29,X28,X5) = c_Set_Oinsert(X29,c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X28,X5),X5) )
| ~ spl0_594 ),
inference(avatar_component_clause,[],[f7665]) ).
fof(f54056,plain,
( spl0_1547
| ~ spl0_150
| ~ spl0_592 ),
inference(avatar_split_clause,[],[f8427,f7657,f2242,f54054]) ).
fof(f54054,plain,
( spl0_1547
<=> ! [X0] : c_SetInterval_Oord__class_OatLeastLessThan(X0,hAPP(c_Suc,X0),tc_nat) = c_Set_Oinsert(X0,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).
fof(f2242,plain,
( spl0_150
<=> ! [X11] : hBOOL(hAPP(c_lessequals(X11,tc_nat),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f7657,plain,
( spl0_592
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X2),tc_nat) = c_Set_Oinsert(X2,c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f8427,plain,
( ! [X0] : c_SetInterval_Oord__class_OatLeastLessThan(X0,hAPP(c_Suc,X0),tc_nat) = c_Set_Oinsert(X0,c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat),tc_nat)
| ~ spl0_150
| ~ spl0_592 ),
inference(resolution,[],[f7658,f2243]) ).
fof(f2243,plain,
( ! [X11] : hBOOL(hAPP(c_lessequals(X11,tc_nat),X11))
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f2242]) ).
fof(f7658,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X2),tc_nat) = c_Set_Oinsert(X2,c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat),tc_nat) )
| ~ spl0_592 ),
inference(avatar_component_clause,[],[f7657]) ).
fof(f54012,plain,
( ~ spl0_34
| spl0_1546
| ~ spl0_153
| ~ spl0_573 ),
inference(avatar_split_clause,[],[f8066,f7524,f2255,f54010,f1666]) ).
fof(f1666,plain,
( spl0_34
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f54010,plain,
( spl0_1546
<=> ! [X121] :
( ~ hBOOL(hAPP(c_lessequals(v_n,tc_nat),X121))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),X121)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).
fof(f7524,plain,
( spl0_573
<=> ! [X11,X12,X5,X16] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X16))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f8066,plain,
( ! [X121] :
( ~ hBOOL(hAPP(c_lessequals(v_n,tc_nat),X121))
| ~ class_Orderings_Opreorder(tc_nat)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),X121)) )
| ~ spl0_153
| ~ spl0_573 ),
inference(resolution,[],[f7525,f2257]) ).
fof(f7525,plain,
( ! [X11,X16,X5,X12] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X16))
| ~ class_Orderings_Opreorder(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X16)) )
| ~ spl0_573 ),
inference(avatar_component_clause,[],[f7524]) ).
fof(f53968,plain,
( ~ spl0_34
| spl0_1545
| ~ spl0_153
| ~ spl0_572 ),
inference(avatar_split_clause,[],[f8024,f7520,f2255,f53966,f1666]) ).
fof(f53966,plain,
( spl0_1545
<=> ! [X121] :
( ~ hBOOL(hAPP(c_lessequals(X121,tc_nat),v_i))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X121,tc_nat),v_n)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).
fof(f7520,plain,
( spl0_572
<=> ! [X11,X12,X5,X16] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X16))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f8024,plain,
( ! [X121] :
( ~ hBOOL(hAPP(c_lessequals(X121,tc_nat),v_i))
| ~ class_Orderings_Opreorder(tc_nat)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X121,tc_nat),v_n)) )
| ~ spl0_153
| ~ spl0_572 ),
inference(resolution,[],[f7521,f2257]) ).
fof(f7521,plain,
( ! [X11,X16,X5,X12] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X16))
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ class_Orderings_Opreorder(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X16)) )
| ~ spl0_572 ),
inference(avatar_component_clause,[],[f7520]) ).
fof(f53903,plain,
( ~ spl0_34
| spl0_1544
| ~ spl0_153
| ~ spl0_570 ),
inference(avatar_split_clause,[],[f7937,f7512,f2255,f53901,f1666]) ).
fof(f53901,plain,
( spl0_1544
<=> ! [X121] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X121,tc_nat),v_i))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X121,tc_nat),v_n)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).
fof(f7512,plain,
( spl0_570
<=> ! [X11,X12,X5,X16] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X16))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f7937,plain,
( ! [X121] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X121,tc_nat),v_i))
| ~ class_Orderings_Opreorder(tc_nat)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X121,tc_nat),v_n)) )
| ~ spl0_153
| ~ spl0_570 ),
inference(resolution,[],[f7513,f2257]) ).
fof(f7513,plain,
( ! [X11,X16,X5,X12] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X16))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| ~ class_Orderings_Opreorder(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X16)) )
| ~ spl0_570 ),
inference(avatar_component_clause,[],[f7512]) ).
fof(f53862,plain,
( ~ spl0_37
| spl0_1543
| ~ spl0_153
| ~ spl0_569 ),
inference(avatar_split_clause,[],[f7895,f7508,f2255,f53860,f1681]) ).
fof(f1681,plain,
( spl0_37
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f53860,plain,
( spl0_1543
<=> ! [X121] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_n,tc_nat),X121))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),X121)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).
fof(f7508,plain,
( spl0_569
<=> ! [X5,X11,X12,X16] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X16,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X16,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f7895,plain,
( ! [X121] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_n,tc_nat),X121))
| ~ class_Orderings_Oorder(tc_nat)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),X121)) )
| ~ spl0_153
| ~ spl0_569 ),
inference(resolution,[],[f7509,f2257]) ).
fof(f7509,plain,
( ! [X11,X16,X5,X12] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X16,X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11))
| ~ class_Orderings_Oorder(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X16,X5),X11)) )
| ~ spl0_569 ),
inference(avatar_component_clause,[],[f7508]) ).
fof(f53858,plain,
( spl0_1542
| ~ spl0_153
| ~ spl0_564 ),
inference(avatar_split_clause,[],[f7702,f7488,f2255,f53856]) ).
fof(f53856,plain,
( spl0_1542
<=> ! [X54] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X54,tc_nat),v_i))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X54),tc_nat),v_n)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).
fof(f7488,plain,
( spl0_564
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),X4))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X4,tc_nat),X0))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X3),tc_nat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f7702,plain,
( ! [X54] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X54,tc_nat),v_i))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X54),tc_nat),v_n)) )
| ~ spl0_153
| ~ spl0_564 ),
inference(resolution,[],[f7489,f2257]) ).
fof(f7489,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X4,tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),X4))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X3),tc_nat),X0)) )
| ~ spl0_564 ),
inference(avatar_component_clause,[],[f7488]) ).
fof(f53854,plain,
( spl0_1541
| ~ spl0_251
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f6195,f5032,f2681,f53852]) ).
fof(f53852,plain,
( spl0_1541
<=> ! [X51,X54,X53,X52] :
( hBOOL(hAPP(c_lessequals(X51,X52),c_Lattices_Oupper__semilattice__class_Osup(X53,c_Lattices_Oupper__semilattice__class_Osup(X51,X54,X52),X52)))
| ~ class_Lattices_Oupper__semilattice(X52) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).
fof(f2681,plain,
( spl0_251
<=> ! [X11,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| hBOOL(hAPP(c_lessequals(X12,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f5032,plain,
( spl0_480
<=> ! [X5,X11,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X11))
| ~ hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5),X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f6195,plain,
( ! [X51,X54,X52,X53] :
( hBOOL(hAPP(c_lessequals(X51,X52),c_Lattices_Oupper__semilattice__class_Osup(X53,c_Lattices_Oupper__semilattice__class_Osup(X51,X54,X52),X52)))
| ~ class_Lattices_Oupper__semilattice(X52) )
| ~ spl0_251
| ~ spl0_480 ),
inference(duplicate_literal_removal,[],[f6177]) ).
fof(f6177,plain,
( ! [X51,X54,X52,X53] :
( hBOOL(hAPP(c_lessequals(X51,X52),c_Lattices_Oupper__semilattice__class_Osup(X53,c_Lattices_Oupper__semilattice__class_Osup(X51,X54,X52),X52)))
| ~ class_Lattices_Oupper__semilattice(X52)
| ~ class_Lattices_Oupper__semilattice(X52) )
| ~ spl0_251
| ~ spl0_480 ),
inference(resolution,[],[f5033,f2682]) ).
fof(f2682,plain,
( ! [X11,X5,X12] :
( hBOOL(hAPP(c_lessequals(X12,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5)))
| ~ class_Lattices_Oupper__semilattice(X5) )
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f2681]) ).
fof(f5033,plain,
( ! [X11,X6,X7,X5] :
( ~ hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5),X5),X11))
| hBOOL(hAPP(c_lessequals(X6,X5),X11))
| ~ class_Lattices_Oupper__semilattice(X5) )
| ~ spl0_480 ),
inference(avatar_component_clause,[],[f5032]) ).
fof(f53850,plain,
( spl0_1540
| ~ spl0_252
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f6192,f5032,f2685,f53848]) ).
fof(f53848,plain,
( spl0_1540
<=> ! [X69,X71,X70,X72] :
( hBOOL(hAPP(c_lessequals(X69,X70),c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X69,X71,X70),X72,X70)))
| ~ class_Lattices_Oupper__semilattice(X70) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).
fof(f2685,plain,
( spl0_252
<=> ! [X11,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f6192,plain,
( ! [X72,X70,X71,X69] :
( hBOOL(hAPP(c_lessequals(X69,X70),c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X69,X71,X70),X72,X70)))
| ~ class_Lattices_Oupper__semilattice(X70) )
| ~ spl0_252
| ~ spl0_480 ),
inference(duplicate_literal_removal,[],[f6181]) ).
fof(f6181,plain,
( ! [X72,X70,X71,X69] :
( hBOOL(hAPP(c_lessequals(X69,X70),c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X69,X71,X70),X72,X70)))
| ~ class_Lattices_Oupper__semilattice(X70)
| ~ class_Lattices_Oupper__semilattice(X70) )
| ~ spl0_252
| ~ spl0_480 ),
inference(resolution,[],[f5033,f2686]) ).
fof(f2686,plain,
( ! [X11,X5,X12] :
( hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5)))
| ~ class_Lattices_Oupper__semilattice(X5) )
| ~ spl0_252 ),
inference(avatar_component_clause,[],[f2685]) ).
fof(f53846,plain,
( spl0_1539
| ~ spl0_251
| ~ spl0_479 ),
inference(avatar_split_clause,[],[f6160,f5028,f2681,f53844]) ).
fof(f53844,plain,
( spl0_1539
<=> ! [X51,X54,X53,X52] :
( hBOOL(hAPP(c_lessequals(X51,X52),c_Lattices_Oupper__semilattice__class_Osup(X53,c_Lattices_Oupper__semilattice__class_Osup(X54,X51,X52),X52)))
| ~ class_Lattices_Oupper__semilattice(X52) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f5028,plain,
( spl0_479
<=> ! [X6,X5,X11,X7] :
( ~ class_Lattices_Oupper__semilattice(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),X11))
| ~ hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5),X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f6160,plain,
( ! [X51,X54,X52,X53] :
( hBOOL(hAPP(c_lessequals(X51,X52),c_Lattices_Oupper__semilattice__class_Osup(X53,c_Lattices_Oupper__semilattice__class_Osup(X54,X51,X52),X52)))
| ~ class_Lattices_Oupper__semilattice(X52) )
| ~ spl0_251
| ~ spl0_479 ),
inference(duplicate_literal_removal,[],[f6142]) ).
fof(f6142,plain,
( ! [X51,X54,X52,X53] :
( hBOOL(hAPP(c_lessequals(X51,X52),c_Lattices_Oupper__semilattice__class_Osup(X53,c_Lattices_Oupper__semilattice__class_Osup(X54,X51,X52),X52)))
| ~ class_Lattices_Oupper__semilattice(X52)
| ~ class_Lattices_Oupper__semilattice(X52) )
| ~ spl0_251
| ~ spl0_479 ),
inference(resolution,[],[f5029,f2682]) ).
fof(f5029,plain,
( ! [X11,X6,X7,X5] :
( ~ hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5),X5),X11))
| hBOOL(hAPP(c_lessequals(X7,X5),X11))
| ~ class_Lattices_Oupper__semilattice(X5) )
| ~ spl0_479 ),
inference(avatar_component_clause,[],[f5028]) ).
fof(f53842,plain,
( spl0_1538
| ~ spl0_252
| ~ spl0_479 ),
inference(avatar_split_clause,[],[f6157,f5028,f2685,f53840]) ).
fof(f53840,plain,
( spl0_1538
<=> ! [X69,X71,X70,X72] :
( hBOOL(hAPP(c_lessequals(X69,X70),c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X71,X69,X70),X72,X70)))
| ~ class_Lattices_Oupper__semilattice(X70) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f6157,plain,
( ! [X72,X70,X71,X69] :
( hBOOL(hAPP(c_lessequals(X69,X70),c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X71,X69,X70),X72,X70)))
| ~ class_Lattices_Oupper__semilattice(X70) )
| ~ spl0_252
| ~ spl0_479 ),
inference(duplicate_literal_removal,[],[f6146]) ).
fof(f6146,plain,
( ! [X72,X70,X71,X69] :
( hBOOL(hAPP(c_lessequals(X69,X70),c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X71,X69,X70),X72,X70)))
| ~ class_Lattices_Oupper__semilattice(X70)
| ~ class_Lattices_Oupper__semilattice(X70) )
| ~ spl0_252
| ~ spl0_479 ),
inference(resolution,[],[f5029,f2686]) ).
fof(f53838,plain,
( spl0_1537
| ~ spl0_188
| ~ spl0_474 ),
inference(avatar_split_clause,[],[f5983,f5008,f2408,f53836]) ).
fof(f53836,plain,
( spl0_1537
<=> ! [X29,X30] :
( ~ class_Orderings_Oorder(X29)
| c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X30,c_Orderings_Obot__class_Obot(X29),X29)
| ~ class_Orderings_Obot(X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).
fof(f2408,plain,
( spl0_188
<=> ! [X5,X11] :
( ~ class_Orderings_Obot(X5)
| hBOOL(hAPP(c_lessequals(c_Orderings_Obot__class_Obot(X5),X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f5008,plain,
( spl0_474
<=> ! [X29,X5,X0] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X29,X5),X0))
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X0,X29,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f5983,plain,
( ! [X29,X30] :
( ~ class_Orderings_Oorder(X29)
| c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X30,c_Orderings_Obot__class_Obot(X29),X29)
| ~ class_Orderings_Obot(X29) )
| ~ spl0_188
| ~ spl0_474 ),
inference(resolution,[],[f5009,f2409]) ).
fof(f2409,plain,
( ! [X11,X5] :
( hBOOL(hAPP(c_lessequals(c_Orderings_Obot__class_Obot(X5),X5),X11))
| ~ class_Orderings_Obot(X5) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f2408]) ).
fof(f5009,plain,
( ! [X29,X0,X5] :
( ~ hBOOL(hAPP(c_lessequals(X29,X5),X0))
| ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X0,X29,X5) )
| ~ spl0_474 ),
inference(avatar_component_clause,[],[f5008]) ).
fof(f53834,plain,
( spl0_1536
| ~ spl0_188
| ~ spl0_470 ),
inference(avatar_split_clause,[],[f5905,f4991,f2408,f53832]) ).
fof(f53832,plain,
( spl0_1536
<=> ! [X29,X30] :
( ~ class_Orderings_Oorder(X29)
| c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X30,c_Orderings_Obot__class_Obot(X29),X29)
| ~ class_Orderings_Obot(X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).
fof(f4991,plain,
( spl0_470
<=> ! [X6,X5,X7] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X6))
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X6,X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f5905,plain,
( ! [X29,X30] :
( ~ class_Orderings_Oorder(X29)
| c_Orderings_Obot__class_Obot(tc_fun(X29,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X30,c_Orderings_Obot__class_Obot(X29),X29)
| ~ class_Orderings_Obot(X29) )
| ~ spl0_188
| ~ spl0_470 ),
inference(resolution,[],[f4992,f2409]) ).
fof(f4992,plain,
( ! [X6,X7,X5] :
( ~ hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X6,X7,X5) )
| ~ spl0_470 ),
inference(avatar_component_clause,[],[f4991]) ).
fof(f53830,plain,
( spl0_1535
| ~ spl0_174
| ~ spl0_1506 ),
inference(avatar_split_clause,[],[f52714,f52711,f2343,f53828]) ).
fof(f53828,plain,
( spl0_1535
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,hAPP(c_Suc,X0),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).
fof(f2343,plain,
( spl0_174
<=> ! [X2] : ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f52711,plain,
( spl0_1506
<=> ! [X14,X15] :
( c_Lattices_Olower__semilattice__class_Oinf(X14,X15,tc_nat) = X14
| hBOOL(hAPP(c_lessequals(X15,tc_nat),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f52714,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,hAPP(c_Suc,X0),tc_nat) = X0
| ~ spl0_174
| ~ spl0_1506 ),
inference(resolution,[],[f52712,f2344]) ).
fof(f2344,plain,
( ! [X2] : ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),X2))
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f2343]) ).
fof(f52712,plain,
( ! [X14,X15] :
( hBOOL(hAPP(c_lessequals(X15,tc_nat),X14))
| c_Lattices_Olower__semilattice__class_Oinf(X14,X15,tc_nat) = X14 )
| ~ spl0_1506 ),
inference(avatar_component_clause,[],[f52711]) ).
fof(f53826,plain,
( spl0_1534
| ~ spl0_421
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f5818,f4972,f4555,f53824]) ).
fof(f53824,plain,
( spl0_1534
<=> ! [X0,X1] :
( ~ class_RealVector_Ometric__space(X0)
| c_Lim_OisCont(c_HOL_Oinverse__class_Oinverse(X0),X1,X0,X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_RealVector_Oreal__normed__div__algebra(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).
fof(f4555,plain,
( spl0_421
<=> ! [X6,X5] :
( ~ class_RealVector_Oreal__normed__div__algebra(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_Lim_OLIM(c_HOL_Oinverse__class_Oinverse(X5),X6,hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f4972,plain,
( spl0_466
<=> ! [X5,X10,X20,X6] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Ometric__space(X20)
| c_Lim_OisCont(X10,X6,X5,X20)
| ~ c_Lim_OLIM(X10,X6,hAPP(X10,X6),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f5818,plain,
( ! [X0,X1] :
( ~ class_RealVector_Ometric__space(X0)
| c_Lim_OisCont(c_HOL_Oinverse__class_Oinverse(X0),X1,X0,X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_RealVector_Oreal__normed__div__algebra(X0) )
| ~ spl0_421
| ~ spl0_466 ),
inference(duplicate_literal_removal,[],[f5794]) ).
fof(f5794,plain,
( ! [X0,X1] :
( ~ class_RealVector_Ometric__space(X0)
| c_Lim_OisCont(c_HOL_Oinverse__class_Oinverse(X0),X1,X0,X0)
| ~ class_RealVector_Ometric__space(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_RealVector_Oreal__normed__div__algebra(X0) )
| ~ spl0_421
| ~ spl0_466 ),
inference(resolution,[],[f4973,f4556]) ).
fof(f4556,plain,
( ! [X6,X5] :
( c_Lim_OLIM(c_HOL_Oinverse__class_Oinverse(X5),X6,hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5,X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| ~ class_RealVector_Oreal__normed__div__algebra(X5) )
| ~ spl0_421 ),
inference(avatar_component_clause,[],[f4555]) ).
fof(f4973,plain,
( ! [X10,X6,X5,X20] :
( ~ c_Lim_OLIM(X10,X6,hAPP(X10,X6),X5,X20)
| ~ class_RealVector_Ometric__space(X20)
| c_Lim_OisCont(X10,X6,X5,X20)
| ~ class_RealVector_Ometric__space(X5) )
| ~ spl0_466 ),
inference(avatar_component_clause,[],[f4972]) ).
fof(f53822,plain,
( spl0_1533
| ~ spl0_220
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f5451,f4881,f2557,f53820]) ).
fof(f53820,plain,
( spl0_1533
<=> ! [X18,X20,X17,X19] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X17,X18,X19),X20,X19),X19),X18))
| ~ class_Lattices_Olower__semilattice(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).
fof(f2557,plain,
( spl0_220
<=> ! [X12,X5,X11] :
( ~ class_Lattices_Olower__semilattice(X5)
| hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f4881,plain,
( spl0_446
<=> ! [X5,X11,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f5451,plain,
( ! [X18,X19,X17,X20] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X17,X18,X19),X20,X19),X19),X18))
| ~ class_Lattices_Olower__semilattice(X19) )
| ~ spl0_220
| ~ spl0_446 ),
inference(duplicate_literal_removal,[],[f5430]) ).
fof(f5430,plain,
( ! [X18,X19,X17,X20] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X17,X18,X19),X20,X19),X19),X18))
| ~ class_Lattices_Olower__semilattice(X19)
| ~ class_Lattices_Olower__semilattice(X19) )
| ~ spl0_220
| ~ spl0_446 ),
inference(resolution,[],[f4882,f2558]) ).
fof(f2558,plain,
( ! [X11,X5,X12] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5),X11))
| ~ class_Lattices_Olower__semilattice(X5) )
| ~ spl0_220 ),
inference(avatar_component_clause,[],[f2557]) ).
fof(f4882,plain,
( ! [X11,X6,X7,X5] :
( ~ hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5)))
| hBOOL(hAPP(c_lessequals(X11,X5),X7))
| ~ class_Lattices_Olower__semilattice(X5) )
| ~ spl0_446 ),
inference(avatar_component_clause,[],[f4881]) ).
fof(f53818,plain,
( spl0_1532
| ~ spl0_219
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f5450,f4881,f2553,f53816]) ).
fof(f53816,plain,
( spl0_1532
<=> ! [X38,X40,X39,X37] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X37,c_Lattices_Olower__semilattice__class_Oinf(X38,X39,X40),X40),X40),X39))
| ~ class_Lattices_Olower__semilattice(X40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).
fof(f2553,plain,
( spl0_219
<=> ! [X11,X5,X12] :
( ~ class_Lattices_Olower__semilattice(X5)
| hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f5450,plain,
( ! [X40,X38,X39,X37] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X37,c_Lattices_Olower__semilattice__class_Oinf(X38,X39,X40),X40),X40),X39))
| ~ class_Lattices_Olower__semilattice(X40) )
| ~ spl0_219
| ~ spl0_446 ),
inference(duplicate_literal_removal,[],[f5436]) ).
fof(f5436,plain,
( ! [X40,X38,X39,X37] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X37,c_Lattices_Olower__semilattice__class_Oinf(X38,X39,X40),X40),X40),X39))
| ~ class_Lattices_Olower__semilattice(X40)
| ~ class_Lattices_Olower__semilattice(X40) )
| ~ spl0_219
| ~ spl0_446 ),
inference(resolution,[],[f4882,f2554]) ).
fof(f2554,plain,
( ! [X11,X5,X12] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5),X12))
| ~ class_Lattices_Olower__semilattice(X5) )
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f2553]) ).
fof(f53814,plain,
( spl0_1531
| ~ spl0_220
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f5422,f4877,f2557,f53812]) ).
fof(f53812,plain,
( spl0_1531
<=> ! [X18,X20,X17,X19] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X17,X18,X19),X20,X19),X19),X17))
| ~ class_Lattices_Olower__semilattice(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).
fof(f4877,plain,
( spl0_445
<=> ! [X5,X11,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),X6))
| ~ hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f5422,plain,
( ! [X18,X19,X17,X20] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X17,X18,X19),X20,X19),X19),X17))
| ~ class_Lattices_Olower__semilattice(X19) )
| ~ spl0_220
| ~ spl0_445 ),
inference(duplicate_literal_removal,[],[f5401]) ).
fof(f5401,plain,
( ! [X18,X19,X17,X20] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X17,X18,X19),X20,X19),X19),X17))
| ~ class_Lattices_Olower__semilattice(X19)
| ~ class_Lattices_Olower__semilattice(X19) )
| ~ spl0_220
| ~ spl0_445 ),
inference(resolution,[],[f4878,f2558]) ).
fof(f4878,plain,
( ! [X11,X6,X7,X5] :
( ~ hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5)))
| hBOOL(hAPP(c_lessequals(X11,X5),X6))
| ~ class_Lattices_Olower__semilattice(X5) )
| ~ spl0_445 ),
inference(avatar_component_clause,[],[f4877]) ).
fof(f53810,plain,
( spl0_1530
| ~ spl0_219
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f5421,f4877,f2553,f53808]) ).
fof(f53808,plain,
( spl0_1530
<=> ! [X38,X40,X39,X37] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X37,c_Lattices_Olower__semilattice__class_Oinf(X38,X39,X40),X40),X40),X38))
| ~ class_Lattices_Olower__semilattice(X40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).
fof(f5421,plain,
( ! [X40,X38,X39,X37] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X37,c_Lattices_Olower__semilattice__class_Oinf(X38,X39,X40),X40),X40),X38))
| ~ class_Lattices_Olower__semilattice(X40) )
| ~ spl0_219
| ~ spl0_445 ),
inference(duplicate_literal_removal,[],[f5407]) ).
fof(f5407,plain,
( ! [X40,X38,X39,X37] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X37,c_Lattices_Olower__semilattice__class_Oinf(X38,X39,X40),X40),X40),X38))
| ~ class_Lattices_Olower__semilattice(X40)
| ~ class_Lattices_Olower__semilattice(X40) )
| ~ spl0_219
| ~ spl0_445 ),
inference(resolution,[],[f4878,f2554]) ).
fof(f53806,plain,
( spl0_1529
| ~ spl0_256
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f4783,f4591,f2701,f53804]) ).
fof(f53804,plain,
( spl0_1529
<=> ! [X130,X132,X128,X131,X129] : hBOOL(hAPP(c_lessequals(hAPP(c_COMBS(c_HOL_Ominus__class_Ominus(tc_nat),X129,X130,X131,X132),X128),tc_nat),X128)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).
fof(f2701,plain,
( spl0_256
<=> ! [X2,X1] : hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),tc_nat),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f4591,plain,
( spl0_429
<=> ! [X24,X54,X20,X31,X55,X5] : hAPP(c_COMBS(X24,X54,X20,X31,X5),X55) = hAPP(hAPP(X24,X55),hAPP(X54,X55)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f4783,plain,
( ! [X132,X130,X131,X128,X129] : hBOOL(hAPP(c_lessequals(hAPP(c_COMBS(c_HOL_Ominus__class_Ominus(tc_nat),X129,X130,X131,X132),X128),tc_nat),X128))
| ~ spl0_256
| ~ spl0_429 ),
inference(superposition,[],[f2702,f4592]) ).
fof(f4592,plain,
( ! [X31,X54,X55,X24,X5,X20] : hAPP(c_COMBS(X24,X54,X20,X31,X5),X55) = hAPP(hAPP(X24,X55),hAPP(X54,X55))
| ~ spl0_429 ),
inference(avatar_component_clause,[],[f4591]) ).
fof(f2702,plain,
( ! [X2,X1] : hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),tc_nat),X1))
| ~ spl0_256 ),
inference(avatar_component_clause,[],[f2701]) ).
fof(f53802,plain,
( spl0_1528
| ~ spl0_234
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f4768,f4591,f2613,f53800]) ).
fof(f53800,plain,
( spl0_1528
<=> ! [X41,X42,X40,X43,X39] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),X40,X41,X42,X43),X39),tc_nat),X39)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).
fof(f2613,plain,
( spl0_234
<=> ! [X4,X3] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f4768,plain,
( ! [X40,X41,X39,X42,X43] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),X40,X41,X42,X43),X39),tc_nat),X39))
| ~ spl0_234
| ~ spl0_429 ),
inference(superposition,[],[f2614,f4592]) ).
fof(f2614,plain,
( ! [X3,X4] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat),X3))
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2613]) ).
fof(f53798,plain,
( spl0_1527
| ~ spl0_230
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f4765,f4591,f2597,f53796]) ).
fof(f53796,plain,
( spl0_1527
<=> ! [X24,X27,X25,X28,X26] : hBOOL(hAPP(c_lessequals(X24,tc_nat),hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),X25,X26,X27,X28),X24))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).
fof(f2597,plain,
( spl0_230
<=> ! [X11,X1] : hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X11))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f4765,plain,
( ! [X28,X26,X27,X24,X25] : hBOOL(hAPP(c_lessequals(X24,tc_nat),hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),X25,X26,X27,X28),X24)))
| ~ spl0_230
| ~ spl0_429 ),
inference(superposition,[],[f2598,f4592]) ).
fof(f2598,plain,
( ! [X11,X1] : hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X11)))
| ~ spl0_230 ),
inference(avatar_component_clause,[],[f2597]) ).
fof(f53714,plain,
( ~ spl0_39
| spl0_1526
| ~ spl0_25
| ~ spl0_304
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f4729,f4587,f3114,f1621,f53712,f1691]) ).
fof(f1691,plain,
( spl0_39
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f53712,plain,
( spl0_1526
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),hAPP(c_Suc,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).
fof(f1621,plain,
( spl0_25
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f3114,plain,
( spl0_304
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f4587,plain,
( spl0_428
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),hAPP(c_Suc,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f4729,plain,
( ! [X0] :
( c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),hAPP(c_Suc,X0))
| ~ class_Power_Opower(tc_nat) )
| ~ spl0_25
| ~ spl0_304
| ~ spl0_428 ),
inference(forward_demodulation,[],[f4726,f3116]) ).
fof(f3116,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_304 ),
inference(avatar_component_clause,[],[f3114]) ).
fof(f4726,plain,
( ! [X0] :
( ~ class_Power_Opower(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Suc,X0)) )
| ~ spl0_25
| ~ spl0_428 ),
inference(resolution,[],[f4588,f1623]) ).
fof(f1623,plain,
( class_Ring__and__Field_Osemiring__0(tc_nat)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f1621]) ).
fof(f4588,plain,
( ! [X2,X5] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),hAPP(c_Suc,X2)) )
| ~ spl0_428 ),
inference(avatar_component_clause,[],[f4587]) ).
fof(f53710,plain,
( spl0_1525
| ~ spl0_174
| ~ spl0_1503 ),
inference(avatar_split_clause,[],[f52521,f52518,f2343,f53708]) ).
fof(f53708,plain,
( spl0_1525
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Suc,X0),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).
fof(f52518,plain,
( spl0_1503
<=> ! [X14,X15] :
( c_Lattices_Olower__semilattice__class_Oinf(X14,X15,tc_nat) = X15
| hBOOL(hAPP(c_lessequals(X14,tc_nat),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f52521,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Suc,X0),X0,tc_nat) = X0
| ~ spl0_174
| ~ spl0_1503 ),
inference(resolution,[],[f52519,f2344]) ).
fof(f52519,plain,
( ! [X14,X15] :
( hBOOL(hAPP(c_lessequals(X14,tc_nat),X15))
| c_Lattices_Olower__semilattice__class_Oinf(X14,X15,tc_nat) = X15 )
| ~ spl0_1503 ),
inference(avatar_component_clause,[],[f52518]) ).
fof(f53637,plain,
( spl0_1524
| ~ spl0_144
| ~ spl0_127
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f4728,f4587,f2131,f2216,f53635]) ).
fof(f53635,plain,
( spl0_1524
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(c_Suc,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).
fof(f2216,plain,
( spl0_144
<=> class_Power_Opower(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f2131,plain,
( spl0_127
<=> class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f4728,plain,
( ! [X2] :
( ~ class_Power_Opower(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(c_Suc,X2)) )
| ~ spl0_127
| ~ spl0_428 ),
inference(resolution,[],[f4588,f2133]) ).
fof(f2133,plain,
( class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex)
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f2131]) ).
fof(f53564,plain,
( spl0_1523
| ~ spl0_104
| ~ spl0_83
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f4727,f4587,f1911,f2016,f53562]) ).
fof(f53562,plain,
( spl0_1523
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Suc,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).
fof(f2016,plain,
( spl0_104
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1911,plain,
( spl0_83
<=> class_Ring__and__Field_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f4727,plain,
( ! [X1] :
( ~ class_Power_Opower(tc_Int_Oint)
| c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Suc,X1)) )
| ~ spl0_83
| ~ spl0_428 ),
inference(resolution,[],[f4588,f1913]) ).
fof(f1913,plain,
( class_Ring__and__Field_Osemiring__0(tc_Int_Oint)
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f1911]) ).
fof(f53459,plain,
( ~ spl0_36
| spl0_1522
| ~ spl0_253
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f4494,f4423,f2689,f53457,f1676]) ).
fof(f1676,plain,
( spl0_36
<=> class_Lattices_Olattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f53457,plain,
( spl0_1522
<=> ! [X38,X37] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X37),c_Lattices_Oupper__semilattice__class_Osup(X38,X37,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).
fof(f2689,plain,
( spl0_253
<=> ! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| hBOOL(hAPP(c_lessequals(X12,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f4423,plain,
( spl0_411
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f4494,plain,
( ! [X38,X37] :
( c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X37),c_Lattices_Oupper__semilattice__class_Osup(X38,X37,tc_nat))
| ~ class_Lattices_Olattice(tc_nat) )
| ~ spl0_253
| ~ spl0_411 ),
inference(resolution,[],[f4424,f2690]) ).
fof(f2690,plain,
( ! [X11,X5,X12] :
( hBOOL(hAPP(c_lessequals(X12,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5)))
| ~ class_Lattices_Olattice(X5) )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f2689]) ).
fof(f4424,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) = c_Orderings_Obot__class_Obot(tc_nat) )
| ~ spl0_411 ),
inference(avatar_component_clause,[],[f4423]) ).
fof(f53455,plain,
( spl0_1521
| ~ spl0_228
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f4487,f4423,f2589,f53453]) ).
fof(f53453,plain,
( spl0_1521
<=> ! [X29] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X29),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X29),X29)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).
fof(f2589,plain,
( spl0_228
<=> ! [X1] : hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f4487,plain,
( ! [X29] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X29),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X29),X29))
| ~ spl0_228
| ~ spl0_411 ),
inference(resolution,[],[f4424,f2590]) ).
fof(f2590,plain,
( ! [X1] : hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X1)))
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f2589]) ).
fof(f53342,plain,
( ~ spl0_36
| spl0_1520
| ~ spl0_222
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f4475,f4423,f2565,f53340,f1676]) ).
fof(f53340,plain,
( spl0_1520
<=> ! [X6,X7] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_nat)),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).
fof(f2565,plain,
( spl0_222
<=> ! [X12,X5,X11] :
( ~ class_Lattices_Olattice(X5)
| hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f4475,plain,
( ! [X6,X7] :
( c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_nat)),X6)
| ~ class_Lattices_Olattice(tc_nat) )
| ~ spl0_222
| ~ spl0_411 ),
inference(resolution,[],[f4424,f2566]) ).
fof(f2566,plain,
( ! [X11,X5,X12] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5),X11))
| ~ class_Lattices_Olattice(X5) )
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f2565]) ).
fof(f53338,plain,
( spl0_1519
| ~ spl0_256
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f4472,f4423,f2701,f53336]) ).
fof(f53336,plain,
( spl0_1519
<=> ! [X2,X3] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X3)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).
fof(f4472,plain,
( ! [X2,X3] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X3)),X2)
| ~ spl0_256
| ~ spl0_411 ),
inference(resolution,[],[f4424,f2702]) ).
fof(f53301,plain,
( spl0_1518
| ~ spl0_307
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f4175,f4039,f3127,f53299]) ).
fof(f53299,plain,
( spl0_1518
<=> ! [X2,X1] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).
fof(f3127,plain,
( spl0_307
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f4039,plain,
( spl0_384
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f4175,plain,
( ! [X2,X1] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1))
| ~ spl0_307
| ~ spl0_384 ),
inference(superposition,[],[f4040,f3128]) ).
fof(f3128,plain,
( ! [X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)
| ~ spl0_307 ),
inference(avatar_component_clause,[],[f3127]) ).
fof(f4040,plain,
( ! [X2,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_384 ),
inference(avatar_component_clause,[],[f4039]) ).
fof(f53297,plain,
( spl0_1517
| ~ spl0_251
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f4131,f3593,f2681,f53295]) ).
fof(f53295,plain,
( spl0_1517
<=> ! [X54,X52,X53] :
( ~ class_Lattices_Oupper__semilattice(X52)
| c_Lattices_Oupper__semilattice__class_Osup(X54,X53,X52) = c_Lattices_Oupper__semilattice__class_Osup(X53,c_Lattices_Oupper__semilattice__class_Osup(X54,X53,X52),X52) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).
fof(f3593,plain,
( spl0_373
<=> ! [X11,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f4131,plain,
( ! [X54,X52,X53] :
( ~ class_Lattices_Oupper__semilattice(X52)
| c_Lattices_Oupper__semilattice__class_Osup(X54,X53,X52) = c_Lattices_Oupper__semilattice__class_Osup(X53,c_Lattices_Oupper__semilattice__class_Osup(X54,X53,X52),X52) )
| ~ spl0_251
| ~ spl0_373 ),
inference(duplicate_literal_removal,[],[f4125]) ).
fof(f4125,plain,
( ! [X54,X52,X53] :
( ~ class_Lattices_Oupper__semilattice(X52)
| c_Lattices_Oupper__semilattice__class_Osup(X54,X53,X52) = c_Lattices_Oupper__semilattice__class_Osup(X53,c_Lattices_Oupper__semilattice__class_Osup(X54,X53,X52),X52)
| ~ class_Lattices_Oupper__semilattice(X52) )
| ~ spl0_251
| ~ spl0_373 ),
inference(resolution,[],[f3594,f2682]) ).
fof(f3594,plain,
( ! [X11,X5,X12] :
( ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = X12 )
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f3593]) ).
fof(f53116,plain,
( spl0_1516
| ~ spl0_22
| ~ spl0_281
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f4107,f3593,f2958,f1606,f53114]) ).
fof(f53114,plain,
( spl0_1516
<=> ! [X14,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_nat) = X15
| hBOOL(hAPP(c_lessequals(X15,tc_nat),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).
fof(f1606,plain,
( spl0_22
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f2958,plain,
( spl0_281
<=> ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(X2,tc_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f4107,plain,
( ! [X14,X15] :
( ~ class_Lattices_Oupper__semilattice(tc_nat)
| c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_nat) = X15
| hBOOL(hAPP(c_lessequals(X15,tc_nat),X14)) )
| ~ spl0_281
| ~ spl0_373 ),
inference(resolution,[],[f3594,f2959]) ).
fof(f2959,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(X2,tc_nat),X1)) )
| ~ spl0_281 ),
inference(avatar_component_clause,[],[f2958]) ).
fof(f53112,plain,
( spl0_1515
| ~ spl0_251
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4078,f3585,f2681,f53110]) ).
fof(f53110,plain,
( spl0_1515
<=> ! [X54,X52,X53] :
( ~ class_Lattices_Oupper__semilattice(X52)
| c_Lattices_Oupper__semilattice__class_Osup(X53,X54,X52) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X53,X54,X52),X54,X52) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).
fof(f3585,plain,
( spl0_371
<=> ! [X12,X5,X11] :
( ~ class_Lattices_Oupper__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X11))
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f4078,plain,
( ! [X54,X52,X53] :
( ~ class_Lattices_Oupper__semilattice(X52)
| c_Lattices_Oupper__semilattice__class_Osup(X53,X54,X52) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X53,X54,X52),X54,X52) )
| ~ spl0_251
| ~ spl0_371 ),
inference(duplicate_literal_removal,[],[f4072]) ).
fof(f4072,plain,
( ! [X54,X52,X53] :
( ~ class_Lattices_Oupper__semilattice(X52)
| c_Lattices_Oupper__semilattice__class_Osup(X53,X54,X52) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X53,X54,X52),X54,X52)
| ~ class_Lattices_Oupper__semilattice(X52) )
| ~ spl0_251
| ~ spl0_371 ),
inference(resolution,[],[f3586,f2682]) ).
fof(f3586,plain,
( ! [X11,X5,X12] :
( ~ hBOOL(hAPP(c_lessequals(X12,X5),X11))
| ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = X11 )
| ~ spl0_371 ),
inference(avatar_component_clause,[],[f3585]) ).
fof(f53108,plain,
( spl0_1514
| ~ spl0_252
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4077,f3585,f2685,f53106]) ).
fof(f53106,plain,
( spl0_1514
<=> ! [X60,X59,X58] :
( ~ class_Lattices_Oupper__semilattice(X58)
| c_Lattices_Oupper__semilattice__class_Osup(X59,X60,X58) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X59,X60,X58),X59,X58) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).
fof(f4077,plain,
( ! [X58,X59,X60] :
( ~ class_Lattices_Oupper__semilattice(X58)
| c_Lattices_Oupper__semilattice__class_Osup(X59,X60,X58) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X59,X60,X58),X59,X58) )
| ~ spl0_252
| ~ spl0_371 ),
inference(duplicate_literal_removal,[],[f4074]) ).
fof(f4074,plain,
( ! [X58,X59,X60] :
( ~ class_Lattices_Oupper__semilattice(X58)
| c_Lattices_Oupper__semilattice__class_Osup(X59,X60,X58) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X59,X60,X58),X59,X58)
| ~ class_Lattices_Oupper__semilattice(X58) )
| ~ spl0_252
| ~ spl0_371 ),
inference(resolution,[],[f3586,f2686]) ).
fof(f52921,plain,
( spl0_1513
| ~ spl0_22
| ~ spl0_281
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4054,f3585,f2958,f1606,f52919]) ).
fof(f52919,plain,
( spl0_1513
<=> ! [X14,X15] :
( c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_nat) = X14
| hBOOL(hAPP(c_lessequals(X14,tc_nat),X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).
fof(f4054,plain,
( ! [X14,X15] :
( ~ class_Lattices_Oupper__semilattice(tc_nat)
| c_Lattices_Oupper__semilattice__class_Osup(X14,X15,tc_nat) = X14
| hBOOL(hAPP(c_lessequals(X14,tc_nat),X15)) )
| ~ spl0_281
| ~ spl0_371 ),
inference(resolution,[],[f3586,f2959]) ).
fof(f52917,plain,
( spl0_1512
| ~ spl0_343
| ~ spl0_363 ),
inference(avatar_split_clause,[],[f3990,f3551,f3464,f52915]) ).
fof(f52915,plain,
( spl0_1512
<=> ! [X20,X21,X19] :
( ~ class_Orderings_Olinorder(X19)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X20,X19),X21))
| hBOOL(hAPP(c_lessequals(X20,X19),X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).
fof(f3464,plain,
( spl0_343
<=> ! [X11,X5,X12] :
( ~ class_Orderings_Olinorder(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f3551,plain,
( spl0_363
<=> ! [X12,X5,X11] :
( ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f3990,plain,
( ! [X21,X19,X20] :
( ~ class_Orderings_Olinorder(X19)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X20,X19),X21))
| hBOOL(hAPP(c_lessequals(X20,X19),X21)) )
| ~ spl0_343
| ~ spl0_363 ),
inference(duplicate_literal_removal,[],[f3989]) ).
fof(f3989,plain,
( ! [X21,X19,X20] :
( ~ class_Orderings_Olinorder(X19)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X20,X19),X21))
| hBOOL(hAPP(c_lessequals(X20,X19),X21))
| ~ class_Orderings_Olinorder(X19) )
| ~ spl0_343
| ~ spl0_363 ),
inference(resolution,[],[f3552,f3465]) ).
fof(f3465,plain,
( ! [X11,X5,X12] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11))
| hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ class_Orderings_Olinorder(X5) )
| ~ spl0_343 ),
inference(avatar_component_clause,[],[f3464]) ).
fof(f3552,plain,
( ! [X11,X5,X12] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11))
| ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12)) )
| ~ spl0_363 ),
inference(avatar_component_clause,[],[f3551]) ).
fof(f52913,plain,
( spl0_1511
| ~ spl0_281
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f3910,f3514,f2958,f52911]) ).
fof(f52911,plain,
( spl0_1511
<=> ! [X8,X7] :
( hBOOL(hAPP(c_lessequals(X7,tc_nat),X8))
| hBOOL(hAPP(c_lessequals(X8,tc_nat),hAPP(c_Suc,X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f3514,plain,
( spl0_354
<=> ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X1),tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f3910,plain,
( ! [X8,X7] :
( hBOOL(hAPP(c_lessequals(X7,tc_nat),X8))
| hBOOL(hAPP(c_lessequals(X8,tc_nat),hAPP(c_Suc,X7))) )
| ~ spl0_281
| ~ spl0_354 ),
inference(resolution,[],[f3515,f2959]) ).
fof(f3515,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X1),tc_nat),X2))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2)) )
| ~ spl0_354 ),
inference(avatar_component_clause,[],[f3514]) ).
fof(f52909,plain,
( spl0_1510
| spl0_501
| ~ spl0_1503 ),
inference(avatar_split_clause,[],[f52652,f52518,f6034,f52906]) ).
fof(f52906,plain,
( spl0_1510
<=> v_i = c_Lattices_Olower__semilattice__class_Oinf(v_n,v_i,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f6034,plain,
( spl0_501
<=> hBOOL(hAPP(c_lessequals(v_n,tc_nat),v_i)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f52652,plain,
( v_i = c_Lattices_Olower__semilattice__class_Oinf(v_n,v_i,tc_nat)
| spl0_501
| ~ spl0_1503 ),
inference(resolution,[],[f52519,f6036]) ).
fof(f6036,plain,
( ~ hBOOL(hAPP(c_lessequals(v_n,tc_nat),v_i))
| spl0_501 ),
inference(avatar_component_clause,[],[f6034]) ).
fof(f52904,plain,
( spl0_1509
| ~ spl0_220
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f3838,f3484,f2557,f52902]) ).
fof(f52902,plain,
( spl0_1509
<=> ! [X13,X12,X11] :
( ~ class_Lattices_Olower__semilattice(X11)
| c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X11) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X11),X12,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f3484,plain,
( spl0_348
<=> ! [X11,X5,X12] :
( ~ class_Lattices_Olower__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f3838,plain,
( ! [X11,X12,X13] :
( ~ class_Lattices_Olower__semilattice(X11)
| c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X11) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X11),X12,X11) )
| ~ spl0_220
| ~ spl0_348 ),
inference(duplicate_literal_removal,[],[f3818]) ).
fof(f3818,plain,
( ! [X11,X12,X13] :
( ~ class_Lattices_Olower__semilattice(X11)
| c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X11) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X11),X12,X11)
| ~ class_Lattices_Olower__semilattice(X11) )
| ~ spl0_220
| ~ spl0_348 ),
inference(resolution,[],[f3485,f2558]) ).
fof(f3485,plain,
( ! [X11,X5,X12] :
( ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = X11 )
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f3484]) ).
fof(f52900,plain,
( spl0_1508
| ~ spl0_219
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f3837,f3484,f2553,f52898]) ).
fof(f52898,plain,
( spl0_1508
<=> ! [X24,X25,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X23) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X23),X25,X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f3837,plain,
( ! [X24,X25,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X23) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X23),X25,X23) )
| ~ spl0_219
| ~ spl0_348 ),
inference(duplicate_literal_removal,[],[f3823]) ).
fof(f3823,plain,
( ! [X24,X25,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X23) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X24,X25,X23),X25,X23)
| ~ class_Lattices_Olower__semilattice(X23) )
| ~ spl0_219
| ~ spl0_348 ),
inference(resolution,[],[f3485,f2554]) ).
fof(f52896,plain,
( spl0_1507
| ~ spl0_229
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f3835,f3484,f2593,f52894]) ).
fof(f52894,plain,
( spl0_1507
<=> ! [X50,X49] :
( ~ class_Lattices_Olower__semilattice(X49)
| c_HOL_Ozero__class_Ozero(X49) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(X49),c_Nat_Osemiring__1__class_Oof__nat(X50,X49),X49)
| ~ class_Ring__and__Field_Oordered__semidom(X49) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f2593,plain,
( spl0_229
<=> ! [X5,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X1,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f3835,plain,
( ! [X50,X49] :
( ~ class_Lattices_Olower__semilattice(X49)
| c_HOL_Ozero__class_Ozero(X49) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(X49),c_Nat_Osemiring__1__class_Oof__nat(X50,X49),X49)
| ~ class_Ring__and__Field_Oordered__semidom(X49) )
| ~ spl0_229
| ~ spl0_348 ),
inference(resolution,[],[f3485,f2594]) ).
fof(f2594,plain,
( ! [X1,X5] :
( hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X1,X5)))
| ~ class_Ring__and__Field_Oordered__semidom(X5) )
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f2593]) ).
fof(f52713,plain,
( spl0_1506
| ~ spl0_23
| ~ spl0_281
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f3819,f3484,f2958,f1611,f52711]) ).
fof(f1611,plain,
( spl0_23
<=> class_Lattices_Olower__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f3819,plain,
( ! [X14,X15] :
( ~ class_Lattices_Olower__semilattice(tc_nat)
| c_Lattices_Olower__semilattice__class_Oinf(X14,X15,tc_nat) = X14
| hBOOL(hAPP(c_lessequals(X15,tc_nat),X14)) )
| ~ spl0_281
| ~ spl0_348 ),
inference(resolution,[],[f3485,f2959]) ).
fof(f52709,plain,
( spl0_1505
| ~ spl0_219
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f3796,f3476,f2553,f52707]) ).
fof(f52707,plain,
( spl0_1505
<=> ! [X24,X25,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_Lattices_Olower__semilattice__class_Oinf(X25,X24,X23) = c_Lattices_Olower__semilattice__class_Oinf(X24,c_Lattices_Olower__semilattice__class_Oinf(X25,X24,X23),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f3476,plain,
( spl0_346
<=> ! [X12,X5,X11] :
( ~ class_Lattices_Olower__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X11))
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f3796,plain,
( ! [X24,X25,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_Lattices_Olower__semilattice__class_Oinf(X25,X24,X23) = c_Lattices_Olower__semilattice__class_Oinf(X24,c_Lattices_Olower__semilattice__class_Oinf(X25,X24,X23),X23) )
| ~ spl0_219
| ~ spl0_346 ),
inference(duplicate_literal_removal,[],[f3782]) ).
fof(f3782,plain,
( ! [X24,X25,X23] :
( ~ class_Lattices_Olower__semilattice(X23)
| c_Lattices_Olower__semilattice__class_Oinf(X25,X24,X23) = c_Lattices_Olower__semilattice__class_Oinf(X24,c_Lattices_Olower__semilattice__class_Oinf(X25,X24,X23),X23)
| ~ class_Lattices_Olower__semilattice(X23) )
| ~ spl0_219
| ~ spl0_346 ),
inference(resolution,[],[f3477,f2554]) ).
fof(f3477,plain,
( ! [X11,X5,X12] :
( ~ hBOOL(hAPP(c_lessequals(X12,X5),X11))
| ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = X12 )
| ~ spl0_346 ),
inference(avatar_component_clause,[],[f3476]) ).
fof(f52705,plain,
( spl0_1504
| ~ spl0_229
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f3794,f3476,f2593,f52703]) ).
fof(f52703,plain,
( spl0_1504
<=> ! [X50,X49] :
( ~ class_Lattices_Olower__semilattice(X49)
| c_HOL_Ozero__class_Ozero(X49) = c_Lattices_Olower__semilattice__class_Oinf(c_Nat_Osemiring__1__class_Oof__nat(X50,X49),c_HOL_Ozero__class_Ozero(X49),X49)
| ~ class_Ring__and__Field_Oordered__semidom(X49) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f3794,plain,
( ! [X50,X49] :
( ~ class_Lattices_Olower__semilattice(X49)
| c_HOL_Ozero__class_Ozero(X49) = c_Lattices_Olower__semilattice__class_Oinf(c_Nat_Osemiring__1__class_Oof__nat(X50,X49),c_HOL_Ozero__class_Ozero(X49),X49)
| ~ class_Ring__and__Field_Oordered__semidom(X49) )
| ~ spl0_229
| ~ spl0_346 ),
inference(resolution,[],[f3477,f2594]) ).
fof(f52520,plain,
( spl0_1503
| ~ spl0_23
| ~ spl0_281
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f3778,f3476,f2958,f1611,f52518]) ).
fof(f3778,plain,
( ! [X14,X15] :
( ~ class_Lattices_Olower__semilattice(tc_nat)
| c_Lattices_Olower__semilattice__class_Oinf(X14,X15,tc_nat) = X15
| hBOOL(hAPP(c_lessequals(X14,tc_nat),X15)) )
| ~ spl0_281
| ~ spl0_346 ),
inference(resolution,[],[f3477,f2959]) ).
fof(f52516,plain,
( spl0_1502
| ~ spl0_266
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f3727,f3460,f2741,f52514]) ).
fof(f52514,plain,
( spl0_1502
<=> ! [X2,X1] :
( hBOOL(hAPP(c_SetInterval_Oord__class_OatMost(hAPP(c_Suc,X1),tc_nat),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord__class_OatMost(X1,tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f2741,plain,
( spl0_266
<=> ! [X25,X5,X11,X12] :
( ~ hBOOL(hAPP(X25,X11))
| hBOOL(hAPP(c_Set_Oinsert(X12,X25,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f3460,plain,
( spl0_342
<=> ! [X0] : c_SetInterval_Oord__class_OatMost(hAPP(c_Suc,X0),tc_nat) = c_Set_Oinsert(hAPP(c_Suc,X0),c_SetInterval_Oord__class_OatMost(X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f3727,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_SetInterval_Oord__class_OatMost(hAPP(c_Suc,X1),tc_nat),X2))
| ~ hBOOL(hAPP(c_SetInterval_Oord__class_OatMost(X1,tc_nat),X2)) )
| ~ spl0_266
| ~ spl0_342 ),
inference(superposition,[],[f2742,f3461]) ).
fof(f3461,plain,
( ! [X0] : c_SetInterval_Oord__class_OatMost(hAPP(c_Suc,X0),tc_nat) = c_Set_Oinsert(hAPP(c_Suc,X0),c_SetInterval_Oord__class_OatMost(X0,tc_nat),tc_nat)
| ~ spl0_342 ),
inference(avatar_component_clause,[],[f3460]) ).
fof(f2742,plain,
( ! [X11,X5,X12,X25] :
( hBOOL(hAPP(c_Set_Oinsert(X12,X25,X5),X11))
| ~ hBOOL(hAPP(X25,X11)) )
| ~ spl0_266 ),
inference(avatar_component_clause,[],[f2741]) ).
fof(f52512,plain,
( spl0_1501
| ~ spl0_48
| ~ spl0_1388 ),
inference(avatar_split_clause,[],[f44283,f44165,f1736,f52510]) ).
fof(f52510,plain,
( spl0_1501
<=> ! [X4] : c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X4,X4,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f1736,plain,
( spl0_48
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f44165,plain,
( spl0_1388
<=> ! [X6,X5] :
( ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X6,X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f44283,plain,
( ! [X4] : c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X4,X4,tc_bool)
| ~ spl0_48
| ~ spl0_1388 ),
inference(resolution,[],[f44166,f1738]) ).
fof(f1738,plain,
( class_Orderings_Oorder(tc_bool)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1736]) ).
fof(f44166,plain,
( ! [X6,X5] :
( ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X6,X6,X5) )
| ~ spl0_1388 ),
inference(avatar_component_clause,[],[f44165]) ).
fof(f52508,plain,
( spl0_1500
| ~ spl0_276
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f3657,f3422,f2938,f52506]) ).
fof(f52506,plain,
( spl0_1500
<=> ! [X4,X5] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X4,tc_nat),X5))
| hBOOL(hAPP(c_lessequals(X5,tc_nat),hAPP(c_Suc,X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f2938,plain,
( spl0_276
<=> ! [X11,X12] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),X12))
| hBOOL(hAPP(c_lessequals(X11,tc_nat),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f3422,plain,
( spl0_333
<=> ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f3657,plain,
( ! [X4,X5] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X4,tc_nat),X5))
| hBOOL(hAPP(c_lessequals(X5,tc_nat),hAPP(c_Suc,X4))) )
| ~ spl0_276
| ~ spl0_333 ),
inference(resolution,[],[f3423,f2939]) ).
fof(f2939,plain,
( ! [X11,X12] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),X12))
| hBOOL(hAPP(c_lessequals(X11,tc_nat),X12)) )
| ~ spl0_276 ),
inference(avatar_component_clause,[],[f2938]) ).
fof(f3423,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,X1)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2)) )
| ~ spl0_333 ),
inference(avatar_component_clause,[],[f3422]) ).
fof(f52503,plain,
( ~ spl0_13
| spl0_1499
| ~ spl0_307
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f3642,f3414,f3127,f52501,f1561]) ).
fof(f1561,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f52501,plain,
( spl0_1499
<=> ! [X0] : hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f3414,plain,
( spl0_331
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Oone__class_Oone(X5)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f3642,plain,
( ! [X0] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0)))
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat) )
| ~ spl0_307
| ~ spl0_331 ),
inference(superposition,[],[f3415,f3128]) ).
fof(f3415,plain,
( ! [X6,X5] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Oone__class_Oone(X5))))
| ~ class_Ring__and__Field_Oordered__semidom(X5) )
| ~ spl0_331 ),
inference(avatar_component_clause,[],[f3414]) ).
fof(f52499,plain,
( spl0_1498
| ~ spl0_276
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f3626,f3406,f2938,f52497]) ).
fof(f52497,plain,
( spl0_1498
<=> ! [X2,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X3))
| hBOOL(hAPP(c_lessequals(X2,tc_nat),hAPP(c_Suc,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f3406,plain,
( spl0_329
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(c_Suc,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f3626,plain,
( ! [X2,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X3))
| hBOOL(hAPP(c_lessequals(X2,tc_nat),hAPP(c_Suc,X3))) )
| ~ spl0_276
| ~ spl0_329 ),
inference(resolution,[],[f3407,f2939]) ).
fof(f3407,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(c_Suc,X2)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2)) )
| ~ spl0_329 ),
inference(avatar_component_clause,[],[f3406]) ).
fof(f51878,plain,
( spl0_1497
| ~ spl0_37
| ~ spl0_1388 ),
inference(avatar_split_clause,[],[f44281,f44165,f1681,f51876]) ).
fof(f51876,plain,
( spl0_1497
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f44281,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X0,X0,tc_nat)
| ~ spl0_37
| ~ spl0_1388 ),
inference(resolution,[],[f44166,f1683]) ).
fof(f1683,plain,
( class_Orderings_Oorder(tc_nat)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f1681]) ).
fof(f49724,plain,
( ~ spl0_1495
| spl0_1496
| ~ spl0_80
| ~ spl0_1382 ),
inference(avatar_split_clause,[],[f44273,f44114,f1896,f49722,f49718]) ).
fof(f49718,plain,
( spl0_1495
<=> class_Orderings_Obot(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f49722,plain,
( spl0_1496
<=> ! [X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Obot__class_Obot(tc_Int_Oint),tc_Int_Oint) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f1896,plain,
( spl0_80
<=> class_Lattices_Oupper__semilattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f44114,plain,
( spl0_1382
<=> ! [X29,X28] :
( ~ class_Lattices_Oupper__semilattice(X28)
| c_Lattices_Oupper__semilattice__class_Osup(X29,c_Orderings_Obot__class_Obot(X28),X28) = X29
| ~ class_Orderings_Obot(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f44273,plain,
( ! [X5] :
( c_Lattices_Oupper__semilattice__class_Osup(X5,c_Orderings_Obot__class_Obot(tc_Int_Oint),tc_Int_Oint) = X5
| ~ class_Orderings_Obot(tc_Int_Oint) )
| ~ spl0_80
| ~ spl0_1382 ),
inference(resolution,[],[f44115,f1898]) ).
fof(f1898,plain,
( class_Lattices_Oupper__semilattice(tc_Int_Oint)
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f1896]) ).
fof(f44115,plain,
( ! [X28,X29] :
( ~ class_Lattices_Oupper__semilattice(X28)
| c_Lattices_Oupper__semilattice__class_Osup(X29,c_Orderings_Obot__class_Obot(X28),X28) = X29
| ~ class_Orderings_Obot(X28) )
| ~ spl0_1382 ),
inference(avatar_component_clause,[],[f44114]) ).
fof(f48635,plain,
( spl0_1494
| ~ spl0_767
| ~ spl0_1387 ),
inference(avatar_split_clause,[],[f44155,f44134,f13466,f48633]) ).
fof(f48633,plain,
( spl0_1494
<=> ! [X6,X5] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_nat),tc_nat),X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f13466,plain,
( spl0_767
<=> ! [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_767])]) ).
fof(f44134,plain,
( spl0_1387
<=> ! [X0,X1] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f44155,plain,
( ! [X6,X5] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,tc_nat),tc_nat),X5))
| ~ spl0_767
| ~ spl0_1387 ),
inference(superposition,[],[f44135,f13467]) ).
fof(f13467,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_767 ),
inference(avatar_component_clause,[],[f13466]) ).
fof(f44135,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_nat)))
| ~ spl0_1387 ),
inference(avatar_component_clause,[],[f44134]) ).
fof(f48576,plain,
( spl0_1493
| ~ spl0_655
| ~ spl0_1387 ),
inference(avatar_split_clause,[],[f44153,f44134,f9712,f48574]) ).
fof(f48574,plain,
( spl0_1493
<=> ! [X2,X1] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f9712,plain,
( spl0_655
<=> ! [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_655])]) ).
fof(f44153,plain,
( ! [X2,X1] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_nat)))
| ~ spl0_655
| ~ spl0_1387 ),
inference(superposition,[],[f44135,f9713]) ).
fof(f9713,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_nat)
| ~ spl0_655 ),
inference(avatar_component_clause,[],[f9712]) ).
fof(f47986,plain,
( spl0_1492
| ~ spl0_261
| ~ spl0_367
| ~ spl0_935 ),
inference(avatar_split_clause,[],[f19913,f15821,f3567,f2721,f47984]) ).
fof(f47984,plain,
( spl0_1492
<=> ! [X45,X44,X46] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X46,X45,tc_fun(X44,tc_bool)),X45,tc_fun(X44,tc_bool)) = X45 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f2721,plain,
( spl0_261
<=> ! [X5,X26] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X26,tc_fun(X5,tc_bool)) = X26 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f3567,plain,
( spl0_367
<=> ! [X25,X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X25,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f15821,plain,
( spl0_935
<=> ! [X5,X27,X25,X26] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),X25,tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X26,X25,tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X27,X25,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f19913,plain,
( ! [X46,X44,X45] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X46,X45,tc_fun(X44,tc_bool)),X45,tc_fun(X44,tc_bool)) = X45
| ~ spl0_261
| ~ spl0_367
| ~ spl0_935 ),
inference(forward_demodulation,[],[f19912,f2722]) ).
fof(f2722,plain,
( ! [X26,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X26,tc_fun(X5,tc_bool)) = X26
| ~ spl0_261 ),
inference(avatar_component_clause,[],[f2721]) ).
fof(f19912,plain,
( ! [X46,X44,X45] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X44,tc_bool)),X45,tc_fun(X44,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X46,X45,tc_fun(X44,tc_bool)),X45,tc_fun(X44,tc_bool))
| ~ spl0_261
| ~ spl0_367
| ~ spl0_935 ),
inference(forward_demodulation,[],[f19865,f3568]) ).
fof(f3568,plain,
( ! [X5,X25] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X25,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ spl0_367 ),
inference(avatar_component_clause,[],[f3567]) ).
fof(f19865,plain,
( ! [X46,X44,X45] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X46,c_Orderings_Obot__class_Obot(tc_fun(X44,tc_bool)),tc_fun(X44,tc_bool)),X45,tc_fun(X44,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X46,X45,tc_fun(X44,tc_bool)),X45,tc_fun(X44,tc_bool))
| ~ spl0_261
| ~ spl0_935 ),
inference(superposition,[],[f15822,f2722]) ).
fof(f15822,plain,
( ! [X26,X27,X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),X25,tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X26,X25,tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X27,X25,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ spl0_935 ),
inference(avatar_component_clause,[],[f15821]) ).
fof(f47974,plain,
( spl0_1491
| ~ spl0_180
| ~ spl0_261
| ~ spl0_308
| ~ spl0_366
| ~ spl0_935 ),
inference(avatar_split_clause,[],[f19907,f15821,f3563,f3131,f2721,f2367,f47972]) ).
fof(f47972,plain,
( spl0_1491
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f2367,plain,
( spl0_180
<=> ! [X25,X5] : c_Lattices_Oupper__semilattice__class_Osup(X25,X25,tc_fun(X5,tc_bool)) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f3131,plain,
( spl0_308
<=> ! [X25,X5,X26] : c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X26,X25,tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f3563,plain,
( spl0_366
<=> ! [X5,X26] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X26,tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f19907,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)) = X0
| ~ spl0_180
| ~ spl0_261
| ~ spl0_308
| ~ spl0_366
| ~ spl0_935 ),
inference(forward_demodulation,[],[f19906,f19905]) ).
fof(f19905,plain,
( ! [X46,X44,X45] : c_Lattices_Olower__semilattice__class_Oinf(X45,c_Lattices_Oupper__semilattice__class_Osup(X46,X45,tc_fun(X44,tc_bool)),tc_fun(X44,tc_bool)) = X45
| ~ spl0_261
| ~ spl0_366
| ~ spl0_935 ),
inference(forward_demodulation,[],[f19904,f2722]) ).
fof(f19904,plain,
( ! [X46,X44,X45] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X44,tc_bool)),X45,tc_fun(X44,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X45,c_Lattices_Oupper__semilattice__class_Osup(X46,X45,tc_fun(X44,tc_bool)),tc_fun(X44,tc_bool))
| ~ spl0_261
| ~ spl0_366
| ~ spl0_935 ),
inference(forward_demodulation,[],[f19852,f3564]) ).
fof(f3564,plain,
( ! [X26,X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X26,tc_fun(X5,tc_bool))
| ~ spl0_366 ),
inference(avatar_component_clause,[],[f3563]) ).
fof(f19852,plain,
( ! [X46,X44,X45] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X44,tc_bool)),X46,tc_fun(X44,tc_bool)),X45,tc_fun(X44,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X45,c_Lattices_Oupper__semilattice__class_Osup(X46,X45,tc_fun(X44,tc_bool)),tc_fun(X44,tc_bool))
| ~ spl0_261
| ~ spl0_935 ),
inference(superposition,[],[f15822,f2722]) ).
fof(f19906,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ spl0_180
| ~ spl0_308
| ~ spl0_935 ),
inference(forward_demodulation,[],[f19855,f3132]) ).
fof(f3132,plain,
( ! [X26,X5,X25] : c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X26,X25,tc_fun(X5,tc_bool))
| ~ spl0_308 ),
inference(avatar_component_clause,[],[f3131]) ).
fof(f19855,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X0,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool))
| ~ spl0_180
| ~ spl0_935 ),
inference(superposition,[],[f15822,f2368]) ).
fof(f2368,plain,
( ! [X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,X25,tc_fun(X5,tc_bool)) = X25
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f2367]) ).
fof(f47970,plain,
( spl0_1490
| ~ spl0_261
| ~ spl0_366
| ~ spl0_935 ),
inference(avatar_split_clause,[],[f19905,f15821,f3563,f2721,f47968]) ).
fof(f47968,plain,
( spl0_1490
<=> ! [X45,X44,X46] : c_Lattices_Olower__semilattice__class_Oinf(X45,c_Lattices_Oupper__semilattice__class_Osup(X46,X45,tc_fun(X44,tc_bool)),tc_fun(X44,tc_bool)) = X45 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f47966,plain,
( spl0_1489
| ~ spl0_262
| ~ spl0_367
| ~ spl0_934 ),
inference(avatar_split_clause,[],[f19825,f15817,f3567,f2725,f47964]) ).
fof(f47964,plain,
( spl0_1489
<=> ! [X25,X27,X26] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X26,tc_bool)),X25,tc_fun(X26,tc_bool)) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f2725,plain,
( spl0_262
<=> ! [X25,X5] : c_Lattices_Oupper__semilattice__class_Osup(X25,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f15817,plain,
( spl0_934
<=> ! [X5,X27,X25,X26] : c_Lattices_Oupper__semilattice__class_Osup(X25,c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f19825,plain,
( ! [X26,X27,X25] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X26,tc_bool)),X25,tc_fun(X26,tc_bool)) = X25
| ~ spl0_262
| ~ spl0_367
| ~ spl0_934 ),
inference(forward_demodulation,[],[f19824,f2726]) ).
fof(f2726,plain,
( ! [X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = X25
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f2725]) ).
fof(f19824,plain,
( ! [X26,X27,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)),tc_fun(X26,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X26,tc_bool)),X25,tc_fun(X26,tc_bool))
| ~ spl0_262
| ~ spl0_367
| ~ spl0_934 ),
inference(forward_demodulation,[],[f19774,f3568]) ).
fof(f19774,plain,
( ! [X26,X27,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,c_Lattices_Olower__semilattice__class_Oinf(X27,c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)),tc_fun(X26,tc_bool)),tc_fun(X26,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X26,tc_bool)),X25,tc_fun(X26,tc_bool))
| ~ spl0_262
| ~ spl0_934 ),
inference(superposition,[],[f15818,f2726]) ).
fof(f15818,plain,
( ! [X26,X27,X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ spl0_934 ),
inference(avatar_component_clause,[],[f15817]) ).
fof(f47962,plain,
( spl0_1488
| ~ spl0_180
| ~ spl0_262
| ~ spl0_308
| ~ spl0_366
| ~ spl0_934 ),
inference(avatar_split_clause,[],[f19822,f15817,f3563,f3131,f2725,f2367,f47960]) ).
fof(f47960,plain,
( spl0_1488
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).
fof(f19822,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = X0
| ~ spl0_180
| ~ spl0_262
| ~ spl0_308
| ~ spl0_366
| ~ spl0_934 ),
inference(forward_demodulation,[],[f19821,f19813]) ).
fof(f19813,plain,
( ! [X26,X27,X25] : c_Lattices_Olower__semilattice__class_Oinf(X25,c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X26,tc_bool)),tc_fun(X26,tc_bool)) = X25
| ~ spl0_262
| ~ spl0_366
| ~ spl0_934 ),
inference(forward_demodulation,[],[f19812,f2726]) ).
fof(f19812,plain,
( ! [X26,X27,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)),tc_fun(X26,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X25,c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X26,tc_bool)),tc_fun(X26,tc_bool))
| ~ spl0_262
| ~ spl0_366
| ~ spl0_934 ),
inference(forward_demodulation,[],[f19761,f3564]) ).
fof(f19761,plain,
( ! [X26,X27,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X26,tc_bool)),X27,tc_fun(X26,tc_bool)),tc_fun(X26,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X25,c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X26,tc_bool)),tc_fun(X26,tc_bool))
| ~ spl0_262
| ~ spl0_934 ),
inference(superposition,[],[f15818,f2726]) ).
fof(f19821,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool))
| ~ spl0_180
| ~ spl0_308
| ~ spl0_934 ),
inference(forward_demodulation,[],[f19768,f3132]) ).
fof(f19768,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X2,X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool))
| ~ spl0_180
| ~ spl0_934 ),
inference(superposition,[],[f15818,f2368]) ).
fof(f47958,plain,
( spl0_1487
| ~ spl0_262
| ~ spl0_366
| ~ spl0_934 ),
inference(avatar_split_clause,[],[f19813,f15817,f3563,f2725,f47956]) ).
fof(f47956,plain,
( spl0_1487
<=> ! [X25,X27,X26] : c_Lattices_Olower__semilattice__class_Oinf(X25,c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X26,tc_bool)),tc_fun(X26,tc_bool)) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f47857,plain,
( spl0_1486
| ~ spl0_1393
| ~ spl0_1485 ),
inference(avatar_split_clause,[],[f47853,f47850,f45651,f47855]) ).
fof(f47855,plain,
( spl0_1486
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f45651,plain,
( spl0_1393
<=> c_HOL_Oone__class_Oone(tc_nat) = hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f47850,plain,
( spl0_1485
<=> ! [X0] : hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f47853,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X0)),X0)
| ~ spl0_1393
| ~ spl0_1485 ),
inference(forward_demodulation,[],[f47851,f45653]) ).
fof(f45653,plain,
( c_HOL_Oone__class_Oone(tc_nat) = hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| ~ spl0_1393 ),
inference(avatar_component_clause,[],[f45651]) ).
fof(f47851,plain,
( ! [X0] : hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X0)),X0)
| ~ spl0_1485 ),
inference(avatar_component_clause,[],[f47850]) ).
fof(f47852,plain,
( spl0_1485
| ~ spl0_150
| ~ spl0_193
| ~ spl0_304
| ~ spl0_695 ),
inference(avatar_split_clause,[],[f11462,f10639,f3114,f2429,f2242,f47850]) ).
fof(f2429,plain,
( spl0_193
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f10639,plain,
( spl0_695
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f11462,plain,
( ! [X0] : hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X0)),X0)
| ~ spl0_150
| ~ spl0_193
| ~ spl0_304
| ~ spl0_695 ),
inference(forward_demodulation,[],[f11461,f3116]) ).
fof(f11461,plain,
( ! [X0] : hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X0)),X0)
| ~ spl0_150
| ~ spl0_193
| ~ spl0_695 ),
inference(forward_demodulation,[],[f11398,f2430]) ).
fof(f2430,plain,
( ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X1)
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f2429]) ).
fof(f11398,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X0)),X0) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X0),X0))
| ~ spl0_150
| ~ spl0_695 ),
inference(resolution,[],[f10640,f2243]) ).
fof(f10640,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)) )
| ~ spl0_695 ),
inference(avatar_component_clause,[],[f10639]) ).
fof(f47848,plain,
( spl0_1484
| ~ spl0_234
| ~ spl0_566 ),
inference(avatar_split_clause,[],[f7799,f7496,f2613,f47846]) ).
fof(f47846,plain,
( spl0_1484
<=> ! [X13,X14] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X14)),X13),tc_nat),X13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f7496,plain,
( spl0_566
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f7799,plain,
( ! [X14,X13] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X14)),X13),tc_nat),X13))
| ~ spl0_234
| ~ spl0_566 ),
inference(superposition,[],[f2614,f7497]) ).
fof(f7497,plain,
( ! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))
| ~ spl0_566 ),
inference(avatar_component_clause,[],[f7496]) ).
fof(f47844,plain,
( spl0_1483
| ~ spl0_230
| ~ spl0_566 ),
inference(avatar_split_clause,[],[f7796,f7496,f2597,f47842]) ).
fof(f47842,plain,
( spl0_1483
<=> ! [X7,X8] : hBOOL(hAPP(c_lessequals(X7,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X8)),X7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f7796,plain,
( ! [X8,X7] : hBOOL(hAPP(c_lessequals(X7,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X8)),X7)))
| ~ spl0_230
| ~ spl0_566 ),
inference(superposition,[],[f2598,f7497]) ).
fof(f47809,plain,
( spl0_1482
| ~ spl0_234
| ~ spl0_565 ),
inference(avatar_split_clause,[],[f7737,f7492,f2613,f47807]) ).
fof(f47807,plain,
( spl0_1482
<=> ! [X12,X11] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X11),hAPP(c_Suc,X12)),tc_nat),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f7492,plain,
( spl0_565
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f7737,plain,
( ! [X11,X12] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X11),hAPP(c_Suc,X12)),tc_nat),X11))
| ~ spl0_234
| ~ spl0_565 ),
inference(superposition,[],[f2614,f7493]) ).
fof(f7493,plain,
( ! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))
| ~ spl0_565 ),
inference(avatar_component_clause,[],[f7492]) ).
fof(f47805,plain,
( spl0_1481
| ~ spl0_230
| ~ spl0_565 ),
inference(avatar_split_clause,[],[f7734,f7492,f2597,f47803]) ).
fof(f47803,plain,
( spl0_1481
<=> ! [X6,X5] : hBOOL(hAPP(c_lessequals(X5,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X5),hAPP(c_Suc,X6)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f7734,plain,
( ! [X6,X5] : hBOOL(hAPP(c_lessequals(X5,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X5),hAPP(c_Suc,X6))))
| ~ spl0_230
| ~ spl0_565 ),
inference(superposition,[],[f2598,f7493]) ).
fof(f47769,plain,
( ~ spl0_22
| spl0_1480
| ~ spl0_174
| ~ spl0_477 ),
inference(avatar_split_clause,[],[f6064,f5020,f2343,f47767,f1606]) ).
fof(f47767,plain,
( spl0_1480
<=> ! [X0,X1] : ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat)),tc_nat),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f5020,plain,
( spl0_477
<=> ! [X5,X11,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X7))
| hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f6064,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat)),tc_nat),X1))
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_174
| ~ spl0_477 ),
inference(resolution,[],[f5021,f2344]) ).
fof(f5021,plain,
( ! [X11,X6,X7,X5] :
( hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5)))
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X7))
| ~ class_Lattices_Oupper__semilattice(X5) )
| ~ spl0_477 ),
inference(avatar_component_clause,[],[f5020]) ).
fof(f47765,plain,
( spl0_1479
| ~ spl0_171
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f6042,f5016,f2331,f47763]) ).
fof(f47763,plain,
( spl0_1479
<=> ! [X13,X12,X11] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X13),X13),X11))
| ~ class_Lattices_Oupper__semilattice(X13)
| ~ class_Orderings_Oorder(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f2331,plain,
( spl0_171
<=> ! [X5,X11] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f5016,plain,
( spl0_476
<=> ! [X5,X11,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f6042,plain,
( ! [X11,X12,X13] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X13),X13),X11))
| ~ class_Lattices_Oupper__semilattice(X13)
| ~ class_Orderings_Oorder(X13) )
| ~ spl0_171
| ~ spl0_476 ),
inference(resolution,[],[f5017,f2332]) ).
fof(f2332,plain,
( ! [X11,X5] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X11))
| ~ class_Orderings_Oorder(X5) )
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f2331]) ).
fof(f5017,plain,
( ! [X11,X6,X7,X5] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X6))
| ~ class_Lattices_Oupper__semilattice(X5) )
| ~ spl0_476 ),
inference(avatar_component_clause,[],[f5016]) ).
fof(f47761,plain,
( spl0_1478
| ~ spl0_172
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f6041,f5016,f2335,f47759]) ).
fof(f47759,plain,
( spl0_1478
<=> ! [X9,X8,X10] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,X10),X10),X8))
| ~ class_Lattices_Oupper__semilattice(X10)
| ~ class_Orderings_Olinorder(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f2335,plain,
( spl0_172
<=> ! [X5,X11] :
( ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f6041,plain,
( ! [X10,X8,X9] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,X10),X10),X8))
| ~ class_Lattices_Oupper__semilattice(X10)
| ~ class_Orderings_Olinorder(X10) )
| ~ spl0_172
| ~ spl0_476 ),
inference(resolution,[],[f5017,f2336]) ).
fof(f2336,plain,
( ! [X11,X5] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X11))
| ~ class_Orderings_Olinorder(X5) )
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f2335]) ).
fof(f47757,plain,
( spl0_1477
| ~ spl0_173
| ~ spl0_476 ),
inference(avatar_split_clause,[],[f6040,f5016,f2339,f47755]) ).
fof(f47755,plain,
( spl0_1477
<=> ! [X6,X5,X7] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X7),X7),X5))
| ~ class_Lattices_Oupper__semilattice(X7)
| ~ class_Orderings_Opreorder(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f2339,plain,
( spl0_173
<=> ! [X5,X11] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f6040,plain,
( ! [X6,X7,X5] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X7),X7),X5))
| ~ class_Lattices_Oupper__semilattice(X7)
| ~ class_Orderings_Opreorder(X7) )
| ~ spl0_173
| ~ spl0_476 ),
inference(resolution,[],[f5017,f2340]) ).
fof(f2340,plain,
( ! [X11,X5] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X11))
| ~ class_Orderings_Opreorder(X5) )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f2339]) ).
fof(f47753,plain,
( spl0_1476
| ~ spl0_171
| ~ spl0_475 ),
inference(avatar_split_clause,[],[f6011,f5012,f2331,f47751]) ).
fof(f47751,plain,
( spl0_1476
<=> ! [X13,X12,X11] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X13),X13),X12))
| ~ class_Lattices_Oupper__semilattice(X13)
| ~ class_Orderings_Oorder(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f5012,plain,
( spl0_475
<=> ! [X5,X11,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f6011,plain,
( ! [X11,X12,X13] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X13),X13),X12))
| ~ class_Lattices_Oupper__semilattice(X13)
| ~ class_Orderings_Oorder(X13) )
| ~ spl0_171
| ~ spl0_475 ),
inference(resolution,[],[f5013,f2332]) ).
fof(f5013,plain,
( ! [X11,X6,X7,X5] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X7))
| ~ class_Lattices_Oupper__semilattice(X5) )
| ~ spl0_475 ),
inference(avatar_component_clause,[],[f5012]) ).
fof(f47749,plain,
( spl0_1475
| ~ spl0_172
| ~ spl0_475 ),
inference(avatar_split_clause,[],[f6010,f5012,f2335,f47747]) ).
fof(f47747,plain,
( spl0_1475
<=> ! [X9,X8,X10] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,X10),X10),X9))
| ~ class_Lattices_Oupper__semilattice(X10)
| ~ class_Orderings_Olinorder(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f6010,plain,
( ! [X10,X8,X9] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X8,X9,X10),X10),X9))
| ~ class_Lattices_Oupper__semilattice(X10)
| ~ class_Orderings_Olinorder(X10) )
| ~ spl0_172
| ~ spl0_475 ),
inference(resolution,[],[f5013,f2336]) ).
fof(f47745,plain,
( spl0_1474
| ~ spl0_173
| ~ spl0_475 ),
inference(avatar_split_clause,[],[f6009,f5012,f2339,f47743]) ).
fof(f47743,plain,
( spl0_1474
<=> ! [X6,X5,X7] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X7),X7),X6))
| ~ class_Lattices_Oupper__semilattice(X7)
| ~ class_Orderings_Opreorder(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f6009,plain,
( ! [X6,X7,X5] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X7),X7),X6))
| ~ class_Lattices_Oupper__semilattice(X7)
| ~ class_Orderings_Opreorder(X7) )
| ~ spl0_173
| ~ spl0_475 ),
inference(resolution,[],[f5013,f2340]) ).
fof(f47741,plain,
( spl0_1473
| ~ spl0_1360
| ~ spl0_1393 ),
inference(avatar_split_clause,[],[f45763,f45651,f41839,f47738]) ).
fof(f47738,plain,
( spl0_1473
<=> hBOOL(hAPP(c_SetInterval_Oord__class_OatMost(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f41839,plain,
( spl0_1360
<=> ! [X4] : hBOOL(hAPP(c_SetInterval_Oord__class_OatMost(hAPP(c_Suc,X4),tc_nat),hAPP(c_Suc,X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f45763,plain,
( hBOOL(hAPP(c_SetInterval_Oord__class_OatMost(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat)))
| ~ spl0_1360
| ~ spl0_1393 ),
inference(superposition,[],[f41840,f45653]) ).
fof(f41840,plain,
( ! [X4] : hBOOL(hAPP(c_SetInterval_Oord__class_OatMost(hAPP(c_Suc,X4),tc_nat),hAPP(c_Suc,X4)))
| ~ spl0_1360 ),
inference(avatar_component_clause,[],[f41839]) ).
fof(f47736,plain,
( spl0_1472
| ~ spl0_187
| ~ spl0_304
| ~ spl0_457 ),
inference(avatar_split_clause,[],[f5615,f4933,f3114,f2404,f47734]) ).
fof(f47734,plain,
( spl0_1472
<=> ! [X9,X8] :
( ~ hBOOL(hAPP(c_lessequals(X9,tc_nat),c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(c_lessequals(X9,tc_nat),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f2404,plain,
( spl0_187
<=> ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f4933,plain,
( spl0_457
<=> ! [X11,X16,X12] :
( ~ hBOOL(hAPP(c_lessequals(X11,tc_nat),X12))
| hBOOL(hAPP(c_lessequals(X11,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f5615,plain,
( ! [X8,X9] :
( ~ hBOOL(hAPP(c_lessequals(X9,tc_nat),c_Orderings_Obot__class_Obot(tc_nat)))
| hBOOL(hAPP(c_lessequals(X9,tc_nat),X8)) )
| ~ spl0_187
| ~ spl0_304
| ~ spl0_457 ),
inference(forward_demodulation,[],[f5613,f3116]) ).
fof(f5613,plain,
( ! [X8,X9] :
( hBOOL(hAPP(c_lessequals(X9,tc_nat),X8))
| ~ hBOOL(hAPP(c_lessequals(X9,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) )
| ~ spl0_187
| ~ spl0_457 ),
inference(superposition,[],[f4934,f2405]) ).
fof(f2405,plain,
( ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2) = X2
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f2404]) ).
fof(f4934,plain,
( ! [X11,X16,X12] :
( hBOOL(hAPP(c_lessequals(X11,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X16)))
| ~ hBOOL(hAPP(c_lessequals(X11,tc_nat),X12)) )
| ~ spl0_457 ),
inference(avatar_component_clause,[],[f4933]) ).
fof(f47732,plain,
( spl0_1471
| ~ spl0_187
| ~ spl0_304
| ~ spl0_453 ),
inference(avatar_split_clause,[],[f5560,f4917,f3114,f2404,f47730]) ).
fof(f47730,plain,
( spl0_1471
<=> ! [X9,X8] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X8,tc_nat),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f4917,plain,
( spl0_453
<=> ! [X4,X0,X3] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f5560,plain,
( ! [X8,X9] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X8,tc_nat),X9)) )
| ~ spl0_187
| ~ spl0_304
| ~ spl0_453 ),
inference(forward_demodulation,[],[f5556,f3116]) ).
fof(f5556,plain,
( ! [X8,X9] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X8,tc_nat),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X9)) )
| ~ spl0_187
| ~ spl0_453 ),
inference(superposition,[],[f4918,f2405]) ).
fof(f4918,plain,
( ! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat),X0))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),X0)) )
| ~ spl0_453 ),
inference(avatar_component_clause,[],[f4917]) ).
fof(f47728,plain,
( spl0_1470
| ~ spl0_171
| ~ spl0_434 ),
inference(avatar_split_clause,[],[f5130,f4829,f2331,f47726]) ).
fof(f47726,plain,
( spl0_1470
<=> ! [X22,X21,X23] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X21,X22),c_Lattices_Olower__semilattice__class_Oinf(X21,X23,X22)))
| ~ class_Lattices_Olower__semilattice(X22)
| ~ class_Orderings_Oorder(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f4829,plain,
( spl0_434
<=> ! [X5,X11,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5),X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f5130,plain,
( ! [X21,X22,X23] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X21,X22),c_Lattices_Olower__semilattice__class_Oinf(X21,X23,X22)))
| ~ class_Lattices_Olower__semilattice(X22)
| ~ class_Orderings_Oorder(X22) )
| ~ spl0_171
| ~ spl0_434 ),
inference(resolution,[],[f4830,f2332]) ).
fof(f4830,plain,
( ! [X11,X6,X7,X5] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X11))
| ~ class_Lattices_Olower__semilattice(X5) )
| ~ spl0_434 ),
inference(avatar_component_clause,[],[f4829]) ).
fof(f47724,plain,
( spl0_1469
| ~ spl0_172
| ~ spl0_434 ),
inference(avatar_split_clause,[],[f5129,f4829,f2335,f47722]) ).
fof(f47722,plain,
( spl0_1469
<=> ! [X20,X18,X19] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X18,X19),c_Lattices_Olower__semilattice__class_Oinf(X18,X20,X19)))
| ~ class_Lattices_Olower__semilattice(X19)
| ~ class_Orderings_Olinorder(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f5129,plain,
( ! [X18,X19,X20] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X18,X19),c_Lattices_Olower__semilattice__class_Oinf(X18,X20,X19)))
| ~ class_Lattices_Olower__semilattice(X19)
| ~ class_Orderings_Olinorder(X19) )
| ~ spl0_172
| ~ spl0_434 ),
inference(resolution,[],[f4830,f2336]) ).
fof(f47720,plain,
( spl0_1468
| ~ spl0_173
| ~ spl0_434 ),
inference(avatar_split_clause,[],[f5128,f4829,f2339,f47718]) ).
fof(f47718,plain,
( spl0_1468
<=> ! [X16,X17,X15] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X15,X16),c_Lattices_Olower__semilattice__class_Oinf(X15,X17,X16)))
| ~ class_Lattices_Olower__semilattice(X16)
| ~ class_Orderings_Opreorder(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f5128,plain,
( ! [X16,X17,X15] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X15,X16),c_Lattices_Olower__semilattice__class_Oinf(X15,X17,X16)))
| ~ class_Lattices_Olower__semilattice(X16)
| ~ class_Orderings_Opreorder(X16) )
| ~ spl0_173
| ~ spl0_434 ),
inference(resolution,[],[f4830,f2340]) ).
fof(f47716,plain,
( spl0_1467
| ~ spl0_171
| ~ spl0_433 ),
inference(avatar_split_clause,[],[f5099,f4825,f2331,f47714]) ).
fof(f47714,plain,
( spl0_1467
<=> ! [X22,X21,X23] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X21,X22),c_Lattices_Olower__semilattice__class_Oinf(X23,X21,X22)))
| ~ class_Lattices_Olower__semilattice(X22)
| ~ class_Orderings_Oorder(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f4825,plain,
( spl0_433
<=> ! [X6,X5,X11,X7] :
( ~ class_Lattices_Olower__semilattice(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5),X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f5099,plain,
( ! [X21,X22,X23] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X21,X22),c_Lattices_Olower__semilattice__class_Oinf(X23,X21,X22)))
| ~ class_Lattices_Olower__semilattice(X22)
| ~ class_Orderings_Oorder(X22) )
| ~ spl0_171
| ~ spl0_433 ),
inference(resolution,[],[f4826,f2332]) ).
fof(f4826,plain,
( ! [X11,X6,X7,X5] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X11))
| ~ class_Lattices_Olower__semilattice(X5) )
| ~ spl0_433 ),
inference(avatar_component_clause,[],[f4825]) ).
fof(f47712,plain,
( spl0_1466
| ~ spl0_172
| ~ spl0_433 ),
inference(avatar_split_clause,[],[f5098,f4825,f2335,f47710]) ).
fof(f47710,plain,
( spl0_1466
<=> ! [X20,X18,X19] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X18,X19),c_Lattices_Olower__semilattice__class_Oinf(X20,X18,X19)))
| ~ class_Lattices_Olower__semilattice(X19)
| ~ class_Orderings_Olinorder(X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f5098,plain,
( ! [X18,X19,X20] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X18,X19),c_Lattices_Olower__semilattice__class_Oinf(X20,X18,X19)))
| ~ class_Lattices_Olower__semilattice(X19)
| ~ class_Orderings_Olinorder(X19) )
| ~ spl0_172
| ~ spl0_433 ),
inference(resolution,[],[f4826,f2336]) ).
fof(f47708,plain,
( spl0_1465
| ~ spl0_173
| ~ spl0_433 ),
inference(avatar_split_clause,[],[f5097,f4825,f2339,f47706]) ).
fof(f47706,plain,
( spl0_1465
<=> ! [X16,X17,X15] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X15,X16),c_Lattices_Olower__semilattice__class_Oinf(X17,X15,X16)))
| ~ class_Lattices_Olower__semilattice(X16)
| ~ class_Orderings_Opreorder(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f5097,plain,
( ! [X16,X17,X15] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X15,X16),c_Lattices_Olower__semilattice__class_Oinf(X17,X15,X16)))
| ~ class_Lattices_Olower__semilattice(X16)
| ~ class_Orderings_Opreorder(X16) )
| ~ spl0_173
| ~ spl0_433 ),
inference(resolution,[],[f4826,f2340]) ).
fof(f47704,plain,
( ~ spl0_1463
| spl0_1464
| ~ spl0_209
| ~ spl0_304
| ~ spl0_427 ),
inference(avatar_split_clause,[],[f4724,f4579,f3114,f2504,f47702,f47698]) ).
fof(f47698,plain,
( spl0_1463
<=> class_RealVector_Oreal__normed__algebra(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f47702,plain,
( spl0_1464
<=> ! [X0] : c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f2504,plain,
( spl0_209
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f4579,plain,
( spl0_427
<=> ! [X6,X5,X11] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X6,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X6),X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f4724,plain,
( ! [X0] :
( c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X0,c_Orderings_Obot__class_Obot(tc_nat),tc_nat,tc_nat)
| ~ class_RealVector_Oreal__normed__algebra(tc_nat) )
| ~ spl0_209
| ~ spl0_304
| ~ spl0_427 ),
inference(forward_demodulation,[],[f4720,f3116]) ).
fof(f4720,plain,
( ! [X0] :
( c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,tc_nat)
| ~ class_RealVector_Oreal__normed__algebra(tc_nat) )
| ~ spl0_209
| ~ spl0_427 ),
inference(superposition,[],[f4580,f2505]) ).
fof(f2505,plain,
( ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2)
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f2504]) ).
fof(f4580,plain,
( ! [X11,X6,X5] :
( c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X6,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X6),X5,X5)
| ~ class_RealVector_Oreal__normed__algebra(X5) )
| ~ spl0_427 ),
inference(avatar_component_clause,[],[f4579]) ).
fof(f47696,plain,
( ~ spl0_1462
| ~ spl0_174
| ~ spl0_1393 ),
inference(avatar_split_clause,[],[f45710,f45651,f2343,f47693]) ).
fof(f47693,plain,
( spl0_1462
<=> hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Orderings_Obot__class_Obot(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f45710,plain,
( ~ hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Orderings_Obot__class_Obot(tc_nat)))
| ~ spl0_174
| ~ spl0_1393 ),
inference(superposition,[],[f2344,f45653]) ).
fof(f47691,plain,
( spl0_1461
| ~ spl0_114
| ~ spl0_407 ),
inference(avatar_split_clause,[],[f4447,f4279,f2066,f47689]) ).
fof(f47689,plain,
( spl0_1461
<=> ! [X4,X5] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X5),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f2066,plain,
( spl0_114
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f4279,plain,
( spl0_407
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f4447,plain,
( ! [X4,X5] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X4),X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X5),X4)
| ~ spl0_114
| ~ spl0_407 ),
inference(resolution,[],[f4280,f2068]) ).
fof(f2068,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f2066]) ).
fof(f4280,plain,
( ! [X6,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X6) )
| ~ spl0_407 ),
inference(avatar_component_clause,[],[f4279]) ).
fof(f47687,plain,
( spl0_1460
| ~ spl0_70
| ~ spl0_407 ),
inference(avatar_split_clause,[],[f4446,f4279,f1846,f47685]) ).
fof(f47685,plain,
( spl0_1460
<=> ! [X2,X3] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X3),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f1846,plain,
( spl0_70
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f4446,plain,
( ! [X2,X3] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X3),X2)
| ~ spl0_70
| ~ spl0_407 ),
inference(resolution,[],[f4280,f1848]) ).
fof(f1848,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint)
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f1846]) ).
fof(f47683,plain,
( spl0_1459
| ~ spl0_20
| ~ spl0_304
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f4444,f4275,f3114,f1596,f47681]) ).
fof(f47681,plain,
( spl0_1459
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_Finite__Set_Osetsum(X0,tc_nat),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f1596,plain,
( spl0_20
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f4275,plain,
( spl0_406
<=> ! [X20,X5,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f4444,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_Finite__Set_Osetsum(X0,tc_nat),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))
| ~ spl0_20
| ~ spl0_304
| ~ spl0_406 ),
inference(forward_demodulation,[],[f4441,f3116]) ).
fof(f4441,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_Finite__Set_Osetsum(X0,tc_nat),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))
| ~ spl0_20
| ~ spl0_406 ),
inference(resolution,[],[f4276,f1598]) ).
fof(f1598,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f1596]) ).
fof(f4276,plain,
( ! [X10,X5,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool))) )
| ~ spl0_406 ),
inference(avatar_component_clause,[],[f4275]) ).
fof(f47679,plain,
( spl0_1458
| ~ spl0_124
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f4443,f4275,f2116,f47677]) ).
fof(f47677,plain,
( spl0_1458
<=> ! [X4,X5] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Finite__Set_Osetsum(X4,tc_Complex_Ocomplex),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f2116,plain,
( spl0_124
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f4443,plain,
( ! [X4,X5] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Finite__Set_Osetsum(X4,tc_Complex_Ocomplex),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)))
| ~ spl0_124
| ~ spl0_406 ),
inference(resolution,[],[f4276,f2118]) ).
fof(f2118,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f2116]) ).
fof(f47675,plain,
( spl0_1457
| ~ spl0_77
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f4442,f4275,f1881,f47673]) ).
fof(f47673,plain,
( spl0_1457
<=> ! [X2,X3] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Finite__Set_Osetsum(X2,tc_Int_Oint),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f1881,plain,
( spl0_77
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f4442,plain,
( ! [X2,X3] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Finite__Set_Osetsum(X2,tc_Int_Oint),X3),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)))
| ~ spl0_77
| ~ spl0_406 ),
inference(resolution,[],[f4276,f1883]) ).
fof(f1883,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint)
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1881]) ).
fof(f47671,plain,
( spl0_1456
| ~ spl0_41
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f4430,f4257,f1701,f47669]) ).
fof(f47669,plain,
( spl0_1456
<=> ! [X0,X1] : c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X0,X1,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OSup__class_OSup(X1,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f1701,plain,
( spl0_41
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f4257,plain,
( spl0_402
<=> ! [X6,X25,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,X25,X5),X5) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_OSup__class_OSup(X25,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f4430,plain,
( ! [X0,X1] : c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X0,X1,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Complete__Lattice_OSup__class_OSup(X1,tc_bool),tc_bool)
| ~ spl0_41
| ~ spl0_402 ),
inference(resolution,[],[f4258,f1703]) ).
fof(f1703,plain,
( class_Complete__Lattice_Ocomplete__lattice(tc_bool)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f1701]) ).
fof(f4258,plain,
( ! [X6,X5,X25] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,X25,X5),X5) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_OSup__class_OSup(X25,X5),X5) )
| ~ spl0_402 ),
inference(avatar_component_clause,[],[f4257]) ).
fof(f47667,plain,
( spl0_1455
| ~ spl0_135
| ~ spl0_399 ),
inference(avatar_split_clause,[],[f4421,f4243,f2171,f47665]) ).
fof(f47665,plain,
( spl0_1455
<=> ! [X2,X3] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),X3)),X3) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f2171,plain,
( spl0_135
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f4243,plain,
( spl0_399
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X7) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f4421,plain,
( ! [X2,X3] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),X3)),X3) = X2
| ~ spl0_135
| ~ spl0_399 ),
inference(resolution,[],[f4244,f2173]) ).
fof(f2173,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f2171]) ).
fof(f4244,plain,
( ! [X6,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X7) = X6 )
| ~ spl0_399 ),
inference(avatar_component_clause,[],[f4243]) ).
fof(f47663,plain,
( spl0_1454
| ~ spl0_93
| ~ spl0_399 ),
inference(avatar_split_clause,[],[f4420,f4243,f1961,f47661]) ).
fof(f47661,plain,
( spl0_1454
<=> ! [X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f1961,plain,
( spl0_93
<=> class_OrderedGroup_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f4420,plain,
( ! [X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X1) = X0
| ~ spl0_93
| ~ spl0_399 ),
inference(resolution,[],[f4244,f1963]) ).
fof(f1963,plain,
( class_OrderedGroup_Ogroup__add(tc_Int_Oint)
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1961]) ).
fof(f47659,plain,
( spl0_1453
| ~ spl0_135
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f4419,f4239,f2171,f47657]) ).
fof(f47657,plain,
( spl0_1453
<=> ! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),X2),X3)),X3) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f4239,plain,
( spl0_398
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X7) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f4419,plain,
( ! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),X2),X3)),X3) = X2
| ~ spl0_135
| ~ spl0_398 ),
inference(resolution,[],[f4240,f2173]) ).
fof(f4240,plain,
( ! [X6,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X7) = X6 )
| ~ spl0_398 ),
inference(avatar_component_clause,[],[f4239]) ).
fof(f47655,plain,
( spl0_1452
| ~ spl0_93
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f4418,f4239,f1961,f47653]) ).
fof(f47653,plain,
( spl0_1452
<=> ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),X0),X1)),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f4418,plain,
( ! [X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),X0),X1)),X1) = X0
| ~ spl0_93
| ~ spl0_398 ),
inference(resolution,[],[f4240,f1963]) ).
fof(f47651,plain,
( spl0_1451
| ~ spl0_170
| ~ spl0_1393 ),
inference(avatar_split_clause,[],[f45709,f45651,f2327,f47648]) ).
fof(f47648,plain,
( spl0_1451
<=> hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f2327,plain,
( spl0_170
<=> ! [X2] : hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f45709,plain,
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat)))
| ~ spl0_170
| ~ spl0_1393 ),
inference(superposition,[],[f2328,f45653]) ).
fof(f2328,plain,
( ! [X2] : hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,X2)))
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f2327]) ).
fof(f47646,plain,
( spl0_1450
| ~ spl0_138
| ~ spl0_392 ),
inference(avatar_split_clause,[],[f4409,f4215,f2186,f47644]) ).
fof(f47644,plain,
( spl0_1450
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f2186,plain,
( spl0_138
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f4215,plain,
( spl0_392
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X11
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f4409,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),X0),X0) )
| ~ spl0_138
| ~ spl0_392 ),
inference(resolution,[],[f4216,f2188]) ).
fof(f2188,plain,
( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f2186]) ).
fof(f4216,plain,
( ! [X11,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X11
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X11) )
| ~ spl0_392 ),
inference(avatar_component_clause,[],[f4215]) ).
fof(f47642,plain,
( spl0_1449
| ~ spl0_114
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f4405,f4207,f2066,f47640]) ).
fof(f47640,plain,
( spl0_1449
<=> ! [X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X4),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X5),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f4207,plain,
( spl0_390
<=> ! [X12,X5,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X12),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f4405,plain,
( ! [X4,X5] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X4),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X5),X4)
| ~ spl0_114
| ~ spl0_390 ),
inference(resolution,[],[f4208,f2068]) ).
fof(f4208,plain,
( ! [X11,X5,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X12),X11) )
| ~ spl0_390 ),
inference(avatar_component_clause,[],[f4207]) ).
fof(f47638,plain,
( spl0_1448
| ~ spl0_70
| ~ spl0_390 ),
inference(avatar_split_clause,[],[f4404,f4207,f1846,f47636]) ).
fof(f47636,plain,
( spl0_1448
<=> ! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X3),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f4404,plain,
( ! [X2,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X3),X2)
| ~ spl0_70
| ~ spl0_390 ),
inference(resolution,[],[f4208,f1848]) ).
fof(f47634,plain,
( spl0_1447
| ~ spl0_208
| ~ spl0_388 ),
inference(avatar_split_clause,[],[f4372,f4199,f2500,f47632]) ).
fof(f47632,plain,
( spl0_1447
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| ~ c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3,X0,X2)
| ~ class_RealVector_Oreal__normed__field(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f2500,plain,
( spl0_208
<=> ! [X9,X5,X11] :
( ~ class_RealVector_Oreal__normed__field(X5)
| c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X11,X9,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f4199,plain,
( spl0_388
<=> ! [X23,X11,X5,X15,X10] :
( ~ class_RealVector_Oreal__normed__field(X5)
| X15 = X23
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ c_Deriv_Oderiv(X10,X11,X23,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f4372,plain,
( ! [X2,X3,X0,X1] :
( X0 = X1
| ~ c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3,X0,X2)
| ~ class_RealVector_Oreal__normed__field(X2) )
| ~ spl0_208
| ~ spl0_388 ),
inference(duplicate_literal_removal,[],[f4371]) ).
fof(f4371,plain,
( ! [X2,X3,X0,X1] :
( X0 = X1
| ~ c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(X2),X1),X3,X0,X2)
| ~ class_RealVector_Oreal__normed__field(X2)
| ~ class_RealVector_Oreal__normed__field(X2) )
| ~ spl0_208
| ~ spl0_388 ),
inference(resolution,[],[f4200,f2501]) ).
fof(f2501,plain,
( ! [X11,X9,X5] :
( c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X11,X9,X5)
| ~ class_RealVector_Oreal__normed__field(X5) )
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f2500]) ).
fof(f4200,plain,
( ! [X10,X11,X15,X5,X23] :
( ~ c_Deriv_Oderiv(X10,X11,X23,X5)
| X15 = X23
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ class_RealVector_Oreal__normed__field(X5) )
| ~ spl0_388 ),
inference(avatar_component_clause,[],[f4199]) ).
fof(f47630,plain,
( spl0_1446
| ~ spl0_201
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f4122,f3593,f2472,f47628]) ).
fof(f47628,plain,
( spl0_1446
<=> ! [X48] :
( ~ class_Lattices_Oupper__semilattice(X48)
| c_HOL_Oone__class_Oone(X48) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ozero__class_Ozero(X48),c_HOL_Oone__class_Oone(X48),X48)
| ~ class_Ring__and__Field_Oordered__semidom(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f2472,plain,
( spl0_201
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Oone__class_Oone(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f4122,plain,
( ! [X48] :
( ~ class_Lattices_Oupper__semilattice(X48)
| c_HOL_Oone__class_Oone(X48) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ozero__class_Ozero(X48),c_HOL_Oone__class_Oone(X48),X48)
| ~ class_Ring__and__Field_Oordered__semidom(X48) )
| ~ spl0_201
| ~ spl0_373 ),
inference(resolution,[],[f3594,f2473]) ).
fof(f2473,plain,
( ! [X5] :
( hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Oone__class_Oone(X5)))
| ~ class_Ring__and__Field_Oordered__semidom(X5) )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f2472]) ).
fof(f47626,plain,
( spl0_1445
| ~ spl0_219
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f4112,f3593,f2553,f47624]) ).
fof(f47624,plain,
( spl0_1445
<=> ! [X25,X27,X26] :
( ~ class_Lattices_Oupper__semilattice(X25)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X26,X27,X25),X27,X25) = X27
| ~ class_Lattices_Olower__semilattice(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f4112,plain,
( ! [X26,X27,X25] :
( ~ class_Lattices_Oupper__semilattice(X25)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X26,X27,X25),X27,X25) = X27
| ~ class_Lattices_Olower__semilattice(X25) )
| ~ spl0_219
| ~ spl0_373 ),
inference(resolution,[],[f3594,f2554]) ).
fof(f47622,plain,
( spl0_1444
| ~ spl0_221
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f4111,f3593,f2561,f47620]) ).
fof(f47620,plain,
( spl0_1444
<=> ! [X22,X24,X23] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X23,X24,X22),X24,X22) = X24
| ~ class_Lattices_Olattice(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f2561,plain,
( spl0_221
<=> ! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f4111,plain,
( ! [X24,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X23,X24,X22),X24,X22) = X24
| ~ class_Lattices_Olattice(X22) )
| ~ spl0_221
| ~ spl0_373 ),
inference(resolution,[],[f3594,f2562]) ).
fof(f2562,plain,
( ! [X11,X5,X12] :
( hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5),X12))
| ~ class_Lattices_Olattice(X5) )
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f2561]) ).
fof(f47618,plain,
( spl0_1443
| ~ spl0_220
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f4106,f3593,f2557,f47616]) ).
fof(f47616,plain,
( spl0_1443
<=> ! [X13,X12,X11] :
( ~ class_Lattices_Oupper__semilattice(X11)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X11),X12,X11) = X12
| ~ class_Lattices_Olower__semilattice(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f4106,plain,
( ! [X11,X12,X13] :
( ~ class_Lattices_Oupper__semilattice(X11)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X11),X12,X11) = X12
| ~ class_Lattices_Olower__semilattice(X11) )
| ~ spl0_220
| ~ spl0_373 ),
inference(resolution,[],[f3594,f2558]) ).
fof(f47614,plain,
( spl0_1442
| ~ spl0_222
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f4105,f3593,f2565,f47612]) ).
fof(f47612,plain,
( spl0_1442
<=> ! [X9,X8,X10] :
( ~ class_Lattices_Oupper__semilattice(X8)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X9,X10,X8),X9,X8) = X9
| ~ class_Lattices_Olattice(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f4105,plain,
( ! [X10,X8,X9] :
( ~ class_Lattices_Oupper__semilattice(X8)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X9,X10,X8),X9,X8) = X9
| ~ class_Lattices_Olattice(X8) )
| ~ spl0_222
| ~ spl0_373 ),
inference(resolution,[],[f3594,f2566]) ).
fof(f47610,plain,
( spl0_1441
| ~ spl0_201
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4069,f3585,f2472,f47608]) ).
fof(f47608,plain,
( spl0_1441
<=> ! [X48] :
( ~ class_Lattices_Oupper__semilattice(X48)
| c_HOL_Oone__class_Oone(X48) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oone__class_Oone(X48),c_HOL_Ozero__class_Ozero(X48),X48)
| ~ class_Ring__and__Field_Oordered__semidom(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f4069,plain,
( ! [X48] :
( ~ class_Lattices_Oupper__semilattice(X48)
| c_HOL_Oone__class_Oone(X48) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oone__class_Oone(X48),c_HOL_Ozero__class_Ozero(X48),X48)
| ~ class_Ring__and__Field_Oordered__semidom(X48) )
| ~ spl0_201
| ~ spl0_371 ),
inference(resolution,[],[f3586,f2473]) ).
fof(f47604,plain,
( spl0_1440
| ~ spl0_219
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4059,f3585,f2553,f47602]) ).
fof(f47602,plain,
( spl0_1440
<=> ! [X25,X27,X26] :
( ~ class_Lattices_Oupper__semilattice(X25)
| c_Lattices_Oupper__semilattice__class_Osup(X26,c_Lattices_Olower__semilattice__class_Oinf(X27,X26,X25),X25) = X26
| ~ class_Lattices_Olower__semilattice(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f4059,plain,
( ! [X26,X27,X25] :
( ~ class_Lattices_Oupper__semilattice(X25)
| c_Lattices_Oupper__semilattice__class_Osup(X26,c_Lattices_Olower__semilattice__class_Oinf(X27,X26,X25),X25) = X26
| ~ class_Lattices_Olower__semilattice(X25) )
| ~ spl0_219
| ~ spl0_371 ),
inference(resolution,[],[f3586,f2554]) ).
fof(f47600,plain,
( spl0_1439
| ~ spl0_221
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4058,f3585,f2561,f47598]) ).
fof(f47598,plain,
( spl0_1439
<=> ! [X22,X24,X23] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_Lattices_Oupper__semilattice__class_Osup(X23,c_Lattices_Olower__semilattice__class_Oinf(X24,X23,X22),X22) = X23
| ~ class_Lattices_Olattice(X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f4058,plain,
( ! [X24,X22,X23] :
( ~ class_Lattices_Oupper__semilattice(X22)
| c_Lattices_Oupper__semilattice__class_Osup(X23,c_Lattices_Olower__semilattice__class_Oinf(X24,X23,X22),X22) = X23
| ~ class_Lattices_Olattice(X22) )
| ~ spl0_221
| ~ spl0_371 ),
inference(resolution,[],[f3586,f2562]) ).
fof(f47596,plain,
( spl0_1438
| ~ spl0_220
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4053,f3585,f2557,f47594]) ).
fof(f47594,plain,
( spl0_1438
<=> ! [X13,X12,X11] :
( ~ class_Lattices_Oupper__semilattice(X11)
| c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X11),X11) = X12
| ~ class_Lattices_Olower__semilattice(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f4053,plain,
( ! [X11,X12,X13] :
( ~ class_Lattices_Oupper__semilattice(X11)
| c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Olower__semilattice__class_Oinf(X12,X13,X11),X11) = X12
| ~ class_Lattices_Olower__semilattice(X11) )
| ~ spl0_220
| ~ spl0_371 ),
inference(resolution,[],[f3586,f2558]) ).
fof(f47544,plain,
( spl0_1437
| ~ spl0_22
| ~ spl0_256
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4049,f3585,f2701,f1606,f47542]) ).
fof(f47542,plain,
( spl0_1437
<=> ! [X2,X3] : c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X3),tc_nat) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f4049,plain,
( ! [X2,X3] :
( ~ class_Lattices_Oupper__semilattice(tc_nat)
| c_Lattices_Oupper__semilattice__class_Osup(X2,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X3),tc_nat) = X2 )
| ~ spl0_256
| ~ spl0_371 ),
inference(resolution,[],[f3586,f2702]) ).
fof(f47512,plain,
( ~ spl0_36
| spl0_1436
| ~ spl0_254
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f3864,f3498,f2693,f47510,f1676]) ).
fof(f47510,plain,
( spl0_1436
<=> ! [X22,X23] : ~ hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Suc,X22),X23,tc_nat),tc_nat),X22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f2693,plain,
( spl0_254
<=> ! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f3498,plain,
( spl0_350
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f3864,plain,
( ! [X22,X23] :
( ~ hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Suc,X22),X23,tc_nat),tc_nat),X22))
| ~ class_Lattices_Olattice(tc_nat) )
| ~ spl0_254
| ~ spl0_350 ),
inference(resolution,[],[f3499,f2694]) ).
fof(f2694,plain,
( ! [X11,X5,X12] :
( hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5)))
| ~ class_Lattices_Olattice(X5) )
| ~ spl0_254 ),
inference(avatar_component_clause,[],[f2693]) ).
fof(f3499,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2)) )
| ~ spl0_350 ),
inference(avatar_component_clause,[],[f3498]) ).
fof(f47508,plain,
( spl0_1435
| ~ spl0_252
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f3834,f3484,f2685,f47506]) ).
fof(f47506,plain,
( spl0_1435
<=> ! [X48,X46,X47] :
( ~ class_Lattices_Olower__semilattice(X46)
| c_Lattices_Olower__semilattice__class_Oinf(X47,c_Lattices_Oupper__semilattice__class_Osup(X47,X48,X46),X46) = X47
| ~ class_Lattices_Oupper__semilattice(X46) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f3834,plain,
( ! [X48,X46,X47] :
( ~ class_Lattices_Olower__semilattice(X46)
| c_Lattices_Olower__semilattice__class_Oinf(X47,c_Lattices_Oupper__semilattice__class_Osup(X47,X48,X46),X46) = X47
| ~ class_Lattices_Oupper__semilattice(X46) )
| ~ spl0_252
| ~ spl0_348 ),
inference(resolution,[],[f3485,f2686]) ).
fof(f47504,plain,
( spl0_1434
| ~ spl0_251
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f3832,f3484,f2681,f47502]) ).
fof(f47502,plain,
( spl0_1434
<=> ! [X41,X40,X42] :
( ~ class_Lattices_Olower__semilattice(X40)
| c_Lattices_Olower__semilattice__class_Oinf(X41,c_Lattices_Oupper__semilattice__class_Osup(X42,X41,X40),X40) = X41
| ~ class_Lattices_Oupper__semilattice(X40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f3832,plain,
( ! [X40,X41,X42] :
( ~ class_Lattices_Olower__semilattice(X40)
| c_Lattices_Olower__semilattice__class_Oinf(X41,c_Lattices_Oupper__semilattice__class_Osup(X42,X41,X40),X40) = X41
| ~ class_Lattices_Oupper__semilattice(X40) )
| ~ spl0_251
| ~ spl0_348 ),
inference(resolution,[],[f3485,f2682]) ).
fof(f47500,plain,
( spl0_1433
| ~ spl0_253
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f3831,f3484,f2689,f47498]) ).
fof(f47498,plain,
( spl0_1433
<=> ! [X38,X37,X39] :
( ~ class_Lattices_Olower__semilattice(X37)
| c_Lattices_Olower__semilattice__class_Oinf(X38,c_Lattices_Oupper__semilattice__class_Osup(X39,X38,X37),X37) = X38
| ~ class_Lattices_Olattice(X37) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f3831,plain,
( ! [X38,X39,X37] :
( ~ class_Lattices_Olower__semilattice(X37)
| c_Lattices_Olower__semilattice__class_Oinf(X38,c_Lattices_Oupper__semilattice__class_Osup(X39,X38,X37),X37) = X38
| ~ class_Lattices_Olattice(X37) )
| ~ spl0_253
| ~ spl0_348 ),
inference(resolution,[],[f3485,f2690]) ).
fof(f47496,plain,
( spl0_1432
| ~ spl0_186
| ~ spl0_1397 ),
inference(avatar_split_clause,[],[f46170,f45668,f2400,f47494]) ).
fof(f47494,plain,
( spl0_1432
<=> ! [X16] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X16
| c_Orderings_Obot__class_Obot(tc_nat) = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f2400,plain,
( spl0_186
<=> ! [X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f45668,plain,
( spl0_1397
<=> ! [X9,X10] :
( c_Orderings_Obot__class_Obot(tc_nat) = X10
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X9) != X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f46170,plain,
( ! [X16] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X16
| c_Orderings_Obot__class_Obot(tc_nat) = X16 )
| ~ spl0_186
| ~ spl0_1397 ),
inference(superposition,[],[f45669,f2401]) ).
fof(f2401,plain,
( ! [X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f2400]) ).
fof(f45669,plain,
( ! [X10,X9] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X9) != X9
| c_Orderings_Obot__class_Obot(tc_nat) = X10 )
| ~ spl0_1397 ),
inference(avatar_component_clause,[],[f45668]) ).
fof(f47492,plain,
( spl0_1431
| ~ spl0_201
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f3829,f3484,f2472,f47490]) ).
fof(f47490,plain,
( spl0_1431
<=> ! [X36] :
( ~ class_Lattices_Olower__semilattice(X36)
| c_HOL_Ozero__class_Ozero(X36) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(X36),c_HOL_Oone__class_Oone(X36),X36)
| ~ class_Ring__and__Field_Oordered__semidom(X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f3829,plain,
( ! [X36] :
( ~ class_Lattices_Olower__semilattice(X36)
| c_HOL_Ozero__class_Ozero(X36) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(X36),c_HOL_Oone__class_Oone(X36),X36)
| ~ class_Ring__and__Field_Oordered__semidom(X36) )
| ~ spl0_201
| ~ spl0_348 ),
inference(resolution,[],[f3485,f2473]) ).
fof(f47445,plain,
( ~ spl0_23
| spl0_1430
| ~ spl0_23
| ~ spl0_225
| ~ spl0_230
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f3799,f3476,f2597,f2577,f1611,f47443,f1611]) ).
fof(f47443,plain,
( spl0_1430
<=> ! [X32,X33] : c_Lattices_Olower__semilattice__class_Oinf(X32,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),X33),tc_nat) = X32 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f2577,plain,
( spl0_225
<=> ! [X12,X5,X11] :
( ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = c_Lattices_Olower__semilattice__class_Oinf(X12,X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f3799,plain,
( ! [X32,X33] :
( c_Lattices_Olower__semilattice__class_Oinf(X32,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),X33),tc_nat) = X32
| ~ class_Lattices_Olower__semilattice(tc_nat) )
| ~ spl0_23
| ~ spl0_225
| ~ spl0_230
| ~ spl0_346 ),
inference(forward_demodulation,[],[f3786,f2771]) ).
fof(f2771,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_nat)
| ~ spl0_23
| ~ spl0_225 ),
inference(resolution,[],[f2578,f1613]) ).
fof(f1613,plain,
( class_Lattices_Olower__semilattice(tc_nat)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f1611]) ).
fof(f2578,plain,
( ! [X11,X5,X12] :
( ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = c_Lattices_Olower__semilattice__class_Oinf(X12,X11,X5) )
| ~ spl0_225 ),
inference(avatar_component_clause,[],[f2577]) ).
fof(f3786,plain,
( ! [X32,X33] :
( ~ class_Lattices_Olower__semilattice(tc_nat)
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X32),X33),X32,tc_nat) = X32 )
| ~ spl0_230
| ~ spl0_346 ),
inference(resolution,[],[f3477,f2598]) ).
fof(f47409,plain,
( ~ spl0_23
| spl0_1429
| ~ spl0_23
| ~ spl0_225
| ~ spl0_228
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f3798,f3476,f2589,f2577,f1611,f47407,f1611]) ).
fof(f47407,plain,
( spl0_1429
<=> ! [X31] : c_Lattices_Olower__semilattice__class_Oinf(X31,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X31),X31),tc_nat) = X31 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f3798,plain,
( ! [X31] :
( c_Lattices_Olower__semilattice__class_Oinf(X31,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X31),X31),tc_nat) = X31
| ~ class_Lattices_Olower__semilattice(tc_nat) )
| ~ spl0_23
| ~ spl0_225
| ~ spl0_228
| ~ spl0_346 ),
inference(forward_demodulation,[],[f3785,f2771]) ).
fof(f3785,plain,
( ! [X31] :
( ~ class_Lattices_Olower__semilattice(tc_nat)
| c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X31),X31),X31,tc_nat) = X31 )
| ~ spl0_228
| ~ spl0_346 ),
inference(resolution,[],[f3477,f2590]) ).
fof(f47405,plain,
( spl0_1428
| ~ spl0_252
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f3793,f3476,f2685,f47403]) ).
fof(f47403,plain,
( spl0_1428
<=> ! [X48,X46,X47] :
( ~ class_Lattices_Olower__semilattice(X46)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X47,X48,X46),X47,X46) = X47
| ~ class_Lattices_Oupper__semilattice(X46) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f3793,plain,
( ! [X48,X46,X47] :
( ~ class_Lattices_Olower__semilattice(X46)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X47,X48,X46),X47,X46) = X47
| ~ class_Lattices_Oupper__semilattice(X46) )
| ~ spl0_252
| ~ spl0_346 ),
inference(resolution,[],[f3477,f2686]) ).
fof(f47401,plain,
( spl0_1427
| ~ spl0_254
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f3792,f3476,f2693,f47399]) ).
fof(f47399,plain,
( spl0_1427
<=> ! [X45,X43,X44] :
( ~ class_Lattices_Olower__semilattice(X43)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X44,X45,X43),X44,X43) = X44
| ~ class_Lattices_Olattice(X43) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).
fof(f3792,plain,
( ! [X44,X45,X43] :
( ~ class_Lattices_Olower__semilattice(X43)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X44,X45,X43),X44,X43) = X44
| ~ class_Lattices_Olattice(X43) )
| ~ spl0_254
| ~ spl0_346 ),
inference(resolution,[],[f3477,f2694]) ).
fof(f47397,plain,
( spl0_1426
| ~ spl0_251
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f3791,f3476,f2681,f47395]) ).
fof(f47395,plain,
( spl0_1426
<=> ! [X41,X40,X42] :
( ~ class_Lattices_Olower__semilattice(X40)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X41,X42,X40),X42,X40) = X42
| ~ class_Lattices_Oupper__semilattice(X40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f3791,plain,
( ! [X40,X41,X42] :
( ~ class_Lattices_Olower__semilattice(X40)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X41,X42,X40),X42,X40) = X42
| ~ class_Lattices_Oupper__semilattice(X40) )
| ~ spl0_251
| ~ spl0_346 ),
inference(resolution,[],[f3477,f2682]) ).
fof(f47393,plain,
( spl0_1425
| ~ spl0_253
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f3790,f3476,f2689,f47391]) ).
fof(f47391,plain,
( spl0_1425
<=> ! [X38,X37,X39] :
( ~ class_Lattices_Olower__semilattice(X37)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X38,X39,X37),X39,X37) = X39
| ~ class_Lattices_Olattice(X37) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f3790,plain,
( ! [X38,X39,X37] :
( ~ class_Lattices_Olower__semilattice(X37)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X38,X39,X37),X39,X37) = X39
| ~ class_Lattices_Olattice(X37) )
| ~ spl0_253
| ~ spl0_346 ),
inference(resolution,[],[f3477,f2690]) ).
fof(f47389,plain,
( spl0_1424
| ~ spl0_201
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f3788,f3476,f2472,f47387]) ).
fof(f47387,plain,
( spl0_1424
<=> ! [X36] :
( ~ class_Lattices_Olower__semilattice(X36)
| c_HOL_Ozero__class_Ozero(X36) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oone__class_Oone(X36),c_HOL_Ozero__class_Ozero(X36),X36)
| ~ class_Ring__and__Field_Oordered__semidom(X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f3788,plain,
( ! [X36] :
( ~ class_Lattices_Olower__semilattice(X36)
| c_HOL_Ozero__class_Ozero(X36) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oone__class_Oone(X36),c_HOL_Ozero__class_Ozero(X36),X36)
| ~ class_Ring__and__Field_Oordered__semidom(X36) )
| ~ spl0_201
| ~ spl0_346 ),
inference(resolution,[],[f3477,f2473]) ).
fof(f47362,plain,
( spl0_1423
| ~ spl0_234
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f3712,f3448,f2613,f47360]) ).
fof(f47360,plain,
( spl0_1423
<=> ! [X13,X14] : ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X14)),tc_nat),X13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f3448,plain,
( spl0_339
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(c_Suc,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f3712,plain,
( ! [X14,X13] : ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X14)),tc_nat),X13))
| ~ spl0_234
| ~ spl0_339 ),
inference(forward_demodulation,[],[f3709,f350]) ).
fof(f350,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__Suc_0) ).
fof(f3709,plain,
( ! [X14,X13] : ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X13)),X14),tc_nat),X13))
| ~ spl0_234
| ~ spl0_339 ),
inference(resolution,[],[f3449,f2614]) ).
fof(f3449,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(c_Suc,X2)))
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2)) )
| ~ spl0_339 ),
inference(avatar_component_clause,[],[f3448]) ).
fof(f47358,plain,
( spl0_1422
| ~ spl0_233
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f3711,f3448,f2609,f47356]) ).
fof(f47356,plain,
( spl0_1422
<=> ! [X11,X12] : ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X12)),tc_nat),X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f2609,plain,
( spl0_233
<=> ! [X4,X3] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X3),tc_nat),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f3711,plain,
( ! [X11,X12] : ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X12)),tc_nat),X12))
| ~ spl0_233
| ~ spl0_339 ),
inference(forward_demodulation,[],[f3708,f351]) ).
fof(f351,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__Suc__right_0) ).
fof(f3708,plain,
( ! [X11,X12] : ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(c_Suc,X12)),tc_nat),X12))
| ~ spl0_233
| ~ spl0_339 ),
inference(resolution,[],[f3449,f2610]) ).
fof(f2610,plain,
( ! [X3,X4] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X3),tc_nat),X3))
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2609]) ).
fof(f47296,plain,
( ~ spl0_36
| spl0_1421
| ~ spl0_253
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f3678,f3430,f2689,f47294,f1676]) ).
fof(f47294,plain,
( spl0_1421
<=> ! [X14,X15] : hBOOL(hAPP(c_HOL_Oord__class_Oless(X14,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(X15,hAPP(c_Suc,X14),tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f3430,plain,
( spl0_335
<=> ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f3678,plain,
( ! [X14,X15] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X14,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(X15,hAPP(c_Suc,X14),tc_nat)))
| ~ class_Lattices_Olattice(tc_nat) )
| ~ spl0_253
| ~ spl0_335 ),
inference(resolution,[],[f3431,f2690]) ).
fof(f3431,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1)) )
| ~ spl0_335 ),
inference(avatar_component_clause,[],[f3430]) ).
fof(f47292,plain,
( spl0_1420
| ~ spl0_234
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f3633,f3406,f2613,f47290]) ).
fof(f47290,plain,
( spl0_1420
<=> ! [X9,X10] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X10)),tc_nat),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f3633,plain,
( ! [X10,X9] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X10)),tc_nat),X9))
| ~ spl0_234
| ~ spl0_329 ),
inference(forward_demodulation,[],[f3631,f350]) ).
fof(f3631,plain,
( ! [X10,X9] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X9)),X10),tc_nat),X9))
| ~ spl0_234
| ~ spl0_329 ),
inference(resolution,[],[f3407,f2614]) ).
fof(f47288,plain,
( spl0_1419
| ~ spl0_233
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f3632,f3406,f2609,f47286]) ).
fof(f47286,plain,
( spl0_1419
<=> ! [X8,X7] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X8)),tc_nat),X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f3632,plain,
( ! [X8,X7] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),X8)),tc_nat),X8))
| ~ spl0_233
| ~ spl0_329 ),
inference(forward_demodulation,[],[f3630,f351]) ).
fof(f3630,plain,
( ! [X8,X7] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X7),hAPP(c_Suc,X8)),tc_nat),X8))
| ~ spl0_233
| ~ spl0_329 ),
inference(resolution,[],[f3407,f2610]) ).
fof(f47284,plain,
( spl0_1418
| ~ spl0_294
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f3401,f3337,f3014,f47281]) ).
fof(f47281,plain,
( spl0_1418
<=> c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_nat),c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f3014,plain,
( spl0_294
<=> ! [X25,X5,X11] : c_Set_Oinsert(X11,X25,X5) = c_Set_Oinsert(X11,c_Set_Oinsert(X11,X25,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f3337,plain,
( spl0_328
<=> c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_nat),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f3401,plain,
( c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_nat),c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),tc_nat)
| ~ spl0_294
| ~ spl0_328 ),
inference(superposition,[],[f3015,f3339]) ).
fof(f3339,plain,
( c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_nat),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)
| ~ spl0_328 ),
inference(avatar_component_clause,[],[f3337]) ).
fof(f3015,plain,
( ! [X11,X5,X25] : c_Set_Oinsert(X11,X25,X5) = c_Set_Oinsert(X11,c_Set_Oinsert(X11,X25,X5),X5)
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f3014]) ).
fof(f47279,plain,
( spl0_1417
| ~ spl0_276
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f3258,f3123,f2938,f47277]) ).
fof(f47277,plain,
( spl0_1417
<=> ! [X2,X1] : hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),tc_nat),hAPP(c_Suc,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f3123,plain,
( spl0_306
<=> ! [X2,X1] : hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),tc_nat),hAPP(c_Suc,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f3258,plain,
( ! [X2,X1] : hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),tc_nat),hAPP(c_Suc,X1)))
| ~ spl0_276
| ~ spl0_306 ),
inference(resolution,[],[f3124,f2939]) ).
fof(f3124,plain,
( ! [X2,X1] : hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),tc_nat),hAPP(c_Suc,X1)))
| ~ spl0_306 ),
inference(avatar_component_clause,[],[f3123]) ).
fof(f47275,plain,
( spl0_1416
| ~ spl0_276
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3238,f3098,f2938,f47273]) ).
fof(f47273,plain,
( spl0_1416
<=> ! [X0,X1] : hBOOL(hAPP(c_lessequals(X0,tc_nat),hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f3098,plain,
( spl0_300
<=> ! [X1,X3] : hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f3238,plain,
( ! [X0,X1] : hBOOL(hAPP(c_lessequals(X0,tc_nat),hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0))))
| ~ spl0_276
| ~ spl0_300 ),
inference(resolution,[],[f3099,f2939]) ).
fof(f3099,plain,
( ! [X3,X1] : hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3))))
| ~ spl0_300 ),
inference(avatar_component_clause,[],[f3098]) ).
fof(f47271,plain,
( spl0_1415
| ~ spl0_276
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3235,f3094,f2938,f47269]) ).
fof(f47269,plain,
( spl0_1415
<=> ! [X0,X1] : hBOOL(hAPP(c_lessequals(X0,tc_nat),hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f3094,plain,
( spl0_299
<=> ! [X1,X3] : hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f3235,plain,
( ! [X0,X1] : hBOOL(hAPP(c_lessequals(X0,tc_nat),hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1))))
| ~ spl0_276
| ~ spl0_299 ),
inference(resolution,[],[f3095,f2939]) ).
fof(f3095,plain,
( ! [X3,X1] : hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1))))
| ~ spl0_299 ),
inference(avatar_component_clause,[],[f3094]) ).
fof(f47244,plain,
( spl0_1414
| ~ spl0_158
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2458,f2425,f2276,f47242]) ).
fof(f47242,plain,
( spl0_1414
<=> ! [X2,X1,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),X3,tc_fun(X1,X2)) = X3
| ~ class_Lattices_Obounded__lattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f2276,plain,
( spl0_158
<=> ! [X57,X56] :
( ~ class_Lattices_Obounded__lattice(X57)
| class_Lattices_Obounded__lattice(tc_fun(X56,X57)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f2425,plain,
( spl0_192
<=> ! [X5,X11] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X5),X11,X5) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f2458,plain,
( ! [X2,X3,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),X3,tc_fun(X1,X2)) = X3
| ~ class_Lattices_Obounded__lattice(X2) )
| ~ spl0_158
| ~ spl0_192 ),
inference(resolution,[],[f2426,f2277]) ).
fof(f2277,plain,
( ! [X56,X57] :
( class_Lattices_Obounded__lattice(tc_fun(X56,X57))
| ~ class_Lattices_Obounded__lattice(X57) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f2276]) ).
fof(f2426,plain,
( ! [X11,X5] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X5),X11,X5) = X11 )
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f2425]) ).
fof(f47240,plain,
( spl0_1413
| ~ spl0_158
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2452,f2421,f2276,f47238]) ).
fof(f47238,plain,
( spl0_1413
<=> ! [X2,X1,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,X3)),tc_fun(X2,X3)) = X1
| ~ class_Lattices_Obounded__lattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f2421,plain,
( spl0_191
<=> ! [X5,X11] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Orderings_Obot__class_Obot(X5),X5) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f2452,plain,
( ! [X2,X3,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,X3)),tc_fun(X2,X3)) = X1
| ~ class_Lattices_Obounded__lattice(X3) )
| ~ spl0_158
| ~ spl0_191 ),
inference(resolution,[],[f2422,f2277]) ).
fof(f2422,plain,
( ! [X11,X5] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Orderings_Obot__class_Obot(X5),X5) = X11 )
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f2421]) ).
fof(f45980,plain,
( spl0_1412
| ~ spl0_187
| ~ spl0_304
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f4650,f4551,f3114,f2404,f45978]) ).
fof(f45978,plain,
( spl0_1412
<=> ! [X9,X8] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X9) != X8
| X8 = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f4551,plain,
( spl0_420
<=> ! [X11,X16,X12] :
( X12 = X16
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X12) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f4650,plain,
( ! [X8,X9] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X9) != X8
| X8 = X9 )
| ~ spl0_187
| ~ spl0_304
| ~ spl0_420 ),
inference(forward_demodulation,[],[f4644,f3116]) ).
fof(f4644,plain,
( ! [X8,X9] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X9) != X8
| X8 = X9 )
| ~ spl0_187
| ~ spl0_420 ),
inference(superposition,[],[f4552,f2405]) ).
fof(f4552,plain,
( ! [X11,X16,X12] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X12) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X16)
| X12 = X16 )
| ~ spl0_420 ),
inference(avatar_component_clause,[],[f4551]) ).
fof(f45976,plain,
( spl0_1411
| ~ spl0_186
| ~ spl0_304
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f4637,f4547,f3114,f2400,f45974]) ).
fof(f45974,plain,
( spl0_1411
<=> ! [X0,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Orderings_Obot__class_Obot(tc_nat)) != X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f4547,plain,
( spl0_419
<=> ! [X2,X0,X1] :
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f4637,plain,
( ! [X0,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Orderings_Obot__class_Obot(tc_nat)) != X0
| X0 = X1 )
| ~ spl0_186
| ~ spl0_304
| ~ spl0_419 ),
inference(forward_demodulation,[],[f4628,f3116]) ).
fof(f4628,plain,
( ! [X0,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) != X0
| X0 = X1 )
| ~ spl0_186
| ~ spl0_419 ),
inference(superposition,[],[f4548,f2401]) ).
fof(f4548,plain,
( ! [X2,X0,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0)
| X1 = X2 )
| ~ spl0_419 ),
inference(avatar_component_clause,[],[f4547]) ).
fof(f45972,plain,
( spl0_1410
| ~ spl0_80
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f4169,f3613,f1896,f45970]) ).
fof(f45970,plain,
( spl0_1410
<=> ! [X9,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_Int_Oint) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f3613,plain,
( spl0_378
<=> ! [X11,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f4169,plain,
( ! [X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_Int_Oint) = c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_Int_Oint),tc_Int_Oint)
| ~ spl0_80
| ~ spl0_378 ),
inference(resolution,[],[f3614,f1898]) ).
fof(f3614,plain,
( ! [X11,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),X5) )
| ~ spl0_378 ),
inference(avatar_component_clause,[],[f3613]) ).
fof(f45968,plain,
( spl0_1409
| ~ spl0_42
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f4168,f3613,f1706,f45966]) ).
fof(f45966,plain,
( spl0_1409
<=> ! [X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f1706,plain,
( spl0_42
<=> class_Lattices_Oupper__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f4168,plain,
( ! [X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_bool),tc_bool)
| ~ spl0_42
| ~ spl0_378 ),
inference(resolution,[],[f3614,f1708]) ).
fof(f1708,plain,
( class_Lattices_Oupper__semilattice(tc_bool)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f1706]) ).
fof(f45964,plain,
( spl0_1408
| ~ spl0_22
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f4166,f3613,f1606,f45962]) ).
fof(f45962,plain,
( spl0_1408
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f4166,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat)
| ~ spl0_22
| ~ spl0_378 ),
inference(resolution,[],[f3614,f1608]) ).
fof(f1608,plain,
( class_Lattices_Oupper__semilattice(tc_nat)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1606]) ).
fof(f45820,plain,
( spl0_1407
| ~ spl0_113
| ~ spl0_138
| ~ spl0_357 ),
inference(avatar_split_clause,[],[f3932,f3526,f2186,f2061,f45818]) ).
fof(f45818,plain,
( spl0_1407
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),X0),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f2061,plain,
( spl0_113
<=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f3526,plain,
( spl0_357
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),c_HOL_Ozero__class_Ozero(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f3932,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),X0),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) )
| ~ spl0_138
| ~ spl0_357 ),
inference(resolution,[],[f3527,f2188]) ).
fof(f3527,plain,
( ! [X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),c_HOL_Ozero__class_Ozero(X5)) )
| ~ spl0_357 ),
inference(avatar_component_clause,[],[f3526]) ).
fof(f45816,plain,
( spl0_1406
| ~ spl0_100
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f3927,f3518,f1996,f45814]) ).
fof(f45814,plain,
( spl0_1406
<=> ! [X9,X8] : c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f1996,plain,
( spl0_100
<=> class_Lattices_Olattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f3518,plain,
( spl0_355
<=> ! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f3927,plain,
( ! [X8,X9] : c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_Int_Oint),tc_Int_Oint)
| ~ spl0_100
| ~ spl0_355 ),
inference(resolution,[],[f3519,f1998]) ).
fof(f1998,plain,
( class_Lattices_Olattice(tc_Int_Oint)
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1996]) ).
fof(f3519,plain,
( ! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5) )
| ~ spl0_355 ),
inference(avatar_component_clause,[],[f3518]) ).
fof(f45812,plain,
( spl0_1405
| ~ spl0_47
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f3926,f3518,f1731,f45810]) ).
fof(f45810,plain,
( spl0_1405
<=> ! [X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_bool),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f1731,plain,
( spl0_47
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f3926,plain,
( ! [X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_bool),tc_bool)
| ~ spl0_47
| ~ spl0_355 ),
inference(resolution,[],[f3519,f1733]) ).
fof(f1733,plain,
( class_Lattices_Olattice(tc_bool)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1731]) ).
fof(f45808,plain,
( spl0_1404
| ~ spl0_36
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f3924,f3518,f1676,f45806]) ).
fof(f45806,plain,
( spl0_1404
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f3924,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat)
| ~ spl0_36
| ~ spl0_355 ),
inference(resolution,[],[f3519,f1678]) ).
fof(f1678,plain,
( class_Lattices_Olattice(tc_nat)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1676]) ).
fof(f45694,plain,
( spl0_1403
| ~ spl0_188
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f3824,f3484,f2408,f45692]) ).
fof(f45692,plain,
( spl0_1403
<=> ! [X27,X26] :
( ~ class_Lattices_Olower__semilattice(X26)
| c_Orderings_Obot__class_Obot(X26) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X26),X27,X26)
| ~ class_Orderings_Obot(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f3824,plain,
( ! [X26,X27] :
( ~ class_Lattices_Olower__semilattice(X26)
| c_Orderings_Obot__class_Obot(X26) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X26),X27,X26)
| ~ class_Orderings_Obot(X26) )
| ~ spl0_188
| ~ spl0_348 ),
inference(resolution,[],[f3485,f2409]) ).
fof(f45690,plain,
( spl0_1402
| ~ spl0_188
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f3783,f3476,f2408,f45688]) ).
fof(f45688,plain,
( spl0_1402
<=> ! [X27,X26] :
( ~ class_Lattices_Olower__semilattice(X26)
| c_Orderings_Obot__class_Obot(X26) = c_Lattices_Olower__semilattice__class_Oinf(X27,c_Orderings_Obot__class_Obot(X26),X26)
| ~ class_Orderings_Obot(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f3783,plain,
( ! [X26,X27] :
( ~ class_Lattices_Olower__semilattice(X26)
| c_Orderings_Obot__class_Obot(X26) = c_Lattices_Olower__semilattice__class_Oinf(X27,c_Orderings_Obot__class_Obot(X26),X26)
| ~ class_Orderings_Obot(X26) )
| ~ spl0_188
| ~ spl0_346 ),
inference(resolution,[],[f3477,f2409]) ).
fof(f45686,plain,
( spl0_1401
| ~ spl0_333
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f3723,f3452,f3422,f45684]) ).
fof(f45684,plain,
( spl0_1401
<=> ! [X11,X10] :
( hBOOL(hAPP(c_lessequals(X10,tc_nat),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f3452,plain,
( spl0_340
<=> ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(c_Suc,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f3723,plain,
( ! [X10,X11] :
( hBOOL(hAPP(c_lessequals(X10,tc_nat),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),X10)) )
| ~ spl0_333
| ~ spl0_340 ),
inference(resolution,[],[f3453,f3423]) ).
fof(f3453,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(c_Suc,X2)))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2)) )
| ~ spl0_340 ),
inference(avatar_component_clause,[],[f3452]) ).
fof(f45682,plain,
( spl0_1400
| ~ spl0_332
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f3701,f3448,f3418,f45680]) ).
fof(f45680,plain,
( spl0_1400
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f3418,plain,
( spl0_332
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f3701,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1)) )
| ~ spl0_332
| ~ spl0_339 ),
inference(resolution,[],[f3449,f3419]) ).
fof(f3419,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,X1)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2)) )
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f3418]) ).
fof(f45678,plain,
( spl0_1399
| ~ spl0_138
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f3685,f3434,f2186,f45676]) ).
fof(f45676,plain,
( spl0_1399
<=> ! [X0] : hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),X0) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f3434,plain,
( spl0_336
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f3685,plain,
( ! [X0] : hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),X0) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),X0)
| ~ spl0_138
| ~ spl0_336 ),
inference(resolution,[],[f3435,f2188]) ).
fof(f3435,plain,
( ! [X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X6) )
| ~ spl0_336 ),
inference(avatar_component_clause,[],[f3434]) ).
fof(f45674,plain,
( spl0_1398
| ~ spl0_329
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f3652,f3418,f3406,f45672]) ).
fof(f45672,plain,
( spl0_1398
<=> ! [X9,X8] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X8,tc_nat),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,tc_nat),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f3652,plain,
( ! [X8,X9] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X8,tc_nat),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,tc_nat),X8)) )
| ~ spl0_329
| ~ spl0_332 ),
inference(resolution,[],[f3419,f3407]) ).
fof(f45670,plain,
( spl0_1397
| ~ spl0_282
| ~ spl0_304
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f3286,f3127,f3114,f2962,f45668]) ).
fof(f2962,plain,
( spl0_282
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f3286,plain,
( ! [X10,X9] :
( c_Orderings_Obot__class_Obot(tc_nat) = X10
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X9) != X9 )
| ~ spl0_282
| ~ spl0_304
| ~ spl0_307 ),
inference(forward_demodulation,[],[f3273,f3116]) ).
fof(f3273,plain,
( ! [X10,X9] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X9) != X9
| c_HOL_Ozero__class_Ozero(tc_nat) = X10 )
| ~ spl0_282
| ~ spl0_307 ),
inference(superposition,[],[f2963,f3128]) ).
fof(f2963,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X2 )
| ~ spl0_282 ),
inference(avatar_component_clause,[],[f2962]) ).
fof(f45666,plain,
( spl0_1396
| ~ spl0_180
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2869,f2681,f2367,f45664]) ).
fof(f45664,plain,
( spl0_1396
<=> ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_fun(X2,tc_bool)),X1))
| ~ class_Lattices_Oupper__semilattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f2869,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_fun(X2,tc_bool)),X1))
| ~ class_Lattices_Oupper__semilattice(tc_fun(X2,tc_bool)) )
| ~ spl0_180
| ~ spl0_251 ),
inference(superposition,[],[f2682,f2368]) ).
fof(f45662,plain,
( spl0_1395
| ~ spl0_175
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2761,f2561,f2347,f45660]) ).
fof(f45660,plain,
( spl0_1395
<=> ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_fun(X2,tc_bool)),X1))
| ~ class_Lattices_Olattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f2347,plain,
( spl0_175
<=> ! [X25,X5] : c_Lattices_Olower__semilattice__class_Oinf(X25,X25,tc_fun(X5,tc_bool)) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f2761,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_fun(X2,tc_bool)),X1))
| ~ class_Lattices_Olattice(tc_fun(X2,tc_bool)) )
| ~ spl0_175
| ~ spl0_221 ),
inference(superposition,[],[f2562,f2348]) ).
fof(f2348,plain,
( ! [X5,X25] : c_Lattices_Olower__semilattice__class_Oinf(X25,X25,tc_fun(X5,tc_bool)) = X25
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f2347]) ).
fof(f45658,plain,
( spl0_1394
| ~ spl0_175
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2753,f2553,f2347,f45656]) ).
fof(f45656,plain,
( spl0_1394
<=> ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_fun(X2,tc_bool)),X1))
| ~ class_Lattices_Olower__semilattice(tc_fun(X2,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f2753,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_fun(X2,tc_bool)),X1))
| ~ class_Lattices_Olower__semilattice(tc_fun(X2,tc_bool)) )
| ~ spl0_175
| ~ spl0_219 ),
inference(superposition,[],[f2554,f2348]) ).
fof(f45654,plain,
( spl0_1393
| ~ spl0_726
| ~ spl0_1390 ),
inference(avatar_split_clause,[],[f44292,f44173,f11880,f45651]) ).
fof(f11880,plain,
( spl0_726
<=> ! [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_726])]) ).
fof(f44173,plain,
( spl0_1390
<=> ! [X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f44292,plain,
( c_HOL_Oone__class_Oone(tc_nat) = hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| ~ spl0_726
| ~ spl0_1390 ),
inference(superposition,[],[f44174,f11881]) ).
fof(f11881,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) = X0
| ~ spl0_726 ),
inference(avatar_component_clause,[],[f11880]) ).
fof(f44174,plain,
( ! [X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))) = X1
| ~ spl0_1390 ),
inference(avatar_component_clause,[],[f44173]) ).
fof(f44230,plain,
( spl0_1392
| ~ spl0_100
| ~ spl0_1273 ),
inference(avatar_split_clause,[],[f41886,f36495,f1996,f44228]) ).
fof(f44228,plain,
( spl0_1392
<=> ! [X9,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,X8,tc_fun(X9,tc_Int_Oint)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f36495,plain,
( spl0_1273
<=> ! [X2,X1,X3] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,X3)) = X1
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f41886,plain,
( ! [X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(X8,X8,tc_fun(X9,tc_Int_Oint)) = X8
| ~ spl0_100
| ~ spl0_1273 ),
inference(resolution,[],[f36496,f1998]) ).
fof(f36496,plain,
( ! [X2,X3,X1] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,X3)) = X1 )
| ~ spl0_1273 ),
inference(avatar_component_clause,[],[f36495]) ).
fof(f44179,plain,
( spl0_1391
| ~ spl0_186
| ~ spl0_209
| ~ spl0_304
| ~ spl0_566 ),
inference(avatar_split_clause,[],[f7833,f7496,f3114,f2504,f2400,f44177]) ).
fof(f44177,plain,
( spl0_1391
<=> ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f7833,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))),X0) = X0
| ~ spl0_186
| ~ spl0_209
| ~ spl0_304
| ~ spl0_566 ),
inference(forward_demodulation,[],[f7832,f3166]) ).
fof(f3166,plain,
( ! [X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_Orderings_Obot__class_Obot(tc_nat)) = X3
| ~ spl0_186
| ~ spl0_304 ),
inference(superposition,[],[f2401,f3116]) ).
fof(f7832,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))),X0)
| ~ spl0_209
| ~ spl0_304
| ~ spl0_566 ),
inference(forward_demodulation,[],[f7784,f3116]) ).
fof(f7784,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),X0)
| ~ spl0_209
| ~ spl0_566 ),
inference(superposition,[],[f7497,f2505]) ).
fof(f44175,plain,
( spl0_1390
| ~ spl0_186
| ~ spl0_210
| ~ spl0_304
| ~ spl0_565 ),
inference(avatar_split_clause,[],[f7772,f7492,f3114,f2508,f2400,f44173]) ).
fof(f2508,plain,
( spl0_210
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f7772,plain,
( ! [X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))) = X1
| ~ spl0_186
| ~ spl0_210
| ~ spl0_304
| ~ spl0_565 ),
inference(forward_demodulation,[],[f7771,f3166]) ).
fof(f7771,plain,
( ! [X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_Orderings_Obot__class_Obot(tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)))
| ~ spl0_210
| ~ spl0_304
| ~ spl0_565 ),
inference(forward_demodulation,[],[f7724,f3116]) ).
fof(f7724,plain,
( ! [X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ spl0_210
| ~ spl0_565 ),
inference(superposition,[],[f7493,f2509]) ).
fof(f2509,plain,
( ! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_210 ),
inference(avatar_component_clause,[],[f2508]) ).
fof(f44171,plain,
( spl0_1389
| ~ spl0_178
| ~ spl0_474 ),
inference(avatar_split_clause,[],[f6006,f5008,f2359,f44169]) ).
fof(f44169,plain,
( spl0_1389
<=> ! [X6,X5] :
( ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X6,X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f2359,plain,
( spl0_178
<=> ! [X5,X11] :
( ~ class_Orderings_Oorder(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f6006,plain,
( ! [X6,X5] :
( ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X6,X6,X5) )
| ~ spl0_178
| ~ spl0_474 ),
inference(duplicate_literal_removal,[],[f5973]) ).
fof(f5973,plain,
( ! [X6,X5] :
( ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X6,X6,X5)
| ~ class_Orderings_Oorder(X5) )
| ~ spl0_178
| ~ spl0_474 ),
inference(resolution,[],[f5009,f2360]) ).
fof(f2360,plain,
( ! [X11,X5] :
( hBOOL(hAPP(c_lessequals(X11,X5),X11))
| ~ class_Orderings_Oorder(X5) )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f2359]) ).
fof(f44167,plain,
( spl0_1388
| ~ spl0_178
| ~ spl0_470 ),
inference(avatar_split_clause,[],[f5928,f4991,f2359,f44165]) ).
fof(f5928,plain,
( ! [X6,X5] :
( ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X6,X6,X5) )
| ~ spl0_178
| ~ spl0_470 ),
inference(duplicate_literal_removal,[],[f5895]) ).
fof(f5895,plain,
( ! [X6,X5] :
( ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X6,X6,X5)
| ~ class_Orderings_Oorder(X5) )
| ~ spl0_178
| ~ spl0_470 ),
inference(resolution,[],[f4992,f2360]) ).
fof(f44136,plain,
( ~ spl0_23
| spl0_1387
| ~ spl0_149
| ~ spl0_433 ),
inference(avatar_split_clause,[],[f5090,f4825,f2238,f44134,f1611]) ).
fof(f2238,plain,
( spl0_149
<=> ! [X2] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f5090,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_nat)))
| ~ class_Lattices_Olower__semilattice(tc_nat) )
| ~ spl0_149
| ~ spl0_433 ),
inference(resolution,[],[f4826,f2239]) ).
fof(f2239,plain,
( ! [X2] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X2))
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f2238]) ).
fof(f44132,plain,
( spl0_1386
| ~ spl0_36
| ~ spl0_1273 ),
inference(avatar_split_clause,[],[f41883,f36495,f1676,f44130]) ).
fof(f44130,plain,
( spl0_1386
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,tc_nat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f41883,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,tc_nat)) = X0
| ~ spl0_36
| ~ spl0_1273 ),
inference(resolution,[],[f36496,f1678]) ).
fof(f44128,plain,
( spl0_1385
| ~ spl0_194
| ~ spl0_304
| ~ spl0_412 ),
inference(avatar_split_clause,[],[f4511,f4427,f3114,f2433,f44126]) ).
fof(f44126,plain,
( spl0_1385
<=> ! [X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),c_Orderings_Obot__class_Obot(tc_nat)))
| c_Orderings_Obot__class_Obot(tc_nat) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f2433,plain,
( spl0_194
<=> ! [X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f4427,plain,
( spl0_412
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f4511,plain,
( ! [X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),c_Orderings_Obot__class_Obot(tc_nat)))
| c_Orderings_Obot__class_Obot(tc_nat) != X1 )
| ~ spl0_194
| ~ spl0_304
| ~ spl0_412 ),
inference(forward_demodulation,[],[f4505,f3116]) ).
fof(f4505,plain,
( ! [X1] :
( c_Orderings_Obot__class_Obot(tc_nat) != X1
| hBOOL(hAPP(c_lessequals(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) )
| ~ spl0_194
| ~ spl0_412 ),
inference(superposition,[],[f4428,f2434]) ).
fof(f2434,plain,
( ! [X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f2433]) ).
fof(f4428,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2)) )
| ~ spl0_412 ),
inference(avatar_component_clause,[],[f4427]) ).
fof(f44124,plain,
( spl0_1384
| ~ spl0_195
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f4140,f3597,f2437,f44122]) ).
fof(f44122,plain,
( spl0_1384
<=> ! [X5] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X5,hAPP(c_Suc,X5),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f2437,plain,
( spl0_195
<=> ! [X6,X25,X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) != c_Set_Oinsert(X6,X25,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f3597,plain,
( spl0_374
<=> ! [X1] : c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X1),tc_nat) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f4140,plain,
( ! [X5] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X5,hAPP(c_Suc,X5),tc_nat)
| ~ spl0_195
| ~ spl0_374 ),
inference(superposition,[],[f2438,f3598]) ).
fof(f3598,plain,
( ! [X1] : c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X1),tc_nat) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)
| ~ spl0_374 ),
inference(avatar_component_clause,[],[f3597]) ).
fof(f2438,plain,
( ! [X6,X5,X25] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) != c_Set_Oinsert(X6,X25,X5)
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f2437]) ).
fof(f44120,plain,
( spl0_1383
| ~ spl0_188
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f4113,f3593,f2408,f44118]) ).
fof(f44118,plain,
( spl0_1383
<=> ! [X29,X28] :
( ~ class_Lattices_Oupper__semilattice(X28)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X28),X29,X28) = X29
| ~ class_Orderings_Obot(X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f4113,plain,
( ! [X28,X29] :
( ~ class_Lattices_Oupper__semilattice(X28)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X28),X29,X28) = X29
| ~ class_Orderings_Obot(X28) )
| ~ spl0_188
| ~ spl0_373 ),
inference(resolution,[],[f3594,f2409]) ).
fof(f44116,plain,
( spl0_1382
| ~ spl0_188
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4060,f3585,f2408,f44114]) ).
fof(f4060,plain,
( ! [X28,X29] :
( ~ class_Lattices_Oupper__semilattice(X28)
| c_Lattices_Oupper__semilattice__class_Osup(X29,c_Orderings_Obot__class_Obot(X28),X28) = X29
| ~ class_Orderings_Obot(X28) )
| ~ spl0_188
| ~ spl0_371 ),
inference(resolution,[],[f3586,f2409]) ).
fof(f44103,plain,
( ~ spl0_34
| spl0_1381
| ~ spl0_184
| ~ spl0_304
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f3699,f3438,f3114,f2392,f44101,f1666]) ).
fof(f44101,plain,
( spl0_1381
<=> ! [X2] : ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),c_Orderings_Obot__class_Obot(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f2392,plain,
( spl0_184
<=> ! [X2] : hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f3438,plain,
( spl0_337
<=> ! [X12,X5,X11] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f3699,plain,
( ! [X2] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),c_Orderings_Obot__class_Obot(tc_nat)))
| ~ class_Orderings_Opreorder(tc_nat) )
| ~ spl0_184
| ~ spl0_304
| ~ spl0_337 ),
inference(forward_demodulation,[],[f3690,f3116]) ).
fof(f3690,plain,
( ! [X2] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ class_Orderings_Opreorder(tc_nat) )
| ~ spl0_184
| ~ spl0_337 ),
inference(resolution,[],[f3439,f2393]) ).
fof(f2393,plain,
( ! [X2] : hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,X2)))
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f2392]) ).
fof(f3439,plain,
( ! [X11,X5,X12] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X11))
| ~ class_Orderings_Opreorder(X5) )
| ~ spl0_337 ),
inference(avatar_component_clause,[],[f3438]) ).
fof(f44099,plain,
( spl0_1380
| ~ spl0_306
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f3649,f3418,f3123,f44097]) ).
fof(f44097,plain,
( spl0_1380
<=> ! [X2,X3] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f3649,plain,
( ! [X2,X3] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X3)))
| ~ spl0_306
| ~ spl0_332 ),
inference(resolution,[],[f3419,f3124]) ).
fof(f44095,plain,
( spl0_1379
| ~ spl0_41
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f3311,f3186,f1701,f44093]) ).
fof(f44093,plain,
( spl0_1379
<=> ! [X0] : c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool),tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f3186,plain,
( spl0_315
<=> ! [X6,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f3311,plain,
( ! [X0] : c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool),tc_bool) = X0
| ~ spl0_41
| ~ spl0_315 ),
inference(resolution,[],[f3187,f1703]) ).
fof(f3187,plain,
( ! [X6,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) = X6 )
| ~ spl0_315 ),
inference(avatar_component_clause,[],[f3186]) ).
fof(f44091,plain,
( spl0_1378
| ~ spl0_119
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3256,f3119,f2091,f44089]) ).
fof(f44089,plain,
( spl0_1378
<=> ! [X4,X5] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Finite__Set_Osetprod(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f2091,plain,
( spl0_119
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f3119,plain,
( spl0_305
<=> ! [X20,X5,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| c_HOL_Oone__class_Oone(X5) = c_Finite__Set_Osetprod(X10,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f3256,plain,
( ! [X4,X5] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Finite__Set_Osetprod(X4,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5,tc_Complex_Ocomplex)
| ~ spl0_119
| ~ spl0_305 ),
inference(resolution,[],[f3120,f2093]) ).
fof(f2093,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex)
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f2091]) ).
fof(f3120,plain,
( ! [X10,X5,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| c_HOL_Oone__class_Oone(X5) = c_Finite__Set_Osetprod(X10,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X5) )
| ~ spl0_305 ),
inference(avatar_component_clause,[],[f3119]) ).
fof(f44087,plain,
( spl0_1377
| ~ spl0_73
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3255,f3119,f1861,f44085]) ).
fof(f44085,plain,
( spl0_1377
<=> ! [X2,X3] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Finite__Set_Osetprod(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f1861,plain,
( spl0_73
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f3255,plain,
( ! [X2,X3] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Finite__Set_Osetprod(X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3,tc_Int_Oint)
| ~ spl0_73
| ~ spl0_305 ),
inference(resolution,[],[f3120,f1863]) ).
fof(f1863,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint)
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f1861]) ).
fof(f44083,plain,
( spl0_1376
| ~ spl0_100
| ~ spl0_1270 ),
inference(avatar_split_clause,[],[f41877,f35889,f1996,f44081]) ).
fof(f44081,plain,
( spl0_1376
<=> ! [X9,X8] : c_Lattices_Olower__semilattice__class_Oinf(X8,X8,tc_fun(X9,tc_Int_Oint)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f35889,plain,
( spl0_1270
<=> ! [X2,X1,X3] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,X3)) = X1
| ~ class_Lattices_Olattice(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f41877,plain,
( ! [X8,X9] : c_Lattices_Olower__semilattice__class_Oinf(X8,X8,tc_fun(X9,tc_Int_Oint)) = X8
| ~ spl0_100
| ~ spl0_1270 ),
inference(resolution,[],[f35890,f1998]) ).
fof(f35890,plain,
( ! [X2,X3,X1] :
( ~ class_Lattices_Olattice(X3)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,X3)) = X1 )
| ~ spl0_1270 ),
inference(avatar_component_clause,[],[f35889]) ).
fof(f44079,plain,
( spl0_1375
| ~ spl0_17
| ~ spl0_305 ),
inference(avatar_split_clause,[],[f3254,f3119,f1581,f44077]) ).
fof(f44077,plain,
( spl0_1375
<=> ! [X0,X1] : c_HOL_Oone__class_Oone(tc_nat) = c_Finite__Set_Osetprod(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f1581,plain,
( spl0_17
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f3254,plain,
( ! [X0,X1] : c_HOL_Oone__class_Oone(tc_nat) = c_Finite__Set_Osetprod(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1,tc_nat)
| ~ spl0_17
| ~ spl0_305 ),
inference(resolution,[],[f3120,f1583]) ).
fof(f1583,plain,
( class_OrderedGroup_Ocomm__monoid__mult(tc_nat)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f1581]) ).
fof(f44005,plain,
( spl0_1374
| ~ spl0_121
| ~ spl0_113
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f3245,f3106,f2061,f2101,f44003]) ).
fof(f44003,plain,
( spl0_1374
<=> ! [X0] : hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f2101,plain,
( spl0_121
<=> class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f3106,plain,
( spl0_302
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f3245,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex)
| hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),X0)) = X0 )
| ~ spl0_113
| ~ spl0_302 ),
inference(resolution,[],[f3107,f2063]) ).
fof(f2063,plain,
( class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f2061]) ).
fof(f3107,plain,
( ! [X6,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ class_Ring__and__Field_Odivision__ring(X5)
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)) = X6 )
| ~ spl0_302 ),
inference(avatar_component_clause,[],[f3106]) ).
fof(f44001,plain,
( spl0_1373
| ~ spl0_260
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3025,f2938,f2717,f43999]) ).
fof(f43999,plain,
( spl0_1373
<=> ! [X0] : hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),v_i),X0),tc_nat),v_n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f2717,plain,
( spl0_260
<=> ! [X0] : hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),v_i),X0),tc_nat),v_n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f3025,plain,
( ! [X0] : hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),v_i),X0),tc_nat),v_n))
| ~ spl0_260
| ~ spl0_276 ),
inference(resolution,[],[f2939,f2718]) ).
fof(f2718,plain,
( ! [X0] : hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),v_i),X0),tc_nat),v_n))
| ~ spl0_260 ),
inference(avatar_component_clause,[],[f2717]) ).
fof(f43763,plain,
( spl0_1372
| ~ spl0_36
| ~ spl0_1270 ),
inference(avatar_split_clause,[],[f41874,f35889,f1676,f43761]) ).
fof(f43761,plain,
( spl0_1372
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X1,tc_nat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f41874,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X1,tc_nat)) = X0
| ~ spl0_36
| ~ spl0_1270 ),
inference(resolution,[],[f35890,f1678]) ).
fof(f42289,plain,
( spl0_1371
| ~ spl0_304
| ~ spl0_1353 ),
inference(avatar_split_clause,[],[f41813,f41810,f3114,f42287]) ).
fof(f42287,plain,
( spl0_1371
<=> ! [X2] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),c_Orderings_Obot__class_Obot(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f41810,plain,
( spl0_1353
<=> ! [X2] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f41813,plain,
( ! [X2] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),c_Orderings_Obot__class_Obot(tc_nat))
| ~ spl0_304
| ~ spl0_1353 ),
inference(forward_demodulation,[],[f41811,f3116]) ).
fof(f41811,plain,
( ! [X2] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_1353 ),
inference(avatar_component_clause,[],[f41810]) ).
fof(f42285,plain,
( spl0_1370
| ~ spl0_304
| ~ spl0_1352 ),
inference(avatar_split_clause,[],[f41808,f41805,f3114,f42283]) ).
fof(f42283,plain,
( spl0_1370
<=> ! [X1] : c_HOL_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Orderings_Obot__class_Obot(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f41805,plain,
( spl0_1352
<=> ! [X1] : c_HOL_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f41808,plain,
( ! [X1] : c_HOL_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_Orderings_Obot__class_Obot(tc_nat))
| ~ spl0_304
| ~ spl0_1352 ),
inference(forward_demodulation,[],[f41806,f3116]) ).
fof(f41806,plain,
( ! [X1] : c_HOL_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_1352 ),
inference(avatar_component_clause,[],[f41805]) ).
fof(f42281,plain,
( spl0_1369
| ~ spl0_304
| ~ spl0_1351 ),
inference(avatar_split_clause,[],[f41803,f41800,f3114,f42279]) ).
fof(f42279,plain,
( spl0_1369
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f41800,plain,
( spl0_1351
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f41803,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X0),c_Orderings_Obot__class_Obot(tc_nat))
| ~ spl0_304
| ~ spl0_1351 ),
inference(forward_demodulation,[],[f41801,f3116]) ).
fof(f41801,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_1351 ),
inference(avatar_component_clause,[],[f41800]) ).
fof(f41899,plain,
( spl0_1368
| ~ spl0_304
| ~ spl0_1332 ),
inference(avatar_split_clause,[],[f41465,f41462,f3114,f41897]) ).
fof(f41897,plain,
( spl0_1368
<=> ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f41462,plain,
( spl0_1332
<=> ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f41465,plain,
( ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_304
| ~ spl0_1332 ),
inference(forward_demodulation,[],[f41463,f3116]) ).
fof(f41463,plain,
( ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_1332 ),
inference(avatar_component_clause,[],[f41462]) ).
fof(f41882,plain,
( ~ spl0_1367
| ~ spl0_205
| spl0_1366 ),
inference(avatar_split_clause,[],[f41867,f41863,f2488,f41879]) ).
fof(f41879,plain,
( spl0_1367
<=> class_Ring__and__Field_Oordered__semidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f2488,plain,
( spl0_205
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Oone__class_Oone(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f41863,plain,
( spl0_1366
<=> hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f41867,plain,
( ~ class_Ring__and__Field_Oordered__semidom(tc_Complex_Ocomplex)
| ~ spl0_205
| spl0_1366 ),
inference(resolution,[],[f41864,f2489]) ).
fof(f2489,plain,
( ! [X5] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Oone__class_Oone(X5)))
| ~ class_Ring__and__Field_Oordered__semidom(X5) )
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f2488]) ).
fof(f41864,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)))
| spl0_1366 ),
inference(avatar_component_clause,[],[f41863]) ).
fof(f41866,plain,
( ~ spl0_1365
| spl0_1366
| ~ spl0_213
| ~ spl0_413 ),
inference(avatar_split_clause,[],[f4521,f4433,f2520,f41863,f41859]) ).
fof(f41859,plain,
( spl0_1365
<=> class_Ring__and__Field_Oordered__idom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f2520,plain,
( spl0_213
<=> ! [X2] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f4433,plain,
( spl0_413
<=> ! [X5,X11] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_Orderings_Obot__class_Obot(tc_nat))))
| ~ class_Ring__and__Field_Oordered__idom(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f4521,plain,
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)))
| ~ class_Ring__and__Field_Oordered__idom(tc_Complex_Ocomplex)
| ~ spl0_213
| ~ spl0_413 ),
inference(superposition,[],[f4434,f2521]) ).
fof(f2521,plain,
( ! [X2] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X2)
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2520]) ).
fof(f4434,plain,
( ! [X11,X5] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_Orderings_Obot__class_Obot(tc_nat))))
| ~ class_Ring__and__Field_Oordered__idom(X5) )
| ~ spl0_413 ),
inference(avatar_component_clause,[],[f4433]) ).
fof(f41857,plain,
( spl0_1364
| ~ spl0_167
| ~ spl0_408 ),
inference(avatar_split_clause,[],[f4460,f4283,f2314,f41855]) ).
fof(f41855,plain,
( spl0_1364
<=> ! [X6,X4,X5,X3] : hBOOL(hAPP(c_Set_Oinsert(X4,c_Set_Oinsert(X3,X5,X6),X6),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f2314,plain,
( spl0_167
<=> ! [X25,X5,X11] : hBOOL(hAPP(c_Set_Oinsert(X11,X25,X5),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f4283,plain,
( spl0_408
<=> ! [X11,X12,X5,X25] : c_Set_Oinsert(X11,c_Set_Oinsert(X12,X25,X5),X5) = c_Set_Oinsert(X12,c_Set_Oinsert(X11,X25,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f4460,plain,
( ! [X3,X6,X4,X5] : hBOOL(hAPP(c_Set_Oinsert(X4,c_Set_Oinsert(X3,X5,X6),X6),X3))
| ~ spl0_167
| ~ spl0_408 ),
inference(superposition,[],[f2315,f4284]) ).
fof(f4284,plain,
( ! [X11,X5,X12,X25] : c_Set_Oinsert(X11,c_Set_Oinsert(X12,X25,X5),X5) = c_Set_Oinsert(X12,c_Set_Oinsert(X11,X25,X5),X5)
| ~ spl0_408 ),
inference(avatar_component_clause,[],[f4283]) ).
fof(f2315,plain,
( ! [X11,X5,X25] : hBOOL(hAPP(c_Set_Oinsert(X11,X25,X5),X11))
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f2314]) ).
fof(f41853,plain,
( spl0_1363
| ~ spl0_257
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f4137,f3597,f2705,f41851]) ).
fof(f41851,plain,
( spl0_1363
<=> ! [X1] : c_GCD_Ogcd__class_OLCM(c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X1),tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f2705,plain,
( spl0_257
<=> ! [X6] : c_GCD_Ogcd__class_OLCM(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f4137,plain,
( ! [X1] : c_GCD_Ogcd__class_OLCM(c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X1),tc_nat),tc_nat) = X1
| ~ spl0_257
| ~ spl0_374 ),
inference(superposition,[],[f2706,f3598]) ).
fof(f2706,plain,
( ! [X6] : c_GCD_Ogcd__class_OLCM(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = X6
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f2705]) ).
fof(f41849,plain,
( spl0_1362
| ~ spl0_258
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f4136,f3597,f2709,f41847]) ).
fof(f41847,plain,
( spl0_1362
<=> ! [X0] : c_GCD_Ogcd__class_OGCD(c_SetInterval_Oord__class_OatLeastLessThan(X0,hAPP(c_Suc,X0),tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f2709,plain,
( spl0_258
<=> ! [X6] : c_GCD_Ogcd__class_OGCD(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f4136,plain,
( ! [X0] : c_GCD_Ogcd__class_OGCD(c_SetInterval_Oord__class_OatLeastLessThan(X0,hAPP(c_Suc,X0),tc_nat),tc_nat) = X0
| ~ spl0_258
| ~ spl0_374 ),
inference(superposition,[],[f2710,f3598]) ).
fof(f2710,plain,
( ! [X6] : c_GCD_Ogcd__class_OGCD(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = X6
| ~ spl0_258 ),
inference(avatar_component_clause,[],[f2709]) ).
fof(f41845,plain,
( spl0_1361
| ~ spl0_174
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f3899,f3510,f2343,f41843]) ).
fof(f41843,plain,
( spl0_1361
<=> ! [X0] : ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,hAPP(c_Suc,X0)),tc_nat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f3510,plain,
( spl0_353
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(c_Suc,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f3899,plain,
( ! [X0] : ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,hAPP(c_Suc,X0)),tc_nat),X0))
| ~ spl0_174
| ~ spl0_353 ),
inference(resolution,[],[f3511,f2344]) ).
fof(f3511,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(c_Suc,X2)))
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2)) )
| ~ spl0_353 ),
inference(avatar_component_clause,[],[f3510]) ).
fof(f41841,plain,
( spl0_1360
| ~ spl0_167
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f3729,f3460,f2314,f41839]) ).
fof(f3729,plain,
( ! [X4] : hBOOL(hAPP(c_SetInterval_Oord__class_OatMost(hAPP(c_Suc,X4),tc_nat),hAPP(c_Suc,X4)))
| ~ spl0_167
| ~ spl0_342 ),
inference(superposition,[],[f2315,f3461]) ).
fof(f41837,plain,
( spl0_1359
| ~ spl0_195
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f3728,f3460,f2437,f41835]) ).
fof(f41835,plain,
( spl0_1359
<=> ! [X3] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) != c_SetInterval_Oord__class_OatMost(hAPP(c_Suc,X3),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f3728,plain,
( ! [X3] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) != c_SetInterval_Oord__class_OatMost(hAPP(c_Suc,X3),tc_nat)
| ~ spl0_195
| ~ spl0_342 ),
inference(superposition,[],[f2438,f3461]) ).
fof(f41833,plain,
( spl0_1358
| ~ spl0_170
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f3634,f3410,f2327,f41831]) ).
fof(f41831,plain,
( spl0_1358
<=> ! [X0] : hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),hAPP(c_Suc,hAPP(c_Suc,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f3410,plain,
( spl0_330
<=> ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f3634,plain,
( ! [X0] : hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),hAPP(c_Suc,hAPP(c_Suc,X0))))
| ~ spl0_170
| ~ spl0_330 ),
inference(resolution,[],[f3411,f2328]) ).
fof(f3411,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2)) )
| ~ spl0_330 ),
inference(avatar_component_clause,[],[f3410]) ).
fof(f41829,plain,
( spl0_1357
| ~ spl0_129
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f3064,f2984,f2141,f41827]) ).
fof(f41827,plain,
( spl0_1357
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f2141,plain,
( spl0_129
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f2984,plain,
( spl0_287
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_HOL_Ozero__class_Ozero(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f3064,plain,
( ! [X2] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl0_129
| ~ spl0_287 ),
inference(resolution,[],[f2985,f2143]) ).
fof(f2143,plain,
( class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex)
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f2141]) ).
fof(f2985,plain,
( ! [X6,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_HOL_Ozero__class_Ozero(X5)) )
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f2984]) ).
fof(f41825,plain,
( spl0_1356
| ~ spl0_86
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f3063,f2984,f1926,f41823]) ).
fof(f41823,plain,
( spl0_1356
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X1),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f1926,plain,
( spl0_86
<=> class_Ring__and__Field_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f3063,plain,
( ! [X1] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X1),c_HOL_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl0_86
| ~ spl0_287 ),
inference(resolution,[],[f2985,f1928]) ).
fof(f1928,plain,
( class_Ring__and__Field_Omult__zero(tc_Int_Oint)
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f1926]) ).
fof(f41821,plain,
( spl0_1355
| ~ spl0_129
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3061,f2980,f2141,f41819]) ).
fof(f41819,plain,
( spl0_1355
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f2980,plain,
( spl0_286
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f3061,plain,
( ! [X2] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),X2)
| ~ spl0_129
| ~ spl0_286 ),
inference(resolution,[],[f2981,f2143]) ).
fof(f2981,plain,
( ! [X6,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),X6) )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f2980]) ).
fof(f41817,plain,
( spl0_1354
| ~ spl0_86
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3060,f2980,f1926,f41815]) ).
fof(f41815,plain,
( spl0_1354
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f3060,plain,
( ! [X1] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),X1)
| ~ spl0_86
| ~ spl0_286 ),
inference(resolution,[],[f2981,f1928]) ).
fof(f41812,plain,
( spl0_1353
| ~ spl0_144
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f3055,f2972,f2216,f41810]) ).
fof(f2972,plain,
( spl0_284
<=> ! [X6,X5] :
( ~ class_Power_Opower(X5)
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f3055,plain,
( ! [X2] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_144
| ~ spl0_284 ),
inference(resolution,[],[f2973,f2218]) ).
fof(f2218,plain,
( class_Power_Opower(tc_Complex_Ocomplex)
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f2216]) ).
fof(f2973,plain,
( ! [X6,X5] :
( ~ class_Power_Opower(X5)
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_284 ),
inference(avatar_component_clause,[],[f2972]) ).
fof(f41807,plain,
( spl0_1352
| ~ spl0_104
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f3054,f2972,f2016,f41805]) ).
fof(f3054,plain,
( ! [X1] : c_HOL_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_104
| ~ spl0_284 ),
inference(resolution,[],[f2973,f2018]) ).
fof(f2018,plain,
( class_Power_Opower(tc_Int_Oint)
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f2016]) ).
fof(f41802,plain,
( spl0_1351
| ~ spl0_39
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f3053,f2972,f1691,f41800]) ).
fof(f3053,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X0),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_39
| ~ spl0_284 ),
inference(resolution,[],[f2973,f1693]) ).
fof(f1693,plain,
( class_Power_Opower(tc_nat)
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f1691]) ).
fof(f41798,plain,
( spl0_1350
| ~ spl0_131
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3052,f2966,f2151,f41796]) ).
fof(f41796,plain,
( spl0_1350
<=> ! [X2] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f2151,plain,
( spl0_131
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f2966,plain,
( spl0_283
<=> ! [X2,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Oone__class_Oone(X5)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f3052,plain,
( ! [X2] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),X2)
| ~ spl0_131
| ~ spl0_283 ),
inference(resolution,[],[f2967,f2153]) ).
fof(f2153,plain,
( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f2151]) ).
fof(f2967,plain,
( ! [X2,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Oone__class_Oone(X5)),X2) )
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f2966]) ).
fof(f41794,plain,
( spl0_1349
| ~ spl0_89
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3051,f2966,f1941,f41792]) ).
fof(f41792,plain,
( spl0_1349
<=> ! [X1] : c_HOL_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f1941,plain,
( spl0_89
<=> class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f3051,plain,
( ! [X1] : c_HOL_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),X1)
| ~ spl0_89
| ~ spl0_283 ),
inference(resolution,[],[f2967,f1943]) ).
fof(f1943,plain,
( class_OrderedGroup_Omonoid__mult(tc_Int_Oint)
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f1941]) ).
fof(f41790,plain,
( spl0_1348
| ~ spl0_29
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3050,f2966,f1641,f41788]) ).
fof(f41788,plain,
( spl0_1348
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f1641,plain,
( spl0_29
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f3050,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0)
| ~ spl0_29
| ~ spl0_283 ),
inference(resolution,[],[f2967,f1643]) ).
fof(f1643,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f1641]) ).
fof(f41786,plain,
( spl0_1347
| ~ spl0_138
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f3031,f2946,f2186,f41784]) ).
fof(f41784,plain,
( spl0_1347
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f2946,plain,
( spl0_278
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Ozero__class_Ozero(X5)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f3031,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),X0)
| ~ spl0_138
| ~ spl0_278 ),
inference(resolution,[],[f2947,f2188]) ).
fof(f2947,plain,
( ! [X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Ozero__class_Ozero(X5)),X6) )
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f2946]) ).
fof(f41761,plain,
( spl0_1346
| ~ spl0_138
| ~ spl0_304
| ~ spl0_336
| ~ spl0_1345 ),
inference(avatar_split_clause,[],[f41756,f41751,f3434,f3114,f2186,f41758]) ).
fof(f41758,plain,
( spl0_1346
<=> hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),c_COMBS(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),tc_nat),c_HOL_OIf(tc_Complex_Ocomplex)),c_lessequals(v_i,tc_nat)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n)))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f41751,plain,
( spl0_1345
<=> hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),c_COMBS(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),tc_nat),c_HOL_OIf(tc_Complex_Ocomplex)),c_lessequals(v_i,tc_nat)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_FFT__Mirabelle_Oroot(v_n)))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f41756,plain,
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),c_COMBS(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),tc_nat),c_HOL_OIf(tc_Complex_Ocomplex)),c_lessequals(v_i,tc_nat)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n)))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))
| ~ spl0_138
| ~ spl0_304
| ~ spl0_336
| ~ spl0_1345 ),
inference(forward_demodulation,[],[f41755,f3685]) ).
fof(f41755,plain,
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),c_COMBS(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),tc_nat),c_HOL_OIf(tc_Complex_Ocomplex)),c_lessequals(v_i,tc_nat)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_FFT__Mirabelle_Oroot(v_n)))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))
| ~ spl0_304
| ~ spl0_1345 ),
inference(forward_demodulation,[],[f41753,f3116]) ).
fof(f41753,plain,
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),c_COMBS(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),tc_nat),c_HOL_OIf(tc_Complex_Ocomplex)),c_lessequals(v_i,tc_nat)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_FFT__Mirabelle_Oroot(v_n)))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat))
| ~ spl0_1345 ),
inference(avatar_component_clause,[],[f41751]) ).
fof(f41754,plain,
spl0_1345,
inference(avatar_split_clause,[],[f1191,f41751]) ).
fof(f1191,axiom,
hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),c_COMBS(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),tc_nat),c_HOL_OIf(tc_Complex_Ocomplex)),c_lessequals(v_i,tc_nat)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_FFT__Mirabelle_Oroot(v_n)))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_calculation_0) ).
fof(f41747,plain,
( spl0_1344
| ~ spl0_304
| ~ spl0_1343 ),
inference(avatar_split_clause,[],[f41743,f41740,f3114,f41745]) ).
fof(f41745,plain,
( spl0_1344
<=> ! [X16,X43,X5,X1] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X16),X43))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1))),hAPP(c_Power_Opower__class_Opower(X5),X16),tc_nat,X5,X5)),tc_nat,X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X16),X1))),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X16)),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X16),X43))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1))),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X16)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1)),tc_nat,X5,X5),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat))
| ~ class_Ring__and__Field_Ocomm__ring(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f41740,plain,
( spl0_1343
<=> ! [X16,X43,X5,X1] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X16),X43))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1))),hAPP(c_Power_Opower__class_Opower(X5),X16),tc_nat,X5,X5)),tc_nat,X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X16),X1))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X16)),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X16),X43))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1))),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X16)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1)),tc_nat,X5,X5),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f41743,plain,
( ! [X1,X16,X5,X43] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X16),X43))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1))),hAPP(c_Power_Opower__class_Opower(X5),X16),tc_nat,X5,X5)),tc_nat,X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X16),X1))),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X16)),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X16),X43))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1))),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X16)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1)),tc_nat,X5,X5),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat))
| ~ class_Ring__and__Field_Ocomm__ring(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5) )
| ~ spl0_304
| ~ spl0_1343 ),
inference(forward_demodulation,[],[f41741,f3116]) ).
fof(f41741,plain,
( ! [X1,X16,X5,X43] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X16),X43))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1))),hAPP(c_Power_Opower__class_Opower(X5),X16),tc_nat,X5,X5)),tc_nat,X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X16),X1))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X16)),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X16),X43))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1))),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X16)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1)),tc_nat,X5,X5),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)) )
| ~ spl0_1343 ),
inference(avatar_component_clause,[],[f41740]) ).
fof(f41742,plain,
spl0_1343,
inference(avatar_split_clause,[],[f1202,f41740]) ).
fof(f1202,axiom,
! [X1,X16,X5,X43] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X16),X43))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1))),hAPP(c_Power_Opower__class_Opower(X5),X16),tc_nat,X5,X5)),tc_nat,X5,X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X16),X1))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X16)),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X16),X43))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1))),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X16)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1)),tc_nat,X5,X5),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_lemma__termdiff1_0) ).
fof(f41735,plain,
( spl0_1342
| ~ spl0_304
| ~ spl0_1341 ),
inference(avatar_split_clause,[],[f41731,f41728,f3114,f41733]) ).
fof(f41733,plain,
( spl0_1342
<=> ! [X11,X12,X5,X2] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X2))),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),hAPP(c_Suc,X2),tc_nat)))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f41728,plain,
( spl0_1341
<=> ! [X11,X12,X5,X2] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X2))),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f41731,plain,
( ! [X2,X11,X5,X12] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X2))),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),hAPP(c_Suc,X2),tc_nat)))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5) )
| ~ spl0_304
| ~ spl0_1341 ),
inference(forward_demodulation,[],[f41729,f3116]) ).
fof(f41729,plain,
( ! [X2,X11,X5,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X2))),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat))) )
| ~ spl0_1341 ),
inference(avatar_component_clause,[],[f41728]) ).
fof(f41730,plain,
spl0_1341,
inference(avatar_split_clause,[],[f1199,f41728]) ).
fof(f1199,axiom,
! [X2,X11,X5,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X2))),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_lemma__realpow__diff__sumr_0) ).
fof(f41723,plain,
( spl0_1340
| ~ spl0_208
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3018,f2930,f2500,f41721]) ).
fof(f41721,plain,
( spl0_1340
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_Lim_OisCont(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f2930,plain,
( spl0_274
<=> ! [X10,X11,X5,X15] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| c_Lim_OisCont(X10,X11,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f3018,plain,
( ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_Lim_OisCont(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2,X0,X0) )
| ~ spl0_208
| ~ spl0_274 ),
inference(duplicate_literal_removal,[],[f3017]) ).
fof(f3017,plain,
( ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_Lim_OisCont(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2,X0,X0)
| ~ class_RealVector_Oreal__normed__field(X0) )
| ~ spl0_208
| ~ spl0_274 ),
inference(resolution,[],[f2931,f2501]) ).
fof(f2931,plain,
( ! [X10,X11,X15,X5] :
( ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ class_RealVector_Oreal__normed__field(X5)
| c_Lim_OisCont(X10,X11,X5,X5) )
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f2930]) ).
fof(f41719,plain,
( spl0_1339
| ~ spl0_304
| ~ spl0_1338 ),
inference(avatar_split_clause,[],[f41715,f41712,f3114,f41717]) ).
fof(f41717,plain,
( spl0_1339
<=> ! [X11,X12,X5,X2] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2))),hAPP(c_Power_Opower__class_Opower(X5),X12),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),hAPP(c_Suc,X2),tc_nat))
| ~ class_Power_Opower(X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f41712,plain,
( spl0_1338
<=> ! [X11,X12,X5,X2] :
( ~ class_Power_Opower(X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2))),hAPP(c_Power_Opower__class_Opower(X5),X12),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f41715,plain,
( ! [X2,X11,X5,X12] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2))),hAPP(c_Power_Opower__class_Opower(X5),X12),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),hAPP(c_Suc,X2),tc_nat))
| ~ class_Power_Opower(X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) )
| ~ spl0_304
| ~ spl0_1338 ),
inference(forward_demodulation,[],[f41713,f3116]) ).
fof(f41713,plain,
( ! [X2,X11,X5,X12] :
( ~ class_Power_Opower(X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2))),hAPP(c_Power_Opower__class_Opower(X5),X12),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat)) )
| ~ spl0_1338 ),
inference(avatar_component_clause,[],[f41712]) ).
fof(f41714,plain,
spl0_1338,
inference(avatar_split_clause,[],[f1200,f41712]) ).
fof(f1200,axiom,
! [X2,X11,X5,X12] :
( ~ class_Power_Opower(X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2))),hAPP(c_Power_Opower__class_Opower(X5),X12),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_lemma__realpow__rev__sumr_0) ).
fof(f41707,plain,
spl0_1337,
inference(avatar_split_clause,[],[f1152,f41705]) ).
fof(f41705,plain,
( spl0_1337
<=> ! [X31,X10,X32,X20,X5,X25,X26] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),X25)),hAPP(hAPP(c_Finite__Set_Osetsum(X31,X5),X32),X26)) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X31,X5),tc_fun(tc_fun(X31,tc_bool),X5),X20),c_Finite__Set_Osetsum(X31,X5)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X5,X5),tc_fun(tc_fun(X31,X5),tc_fun(X31,X5)),X20),c_COMBB(X5,X5,X31)),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Otimes__class_Otimes(X5)),X10)),X20,tc_fun(X31,X5),tc_fun(X31,X5)),X32)),X20,tc_fun(X31,tc_bool),X5),X26)),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f1152,axiom,
! [X31,X10,X26,X5,X25,X32,X20] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),X25)),hAPP(hAPP(c_Finite__Set_Osetsum(X31,X5),X32),X26)) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X31,X5),tc_fun(tc_fun(X31,tc_bool),X5),X20),c_Finite__Set_Osetsum(X31,X5)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X5,X5),tc_fun(tc_fun(X31,X5),tc_fun(X31,X5)),X20),c_COMBB(X5,X5,X31)),hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Otimes__class_Otimes(X5)),X10)),X20,tc_fun(X31,X5),tc_fun(X31,X5)),X32)),X20,tc_fun(X31,tc_bool),X5),X26)),X25) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__product_0) ).
fof(f41701,plain,
( spl0_1336
| ~ spl0_304
| ~ spl0_1335 ),
inference(avatar_split_clause,[],[f41697,f41694,f3114,f41699]) ).
fof(f41699,plain,
( spl0_1336
<=> ! [X11,X12,X5,X2] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),hAPP(c_Suc,X2))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),hAPP(c_Suc,X2))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X12)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),hAPP(c_Suc,X2),tc_nat)))
| ~ class_Ring__and__Field_Ocomm__ring(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f41694,plain,
( spl0_1335
<=> ! [X11,X12,X5,X2] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),hAPP(c_Suc,X2))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),hAPP(c_Suc,X2))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X12)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f41697,plain,
( ! [X2,X11,X5,X12] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),hAPP(c_Suc,X2))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),hAPP(c_Suc,X2))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X12)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),hAPP(c_Suc,X2),tc_nat)))
| ~ class_Ring__and__Field_Ocomm__ring(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5) )
| ~ spl0_304
| ~ spl0_1335 ),
inference(forward_demodulation,[],[f41695,f3116]) ).
fof(f41695,plain,
( ! [X2,X11,X5,X12] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),hAPP(c_Suc,X2))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),hAPP(c_Suc,X2))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X12)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat))) )
| ~ spl0_1335 ),
inference(avatar_component_clause,[],[f41694]) ).
fof(f41696,plain,
spl0_1335,
inference(avatar_split_clause,[],[f1201,f41694]) ).
fof(f1201,axiom,
! [X2,X11,X5,X12] :
( ~ class_Ring__and__Field_Ocomm__ring(X5)
| ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),hAPP(c_Suc,X2))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),hAPP(c_Suc,X2))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X12)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),hAPP(c_Power_Opower__class_Opower(X5),X11)),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),hAPP(c_Power_Opower__class_Opower(X5),X12)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2)),tc_nat,X5,X5)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,X2),tc_nat))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_lemma__realpow__diff__sumr2_0) ).
fof(f41474,plain,
( spl0_1334
| ~ spl0_304
| ~ spl0_1333 ),
inference(avatar_split_clause,[],[f41470,f41467,f3114,f41472]) ).
fof(f41472,plain,
( spl0_1334
<=> ! [X42,X10,X11,X14,X5,X32] :
( c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X14),hAPP(X32,X11))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X42),hAPP(X10,X11)))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X32,X11)),hAPP(c_Suc,hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))))),X5)
| ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X14,X5)
| ~ c_Deriv_Oderiv(X32,X11,X42,X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(X32,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f41467,plain,
( spl0_1333
<=> ! [X42,X10,X11,X14,X5,X32] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X14,X5)
| ~ c_Deriv_Oderiv(X32,X11,X42,X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(X32,X11)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X14),hAPP(X32,X11))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X42),hAPP(X10,X11)))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X32,X11)),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))))),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f41470,plain,
( ! [X10,X11,X14,X5,X42,X32] :
( c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X14),hAPP(X32,X11))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X42),hAPP(X10,X11)))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X32,X11)),hAPP(c_Suc,hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))))),X5)
| ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X14,X5)
| ~ c_Deriv_Oderiv(X32,X11,X42,X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(X32,X11) )
| ~ spl0_304
| ~ spl0_1333 ),
inference(forward_demodulation,[],[f41468,f3116]) ).
fof(f41468,plain,
( ! [X10,X11,X14,X5,X42,X32] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X14,X5)
| ~ c_Deriv_Oderiv(X32,X11,X42,X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(X32,X11)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X14),hAPP(X32,X11))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X42),hAPP(X10,X11)))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X32,X11)),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))))),X5) )
| ~ spl0_1333 ),
inference(avatar_component_clause,[],[f41467]) ).
fof(f41469,plain,
spl0_1333,
inference(avatar_split_clause,[],[f1114,f41467]) ).
fof(f1114,axiom,
! [X10,X11,X14,X5,X42,X32] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X14,X5)
| ~ c_Deriv_Oderiv(X32,X11,X42,X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(X32,X11)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X14),hAPP(X32,X11))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X42),hAPP(X10,X11)))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X32,X11)),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))))),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__quotient_0) ).
fof(f41464,plain,
( spl0_1332
| ~ spl0_214
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2899,f2713,f2524,f41462]) ).
fof(f2524,plain,
( spl0_214
<=> ! [X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f2713,plain,
( spl0_259
<=> ! [X29,X28] : c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X29),X28,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X28,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2899,plain,
( ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_214
| ~ spl0_259 ),
inference(superposition,[],[f2714,f2525]) ).
fof(f2525,plain,
( ! [X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_214 ),
inference(avatar_component_clause,[],[f2524]) ).
fof(f2714,plain,
( ! [X28,X29] : c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X29),X28,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X28,tc_nat)
| ~ spl0_259 ),
inference(avatar_component_clause,[],[f2713]) ).
fof(f41244,plain,
spl0_1331,
inference(avatar_split_clause,[],[f1117,f41242]) ).
fof(f41242,plain,
( spl0_1331
<=> ! [X10,X32,X11,X5,X15,X23] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ c_Deriv_Oderiv(X32,X11,X23,X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(X32,X11)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X15),hAPP(X32,X11))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(X10,X11)),X23))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(X32,X11)),hAPP(X32,X11))),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f1117,axiom,
! [X10,X11,X15,X5,X32,X23] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ c_Deriv_Oderiv(X32,X11,X23,X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(X32,X11)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X15),hAPP(X32,X11))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(X10,X11)),X23))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(X32,X11)),hAPP(X32,X11))),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__divide_0) ).
fof(f41237,plain,
spl0_1330,
inference(avatar_split_clause,[],[f1210,f41235]) ).
fof(f41235,plain,
( spl0_1330
<=> ! [X31,X10,X20,X5,X25,X26] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X31,X5),tc_fun(tc_fun(X31,tc_bool),X5),X20),c_Finite__Set_Osetsum(X31,X5)),X10),X20,tc_fun(X31,tc_bool),X5),X26)),X25) = hAPP(hAPP(c_Finite__Set_Osetsum(X31,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X20,X5),tc_fun(tc_fun(X20,tc_bool),X5),X31),c_Finite__Set_Osetsum(X20,X5)),c_COMBC(X10,X20,X31,X5)),X31,tc_fun(X20,tc_bool),X5),X25)),X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f1210,axiom,
! [X31,X10,X26,X5,X25,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X31,X5),tc_fun(tc_fun(X31,tc_bool),X5),X20),c_Finite__Set_Osetsum(X31,X5)),X10),X20,tc_fun(X31,tc_bool),X5),X26)),X25) = hAPP(hAPP(c_Finite__Set_Osetsum(X31,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X20,X5),tc_fun(tc_fun(X20,tc_bool),X5),X31),c_Finite__Set_Osetsum(X20,X5)),c_COMBC(X10,X20,X31,X5)),X31,tc_fun(X20,tc_bool),X5),X25)),X26) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__commute_0) ).
fof(f41230,plain,
spl0_1329,
inference(avatar_split_clause,[],[f953,f41228]) ).
fof(f41228,plain,
( spl0_1329
<=> ! [X5,X11,X7,X12,X6] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X6)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X12),X7))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X6)),X7))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X12),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f953,axiom,
! [X11,X6,X7,X5,X12] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X6)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X12),X7))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X6)),X7))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X12),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult_Oprod__diff__prod_0) ).
fof(f41225,plain,
spl0_1328,
inference(avatar_split_clause,[],[f837,f41223]) ).
fof(f41223,plain,
( spl0_1328
<=> ! [X5,X6,X14,X9,X43,X7] :
( ~ class_RealVector_Oreal__field(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X14))),X43) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X14)),X43))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X9)),X43)),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f837,axiom,
! [X6,X9,X7,X14,X5,X43] :
( ~ class_RealVector_Oreal__field(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X14))),X43) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X14)),X43))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X9)),X43)),X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__mult__lemma_0) ).
fof(f41216,plain,
( ~ spl0_23
| spl0_1320
| ~ spl0_219
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2854,f2669,f2553,f40867,f1611]) ).
fof(f40867,plain,
( spl0_1320
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f2669,plain,
( spl0_248
<=> ! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f2854,plain,
( ! [X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Lattices_Olower__semilattice(tc_nat) )
| ~ spl0_219
| ~ spl0_248 ),
inference(resolution,[],[f2670,f2554]) ).
fof(f2670,plain,
( ! [X2] :
( ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))
| c_HOL_Ozero__class_Ozero(tc_nat) = X2 )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2669]) ).
fof(f41215,plain,
( spl0_1327
| ~ spl0_304
| ~ spl0_1325 ),
inference(avatar_split_clause,[],[f41207,f41204,f3114,f41213]) ).
fof(f41213,plain,
( spl0_1327
<=> ! [X10,X0,X5,X2] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0),tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat)))
| ~ class_OrderedGroup_Oab__group__add(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f41204,plain,
( spl0_1325
<=> ! [X10,X0,X5,X2] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0),tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f41207,plain,
( ! [X2,X10,X0,X5] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0),tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat)))
| ~ class_OrderedGroup_Oab__group__add(X5) )
| ~ spl0_304
| ~ spl0_1325 ),
inference(forward_demodulation,[],[f41205,f3116]) ).
fof(f41205,plain,
( ! [X2,X10,X0,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0),tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))) )
| ~ spl0_1325 ),
inference(avatar_component_clause,[],[f41204]) ).
fof(f41211,plain,
( spl0_1326
| ~ spl0_304
| ~ spl0_1324 ),
inference(avatar_split_clause,[],[f41202,f41199,f3114,f41209]) ).
fof(f41209,plain,
( spl0_1326
<=> ! [X10,X0,X5,X2] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat)))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f41199,plain,
( spl0_1324
<=> ! [X10,X0,X5,X2] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f41202,plain,
( ! [X2,X10,X0,X5] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat)))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) )
| ~ spl0_304
| ~ spl0_1324 ),
inference(forward_demodulation,[],[f41200,f3116]) ).
fof(f41200,plain,
( ! [X2,X10,X0,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))) )
| ~ spl0_1324 ),
inference(avatar_component_clause,[],[f41199]) ).
fof(f41206,plain,
spl0_1325,
inference(avatar_split_clause,[],[f1196,f41204]) ).
fof(f1196,axiom,
! [X2,X10,X0,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0),tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sumr__offset_0) ).
fof(f41201,plain,
spl0_1324,
inference(avatar_split_clause,[],[f1121,f41199]) ).
fof(f1121,axiom,
! [X2,X10,X0,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sumr__offset3_0) ).
fof(f41142,plain,
spl0_1323,
inference(avatar_split_clause,[],[f1111,f41140]) ).
fof(f41140,plain,
( spl0_1323
<=> ! [X18,X20,X21,X5,X49] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_SEQ_OLIMSEQ(hAPP(X18,c_SEQ_Osko__SEQ__XLIMSEQ__setsum__1__1(X21,X49,X18,X5,X20)),hAPP(X21,c_SEQ_Osko__SEQ__XLIMSEQ__setsum__1__1(X21,X49,X18,X5,X20)),X20)
| c_SEQ_OLIMSEQ(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X5,X20),tc_fun(tc_fun(X5,tc_bool),X20),tc_nat),c_Finite__Set_Osetsum(X5,X20)),c_COMBC(X18,X5,tc_nat,X20)),tc_nat,tc_fun(X5,tc_bool),X20),X49),hAPP(hAPP(c_Finite__Set_Osetsum(X5,X20),X21),X49),X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f1111,axiom,
! [X21,X49,X18,X5,X20] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_SEQ_OLIMSEQ(hAPP(X18,c_SEQ_Osko__SEQ__XLIMSEQ__setsum__1__1(X21,X49,X18,X5,X20)),hAPP(X21,c_SEQ_Osko__SEQ__XLIMSEQ__setsum__1__1(X21,X49,X18,X5,X20)),X20)
| c_SEQ_OLIMSEQ(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(X5,X20),tc_fun(tc_fun(X5,tc_bool),X20),tc_nat),c_Finite__Set_Osetsum(X5,X20)),c_COMBC(X18,X5,tc_nat,X20)),tc_nat,tc_fun(X5,tc_bool),X20),X49),hAPP(hAPP(c_Finite__Set_Osetsum(X5,X20),X21),X49),X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__setsum_1) ).
fof(f41008,plain,
( spl0_1322
| ~ spl0_304
| ~ spl0_1321 ),
inference(avatar_split_clause,[],[f40875,f40872,f3114,f41006]) ).
fof(f41006,plain,
( spl0_1322
<=> ! [X15,X10,X11,X5,X2] :
( c_Deriv_Oderiv(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(tc_nat,X5),X5),c_Power_Opower__class_Opower(X5)),X10),X5,tc_nat,X5),X2),X11,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X10,X11)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)))))),X5)
| ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f40872,plain,
( spl0_1321
<=> ! [X2,X10,X11,X5,X15] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| c_Deriv_Oderiv(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(tc_nat,X5),X5),c_Power_Opower__class_Opower(X5)),X10),X5,tc_nat,X5),X2),X11,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X10,X11)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))))),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f40875,plain,
( ! [X2,X10,X11,X15,X5] :
( c_Deriv_Oderiv(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(tc_nat,X5),X5),c_Power_Opower__class_Opower(X5)),X10),X5,tc_nat,X5),X2),X11,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X10,X11)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)))))),X5)
| ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5) )
| ~ spl0_304
| ~ spl0_1321 ),
inference(forward_demodulation,[],[f40873,f3116]) ).
fof(f40873,plain,
( ! [X2,X10,X11,X15,X5] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| c_Deriv_Oderiv(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(tc_nat,X5),X5),c_Power_Opower__class_Opower(X5)),X10),X5,tc_nat,X5),X2),X11,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X10,X11)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))))),X5) )
| ~ spl0_1321 ),
inference(avatar_component_clause,[],[f40872]) ).
fof(f40874,plain,
spl0_1321,
inference(avatar_split_clause,[],[f999,f40872]) ).
fof(f999,axiom,
! [X2,X10,X11,X15,X5] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| c_Deriv_Oderiv(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(tc_nat,X5),X5),c_Power_Opower__class_Opower(X5)),X10),X5,tc_nat,X5),X2),X11,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X10,X11)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))))),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__power_0) ).
fof(f40869,plain,
( ~ spl0_36
| spl0_1320
| ~ spl0_221
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2853,f2669,f2561,f40867,f1676]) ).
fof(f2853,plain,
( ! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Lattices_Olattice(tc_nat) )
| ~ spl0_221
| ~ spl0_248 ),
inference(resolution,[],[f2670,f2562]) ).
fof(f40865,plain,
spl0_1319,
inference(avatar_split_clause,[],[f502,f40863]) ).
fof(f40863,plain,
( spl0_1319
<=> ! [X2,X10,X11,X5,X15] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| c_Deriv_Oderiv(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(tc_nat,X5),X5),c_Power_Opower__class_Opower(X5)),X10),X5,tc_nat,X5),hAPP(c_Suc,X2)),X11,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Oone__class_Oone(X5)),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X10,X11)),X2))),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f502,axiom,
! [X2,X10,X11,X15,X5] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| c_Deriv_Oderiv(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(tc_nat,X5),X5),c_Power_Opower__class_Opower(X5)),X10),X5,tc_nat,X5),hAPP(c_Suc,X2)),X11,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Oone__class_Oone(X5)),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(X10,X11)),X2))),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__power__Suc_0) ).
fof(f40150,plain,
spl0_1318,
inference(avatar_split_clause,[],[f846,f40148]) ).
fof(f40148,plain,
( spl0_1318
<=> ! [X5,X4,X0,X6,X3] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X4))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X3))) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X0))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f846,axiom,
! [X3,X0,X6,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X4))),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X3))) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X0))),X3) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__divides__special_0) ).
fof(f40146,plain,
spl0_1317,
inference(avatar_split_clause,[],[f340,f40144]) ).
fof(f40144,plain,
( spl0_1317
<=> ! [X28,X4,X3,X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X3)),X28)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f340,axiom,
! [X2,X3,X28,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X3)),X28)),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__diff__add__eq2_0) ).
fof(f40142,plain,
spl0_1316,
inference(avatar_split_clause,[],[f339,f40140]) ).
fof(f40140,plain,
( spl0_1316
<=> ! [X28,X4,X3,X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X28)),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f339,axiom,
! [X2,X3,X28,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X28)),X1)),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__diff__add__eq1_0) ).
fof(f40136,plain,
( spl0_1315
| ~ spl0_304
| ~ spl0_1311 ),
inference(avatar_split_clause,[],[f38837,f38834,f3114,f40134]) ).
fof(f40134,plain,
( spl0_1315
<=> ! [X10,X13,X5,X2] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)),X13)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X10),tc_nat,X5,X5),X13)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))
| ~ class_Ring__and__Field_Oring__1(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f38834,plain,
( spl0_1311
<=> ! [X10,X13,X5,X2] :
( ~ class_Ring__and__Field_Oring__1(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)),X13)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X10),tc_nat,X5,X5),X13)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f38837,plain,
( ! [X2,X10,X5,X13] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)),X13)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X10),tc_nat,X5,X5),X13)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))
| ~ class_Ring__and__Field_Oring__1(X5) )
| ~ spl0_304
| ~ spl0_1311 ),
inference(forward_demodulation,[],[f38835,f3116]) ).
fof(f38835,plain,
( ! [X2,X10,X5,X13] :
( ~ class_Ring__and__Field_Oring__1(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)),X13)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X10),tc_nat,X5,X5),X13)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) )
| ~ spl0_1311 ),
inference(avatar_component_clause,[],[f38834]) ).
fof(f40131,plain,
( ~ spl0_23
| spl0_1314
| ~ spl0_220
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2851,f2669,f2557,f39203,f1611]) ).
fof(f39203,plain,
( spl0_1314
<=> ! [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_1314])]) ).
fof(f2851,plain,
( ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Lattices_Olower__semilattice(tc_nat) )
| ~ spl0_220
| ~ spl0_248 ),
inference(resolution,[],[f2670,f2558]) ).
fof(f39205,plain,
( ~ spl0_36
| spl0_1314
| ~ spl0_222
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2850,f2669,f2565,f39203,f1676]) ).
fof(f2850,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Lattices_Olattice(tc_nat) )
| ~ spl0_222
| ~ spl0_248 ),
inference(resolution,[],[f2670,f2566]) ).
fof(f38847,plain,
( spl0_1313
| ~ spl0_308
| ~ spl0_324
| ~ spl0_934
| ~ spl0_936
| ~ spl0_1312 ),
inference(avatar_split_clause,[],[f38843,f38839,f15886,f15817,f3224,f3131,f38845]) ).
fof(f38845,plain,
( spl0_1313
<=> ! [X5,X27,X25,X26] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X27,X25,tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X26,c_Lattices_Olower__semilattice__class_Oinf(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X26,c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X27,X25,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f3224,plain,
( spl0_324
<=> ! [X25,X5,X26] : c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X26,X25,tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f15886,plain,
( spl0_936
<=> ! [X5,X27,X25,X26] : c_Lattices_Olower__semilattice__class_Oinf(X25,c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f38839,plain,
( spl0_1312
<=> ! [X5,X27,X25,X26] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X27,X25,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X27,X25,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f38843,plain,
( ! [X26,X27,X5,X25] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X27,X25,tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X26,c_Lattices_Olower__semilattice__class_Oinf(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X26,c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X27,X25,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ spl0_308
| ~ spl0_324
| ~ spl0_934
| ~ spl0_936
| ~ spl0_1312 ),
inference(forward_demodulation,[],[f38842,f19926]) ).
fof(f19926,plain,
( ! [X3,X6,X4,X5] : c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X6,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X3,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X3,X6,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ spl0_308
| ~ spl0_936 ),
inference(superposition,[],[f15887,f3132]) ).
fof(f15887,plain,
( ! [X26,X27,X5,X25] : c_Lattices_Olower__semilattice__class_Oinf(X25,c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ spl0_936 ),
inference(avatar_component_clause,[],[f15886]) ).
fof(f38842,plain,
( ! [X26,X27,X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X27,X25,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X27,X25,tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X26,c_Lattices_Olower__semilattice__class_Oinf(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ spl0_324
| ~ spl0_934
| ~ spl0_1312 ),
inference(forward_demodulation,[],[f38840,f19756]) ).
fof(f19756,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_324
| ~ spl0_934 ),
inference(superposition,[],[f15818,f3225]) ).
fof(f3225,plain,
( ! [X26,X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X26,X25,tc_fun(X5,tc_bool))
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f3224]) ).
fof(f38840,plain,
( ! [X26,X27,X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X27,X25,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X27,X25,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool))
| ~ spl0_1312 ),
inference(avatar_component_clause,[],[f38839]) ).
fof(f38841,plain,
spl0_1312,
inference(avatar_split_clause,[],[f1478,f38839]) ).
fof(f1478,plain,
! [X26,X27,X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X27,X25,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X27,X25,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
inference(forward_demodulation,[],[f1082,f441]) ).
fof(f441,axiom,
! [X26,X5,X25] : c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X26,X25,tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Int__commute_0) ).
fof(f1082,axiom,
! [X26,X27,X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X27,X25,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X27,X25,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Un__Int__crazy_0) ).
fof(f38836,plain,
spl0_1311,
inference(avatar_split_clause,[],[f1198,f38834]) ).
fof(f1198,axiom,
! [X2,X10,X5,X13] :
( ~ class_Ring__and__Field_Oring__1(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)),X13)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X10),tc_nat,X5,X5),X13)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sumr__diff__mult__const2_0) ).
fof(f38832,plain,
spl0_1310,
inference(avatar_split_clause,[],[f1124,f38830]) ).
fof(f38830,plain,
( spl0_1310
<=> ! [X11,X8,X12,X5,X16] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| c_HOL_Ozero__class_Ozero(X5) = X16
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X8),X16)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X8),X12))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f1124,axiom,
! [X11,X8,X16,X5,X12] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| c_HOL_Ozero__class_Ozero(X5) = X16
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X8),X16)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X8),X12))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X16)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__frac__eq_0) ).
fof(f38828,plain,
spl0_1309,
inference(avatar_split_clause,[],[f1093,f38826]) ).
fof(f38826,plain,
( spl0_1309
<=> ! [X10,X11,X5,X15] :
( ~ class_RealVector_Oreal__normed__field(X5)
| c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Ominus__class_Ominus(X5)),X10),X5,X5,X5),hAPP(X10,X11))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(X5),X5,X5,X5),X11),X5,X5,X5),X11,X15,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f1093,axiom,
! [X10,X11,X15,X5] :
( ~ class_RealVector_Oreal__normed__field(X5)
| c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Ominus__class_Ominus(X5)),X10),X5,X5,X5),hAPP(X10,X11))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(X5),X5,X5,X5),X11),X5,X5,X5),X11,X15,X5,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__iff2_1) ).
fof(f38824,plain,
spl0_1308,
inference(avatar_split_clause,[],[f1092,f38822]) ).
fof(f38822,plain,
( spl0_1308
<=> ! [X10,X11,X5,X15] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Ominus__class_Ominus(X5)),X10),X5,X5,X5),hAPP(X10,X11))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(X5),X5,X5,X5),X11),X5,X5,X5),X11,X15,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f1092,axiom,
! [X10,X11,X15,X5] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Ominus__class_Ominus(X5)),X10),X5,X5,X5),hAPP(X10,X11))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(X5),X5,X5,X5),X11),X5,X5,X5),X11,X15,X5,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__iff2_0) ).
fof(f38820,plain,
spl0_1307,
inference(avatar_split_clause,[],[f642,f38818]) ).
fof(f38818,plain,
( spl0_1307
<=> ! [X11,X8,X12,X5,X16] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| c_HOL_Ozero__class_Ozero(X5) = X16
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X8),X16)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X8),X12))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f642,axiom,
! [X11,X8,X16,X5,X12] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| c_HOL_Ozero__class_Ozero(X5) = X16
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X8),X16)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X8),X12))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X16)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__frac__eq_0) ).
fof(f38816,plain,
spl0_1306,
inference(avatar_split_clause,[],[f399,f38814]) ).
fof(f38814,plain,
( spl0_1306
<=> ! [X28,X4,X3,X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X3)),X28)),X2)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f399,axiom,
! [X2,X3,X28,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X3)),X28)),X2)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__le__add__iff2_1) ).
fof(f38812,plain,
spl0_1305,
inference(avatar_split_clause,[],[f398,f38810]) ).
fof(f38810,plain,
( spl0_1305
<=> ! [X28,X4,X3,X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X3)),X28)),X2)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f398,axiom,
! [X2,X3,X28,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X3)),X28)),X2)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__le__add__iff2_0) ).
fof(f38808,plain,
spl0_1304,
inference(avatar_split_clause,[],[f397,f38806]) ).
fof(f38806,plain,
( spl0_1304
<=> ! [X28,X4,X3,X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X28)),X1),tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f397,axiom,
! [X2,X3,X28,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X28)),X1),tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__le__add__iff1_1) ).
fof(f38804,plain,
spl0_1303,
inference(avatar_split_clause,[],[f396,f38802]) ).
fof(f38802,plain,
( spl0_1303
<=> ! [X28,X4,X3,X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X28)),X1),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f396,axiom,
! [X2,X3,X28,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X28)),X1),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__le__add__iff1_0) ).
fof(f38800,plain,
spl0_1302,
inference(avatar_split_clause,[],[f250,f38798]) ).
fof(f38798,plain,
( spl0_1302
<=> ! [X28,X4,X3,X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X28)),X1),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f250,axiom,
! [X2,X3,X28,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X28)),X1),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__less__add__iff1_0) ).
fof(f38796,plain,
spl0_1301,
inference(avatar_split_clause,[],[f249,f38794]) ).
fof(f38794,plain,
( spl0_1301
<=> ! [X28,X4,X3,X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X28)),X1),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f249,axiom,
! [X2,X3,X28,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X28)),X1),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__less__add__iff1_1) ).
fof(f38792,plain,
spl0_1300,
inference(avatar_split_clause,[],[f248,f38790]) ).
fof(f38790,plain,
( spl0_1300
<=> ! [X28,X4,X3,X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X3)),X28)),X2)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f248,axiom,
! [X2,X3,X28,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X3)),X28)),X2)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__less__add__iff2_0) ).
fof(f38788,plain,
spl0_1299,
inference(avatar_split_clause,[],[f247,f38786]) ).
fof(f38786,plain,
( spl0_1299
<=> ! [X28,X4,X3,X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X3)),X28)),X2)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f247,axiom,
! [X2,X3,X28,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X3)),X28)),X2)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__less__add__iff2_1) ).
fof(f38403,plain,
spl0_1298,
inference(avatar_split_clause,[],[f1105,f38401]) ).
fof(f38401,plain,
( spl0_1298
<=> ! [X10,X32,X11,X5,X15,X23] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ c_Deriv_Oderiv(X32,X11,X23,X5)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Otimes__class_Otimes(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(X10,X11)),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X15),hAPP(X32,X11))),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f1105,axiom,
! [X10,X11,X15,X5,X32,X23] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ c_Deriv_Oderiv(X32,X11,X23,X5)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Otimes__class_Otimes(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(X10,X11)),X23)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X15),hAPP(X32,X11))),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__mult_H_0) ).
fof(f38399,plain,
spl0_1297,
inference(avatar_split_clause,[],[f1104,f38397]) ).
fof(f38397,plain,
( spl0_1297
<=> ! [X10,X47,X11,X5,X32,X46] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X46,X5)
| ~ c_Deriv_Oderiv(X32,X11,X47,X5)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Otimes__class_Otimes(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X46),hAPP(X32,X11))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X47),hAPP(X10,X11))),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f1104,axiom,
! [X10,X46,X11,X47,X5,X32] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X46,X5)
| ~ c_Deriv_Oderiv(X32,X11,X47,X5)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Otimes__class_Otimes(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X46),hAPP(X32,X11))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X47),hAPP(X10,X11))),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__mult_0) ).
fof(f36951,plain,
( spl0_1296
| ~ spl0_124
| ~ spl0_152
| ~ spl0_214
| ~ spl0_304
| ~ spl0_406
| ~ spl0_1281 ),
inference(avatar_split_clause,[],[f36663,f36624,f4275,f3114,f2524,f2250,f2116,f36949]) ).
fof(f36949,plain,
( spl0_1296
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_FFT__Mirabelle_ODFT(c_Orderings_Obot__class_Obot(tc_nat),X0,v_i) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f2250,plain,
( spl0_152
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f36624,plain,
( spl0_1281
<=> ! [X6,X2] : c_FFT__Mirabelle_ODFT(X2,X6,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i))),X6,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f36663,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_FFT__Mirabelle_ODFT(c_Orderings_Obot__class_Obot(tc_nat),X0,v_i)
| ~ spl0_124
| ~ spl0_152
| ~ spl0_214
| ~ spl0_304
| ~ spl0_406
| ~ spl0_1281 ),
inference(forward_demodulation,[],[f36662,f3116]) ).
fof(f36662,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_FFT__Mirabelle_ODFT(c_HOL_Ozero__class_Ozero(tc_nat),X0,v_i)
| ~ spl0_124
| ~ spl0_152
| ~ spl0_214
| ~ spl0_406
| ~ spl0_1281 ),
inference(forward_demodulation,[],[f36661,f4443]) ).
fof(f36661,plain,
( ! [X0] : c_FFT__Mirabelle_ODFT(c_HOL_Ozero__class_Ozero(tc_nat),X0,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i))),X0,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)))
| ~ spl0_152
| ~ spl0_214
| ~ spl0_1281 ),
inference(forward_demodulation,[],[f36648,f2525]) ).
fof(f36648,plain,
( ! [X0] : c_FFT__Mirabelle_ODFT(c_HOL_Ozero__class_Ozero(tc_nat),X0,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i))),X0,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))
| ~ spl0_152
| ~ spl0_1281 ),
inference(superposition,[],[f36625,f2252]) ).
fof(f2252,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f2250]) ).
fof(f36625,plain,
( ! [X2,X6] : c_FFT__Mirabelle_ODFT(X2,X6,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i))),X6,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))
| ~ spl0_1281 ),
inference(avatar_component_clause,[],[f36624]) ).
fof(f36809,plain,
spl0_1295,
inference(avatar_split_clause,[],[f1171,f36807]) ).
fof(f36807,plain,
( spl0_1295
<=> ! [X39,X10,X5,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X39))
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X2,X39,tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,X39,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f1171,axiom,
! [X2,X39,X10,X1,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X39))
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X2,X39,tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,X39,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__diff__nat__ivl_0) ).
fof(f36805,plain,
spl0_1294,
inference(avatar_split_clause,[],[f1084,f36803]) ).
fof(f36803,plain,
( spl0_1294
<=> ! [X39,X10,X5,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X39))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X2,X39,tc_nat))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,X39,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f1084,axiom,
! [X2,X39,X10,X1,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X39))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X2,X39,tc_nat))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,X39,tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__add__nat__ivl_0) ).
fof(f36801,plain,
spl0_1293,
inference(avatar_split_clause,[],[f841,f36799]) ).
fof(f36799,plain,
( spl0_1293
<=> ! [X5,X42,X14,X6,X9,X7] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X42)),X9),X5),X14))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f841,axiom,
! [X6,X9,X7,X14,X5,X42] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X42)),X9),X5),X14))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__add__iff1_0) ).
fof(f36797,plain,
spl0_1292,
inference(avatar_split_clause,[],[f840,f36795]) ).
fof(f36795,plain,
( spl0_1292
<=> ! [X5,X42,X14,X6,X9,X7] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X42)),X9),X5),X14))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f840,axiom,
! [X6,X9,X7,X14,X5,X42] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X42)),X9),X5),X14))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__add__iff1_1) ).
fof(f36793,plain,
spl0_1291,
inference(avatar_split_clause,[],[f839,f36791]) ).
fof(f36791,plain,
( spl0_1291
<=> ! [X5,X42,X9,X14,X6,X7] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| hBOOL(hAPP(c_lessequals(X9,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X6)),X42)),X14)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f839,axiom,
! [X6,X9,X7,X14,X5,X42] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| hBOOL(hAPP(c_lessequals(X9,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X6)),X42)),X14)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__add__iff2_0) ).
fof(f36789,plain,
spl0_1290,
inference(avatar_split_clause,[],[f838,f36787]) ).
fof(f36787,plain,
( spl0_1290
<=> ! [X5,X42,X9,X14,X6,X7] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_lessequals(X9,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X6)),X42)),X14)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f838,axiom,
! [X6,X9,X7,X14,X5,X42] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_lessequals(X9,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X6)),X42)),X14)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__add__iff2_1) ).
fof(f36785,plain,
spl0_1289,
inference(avatar_split_clause,[],[f836,f36783]) ).
fof(f36783,plain,
( spl0_1289
<=> ! [X5,X42,X14,X6,X9,X7] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X42)),X9),X5),X14))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f836,axiom,
! [X6,X9,X7,X14,X5,X42] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X42)),X9),X5),X14))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__add__iff1_0) ).
fof(f36781,plain,
spl0_1288,
inference(avatar_split_clause,[],[f835,f36779]) ).
fof(f36779,plain,
( spl0_1288
<=> ! [X5,X42,X14,X6,X9,X7] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X42)),X9),X5),X14))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f835,axiom,
! [X6,X9,X7,X14,X5,X42] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X42)),X9),X5),X14))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__add__iff1_1) ).
fof(f36777,plain,
spl0_1287,
inference(avatar_split_clause,[],[f834,f36775]) ).
fof(f36775,plain,
( spl0_1287
<=> ! [X5,X42,X9,X14,X6,X7] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X6)),X42)),X14)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f834,axiom,
! [X6,X9,X7,X14,X5,X42] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X6)),X42)),X14)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__add__iff2_0) ).
fof(f36773,plain,
( spl0_1286
| ~ spl0_124
| ~ spl0_152
| ~ spl0_214
| ~ spl0_304
| ~ spl0_406
| ~ spl0_1279 ),
inference(avatar_split_clause,[],[f36642,f36616,f4275,f3114,f2524,f2250,f2116,f36771]) ).
fof(f36771,plain,
( spl0_1286
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_FFT__Mirabelle_OIDFT(c_Orderings_Obot__class_Obot(tc_nat),X0,v_i) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f36616,plain,
( spl0_1279
<=> ! [X6,X2] : c_FFT__Mirabelle_OIDFT(X2,X6,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),X6),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f36642,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_FFT__Mirabelle_OIDFT(c_Orderings_Obot__class_Obot(tc_nat),X0,v_i)
| ~ spl0_124
| ~ spl0_152
| ~ spl0_214
| ~ spl0_304
| ~ spl0_406
| ~ spl0_1279 ),
inference(forward_demodulation,[],[f36641,f3116]) ).
fof(f36641,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_FFT__Mirabelle_OIDFT(c_HOL_Ozero__class_Ozero(tc_nat),X0,v_i)
| ~ spl0_124
| ~ spl0_152
| ~ spl0_214
| ~ spl0_406
| ~ spl0_1279 ),
inference(forward_demodulation,[],[f36640,f4443]) ).
fof(f36640,plain,
( ! [X0] : c_FFT__Mirabelle_OIDFT(c_HOL_Ozero__class_Ozero(tc_nat),X0,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),X0),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)))
| ~ spl0_152
| ~ spl0_214
| ~ spl0_1279 ),
inference(forward_demodulation,[],[f36627,f2525]) ).
fof(f36627,plain,
( ! [X0] : c_FFT__Mirabelle_OIDFT(c_HOL_Ozero__class_Ozero(tc_nat),X0,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),X0),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))
| ~ spl0_152
| ~ spl0_1279 ),
inference(superposition,[],[f36617,f2252]) ).
fof(f36617,plain,
( ! [X2,X6] : c_FFT__Mirabelle_OIDFT(X2,X6,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),X6),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))
| ~ spl0_1279 ),
inference(avatar_component_clause,[],[f36616]) ).
fof(f36769,plain,
spl0_1285,
inference(avatar_split_clause,[],[f833,f36767]) ).
fof(f36767,plain,
( spl0_1285
<=> ! [X5,X42,X9,X14,X6,X7] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X6)),X42)),X14)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f833,axiom,
! [X6,X9,X7,X14,X5,X42] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X6)),X42)),X14)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__add__iff2_1) ).
fof(f36682,plain,
spl0_1284,
inference(avatar_split_clause,[],[f1193,f36680]) ).
fof(f36680,plain,
( spl0_1284
<=> ! [X10,X0,X5,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0))),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f1193,axiom,
! [X2,X10,X0,X1,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0))),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__shift__bounds__nat__ivl_0) ).
fof(f36678,plain,
spl0_1283,
inference(avatar_split_clause,[],[f105,f36676]) ).
fof(f36676,plain,
( spl0_1283
<=> ! [X28,X4,X3,X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X28)),X1) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f105,axiom,
! [X2,X3,X28,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X28)),X1) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__eq__add__iff1_0) ).
fof(f36672,plain,
spl0_1282,
inference(avatar_split_clause,[],[f902,f36670]) ).
fof(f36670,plain,
( spl0_1282
<=> ! [X5,X6,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X6)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f902,axiom,
! [X2,X1,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X6)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__diff__rev__if_1) ).
fof(f36626,plain,
( spl0_1281
| ~ spl0_304
| ~ spl0_1278 ),
inference(avatar_split_clause,[],[f36519,f36516,f3114,f36624]) ).
fof(f36516,plain,
( spl0_1278
<=> ! [X6,X2] : c_FFT__Mirabelle_ODFT(X2,X6,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i))),X6,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f36519,plain,
( ! [X2,X6] : c_FFT__Mirabelle_ODFT(X2,X6,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i))),X6,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))
| ~ spl0_304
| ~ spl0_1278 ),
inference(forward_demodulation,[],[f36517,f3116]) ).
fof(f36517,plain,
( ! [X2,X6] : c_FFT__Mirabelle_ODFT(X2,X6,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i))),X6,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat))
| ~ spl0_1278 ),
inference(avatar_component_clause,[],[f36516]) ).
fof(f36622,plain,
( spl0_1280
| ~ spl0_182
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2542,f2492,f2384,f36620]) ).
fof(f36620,plain,
( spl0_1280
<=> ! [X0,X1] :
( ~ c_Series_Osummable(X0,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_SEQ_OCauchy(X0,X1)
| ~ class_RealVector_Ometric__space(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f2384,plain,
( spl0_182
<=> ! [X6,X18,X5] :
( ~ class_RealVector_Ometric__space(X5)
| c_SEQ_OCauchy(X18,X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f2492,plain,
( spl0_206
<=> ! [X5,X10] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5)
| c_SEQ_OLIMSEQ(X10,c_HOL_Ozero__class_Ozero(X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f2542,plain,
( ! [X0,X1] :
( ~ c_Series_Osummable(X0,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_SEQ_OCauchy(X0,X1)
| ~ class_RealVector_Ometric__space(X1) )
| ~ spl0_182
| ~ spl0_206 ),
inference(resolution,[],[f2493,f2385]) ).
fof(f2385,plain,
( ! [X18,X6,X5] :
( ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| c_SEQ_OCauchy(X18,X5)
| ~ class_RealVector_Ometric__space(X5) )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f2384]) ).
fof(f2493,plain,
( ! [X10,X5] :
( c_SEQ_OLIMSEQ(X10,c_HOL_Ozero__class_Ozero(X5),X5)
| ~ c_Series_Osummable(X10,X5)
| ~ class_RealVector_Oreal__normed__vector(X5) )
| ~ spl0_206 ),
inference(avatar_component_clause,[],[f2492]) ).
fof(f36618,plain,
( spl0_1279
| ~ spl0_304
| ~ spl0_1277 ),
inference(avatar_split_clause,[],[f36514,f36511,f3114,f36616]) ).
fof(f36511,plain,
( spl0_1277
<=> ! [X6,X2] : c_FFT__Mirabelle_OIDFT(X2,X6,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),X6),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f36514,plain,
( ! [X2,X6] : c_FFT__Mirabelle_OIDFT(X2,X6,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),X6),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))
| ~ spl0_304
| ~ spl0_1277 ),
inference(forward_demodulation,[],[f36512,f3116]) ).
fof(f36512,plain,
( ! [X2,X6] : c_FFT__Mirabelle_OIDFT(X2,X6,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),X6),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat))
| ~ spl0_1277 ),
inference(avatar_component_clause,[],[f36511]) ).
fof(f36518,plain,
spl0_1278,
inference(avatar_split_clause,[],[f1197,f36516]) ).
fof(f1197,axiom,
! [X2,X6] : c_FFT__Mirabelle_ODFT(X2,X6,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i))),X6,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DFT__def_0) ).
fof(f36513,plain,
spl0_1277,
inference(avatar_split_clause,[],[f1188,f36511]) ).
fof(f1188,axiom,
! [X2,X6] : c_FFT__Mirabelle_OIDFT(X2,X6,v_i) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),X6),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2))),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_IDFT__def_0) ).
fof(f36509,plain,
spl0_1276,
inference(avatar_split_clause,[],[f1125,f36507]) ).
fof(f36507,plain,
( spl0_1276
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) = X7
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X6))),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f1125,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) = X7
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X6))),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_division__ring__inverse__diff_0) ).
fof(f36505,plain,
spl0_1275,
inference(avatar_split_clause,[],[f661,f36503]) ).
fof(f36503,plain,
( spl0_1275
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f661,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__add_0) ).
fof(f36501,plain,
spl0_1274,
inference(avatar_split_clause,[],[f660,f36499]) ).
fof(f36499,plain,
( spl0_1274
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7))),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f660,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) = X7
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7))),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_division__ring__inverse__add_0) ).
fof(f36497,plain,
( spl0_1273
| ~ spl0_155
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2375,f2363,f2264,f36495]) ).
fof(f2264,plain,
( spl0_155
<=> ! [X57,X56] :
( ~ class_Lattices_Olattice(X57)
| class_Lattices_Oupper__semilattice(tc_fun(X56,X57)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f2363,plain,
( spl0_179
<=> ! [X5,X11] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X11,X5) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f2375,plain,
( ! [X2,X3,X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,X3)) = X1
| ~ class_Lattices_Olattice(X3) )
| ~ spl0_155
| ~ spl0_179 ),
inference(resolution,[],[f2364,f2265]) ).
fof(f2265,plain,
( ! [X56,X57] :
( class_Lattices_Oupper__semilattice(tc_fun(X56,X57))
| ~ class_Lattices_Olattice(X57) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f2264]) ).
fof(f2364,plain,
( ! [X11,X5] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X11,X5) = X11 )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f2363]) ).
fof(f36493,plain,
spl0_1272,
inference(avatar_split_clause,[],[f259,f36491]) ).
fof(f36491,plain,
( spl0_1272
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f259,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__left__mono__neg_0) ).
fof(f36488,plain,
( spl0_1271
| ~ spl0_304
| ~ spl0_1269 ),
inference(avatar_split_clause,[],[f35106,f35103,f3114,f36486]) ).
fof(f36486,plain,
( spl0_1271
<=> ! [X2,X5,X11] :
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X2)),c_HOL_Oone__class_Oone(X5))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),c_HOL_Oone__class_Oone(X5))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_Power_Opower__class_Opower(X5),X11)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))
| ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Oone__class_Oone(X5) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f35103,plain,
( spl0_1269
<=> ! [X2,X5,X11] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Oone__class_Oone(X5) = X11
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_Power_Opower__class_Opower(X5),X11)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X2)),c_HOL_Oone__class_Oone(X5))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),c_HOL_Oone__class_Oone(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f35106,plain,
( ! [X2,X11,X5] :
( hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X2)),c_HOL_Oone__class_Oone(X5))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),c_HOL_Oone__class_Oone(X5))) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_Power_Opower__class_Opower(X5),X11)),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))
| ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Oone__class_Oone(X5) = X11 )
| ~ spl0_304
| ~ spl0_1269 ),
inference(forward_demodulation,[],[f35104,f3116]) ).
fof(f35104,plain,
( ! [X2,X11,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Oone__class_Oone(X5) = X11
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_Power_Opower__class_Opower(X5),X11)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X2)),c_HOL_Oone__class_Oone(X5))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),c_HOL_Oone__class_Oone(X5))) )
| ~ spl0_1269 ),
inference(avatar_component_clause,[],[f35103]) ).
fof(f35891,plain,
( spl0_1270
| ~ spl0_156
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f2371,f2351,f2268,f35889]) ).
fof(f2268,plain,
( spl0_156
<=> ! [X57,X56] :
( ~ class_Lattices_Olattice(X57)
| class_Lattices_Olower__semilattice(tc_fun(X56,X57)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f2351,plain,
( spl0_176
<=> ! [X5,X11] :
( ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X11,X5) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f2371,plain,
( ! [X2,X3,X1] :
( c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,X3)) = X1
| ~ class_Lattices_Olattice(X3) )
| ~ spl0_156
| ~ spl0_176 ),
inference(resolution,[],[f2352,f2269]) ).
fof(f2269,plain,
( ! [X56,X57] :
( class_Lattices_Olower__semilattice(tc_fun(X56,X57))
| ~ class_Lattices_Olattice(X57) )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f2268]) ).
fof(f2352,plain,
( ! [X11,X5] :
( ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X11,X5) = X11 )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f2351]) ).
fof(f35105,plain,
spl0_1269,
inference(avatar_split_clause,[],[f1120,f35103]) ).
fof(f1120,axiom,
! [X2,X11,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Oone__class_Oone(X5) = X11
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(c_Power_Opower__class_Opower(X5),X11)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X2)),c_HOL_Oone__class_Oone(X5))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),c_HOL_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_geometric__sum_0) ).
fof(f35101,plain,
spl0_1268,
inference(avatar_split_clause,[],[f1099,f35099]) ).
fof(f35099,plain,
( spl0_1268
<=> ! [X38,X10,X20,X6,X5,X32,X7] :
( ~ class_RealVector_Oreal__normed__field(X20)
| c_HOL_Ozero__class_Ozero(X20) = X7
| ~ c_Limits_Otendsto(X10,X6,X38,X5,X20)
| ~ c_Limits_Otendsto(X32,X7,X38,X5,X20)
| c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oinverse__class_Odivide(X20)),X10),X32,X5,X20,X20),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X20),X6),X7),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f1099,axiom,
! [X38,X10,X6,X7,X5,X32,X20] :
( ~ class_RealVector_Oreal__normed__field(X20)
| c_HOL_Ozero__class_Ozero(X20) = X7
| ~ c_Limits_Otendsto(X10,X6,X38,X5,X20)
| ~ c_Limits_Otendsto(X32,X7,X38,X5,X20)
| c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oinverse__class_Odivide(X20)),X10),X32,X5,X20,X20),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X20),X6),X7),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_tendsto__divide_0) ).
fof(f35097,plain,
spl0_1267,
inference(avatar_split_clause,[],[f918,f35095]) ).
fof(f35095,plain,
( spl0_1267
<=> ! [X5,X9,X7,X14,X6] :
( ~ class_Ring__and__Field_Opordered__semiring(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(X9,X5),X14))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f918,axiom,
! [X6,X9,X7,X14,X5] :
( ~ class_Ring__and__Field_Opordered__semiring(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(X9,X5),X14))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__mono_H_0) ).
fof(f35093,plain,
spl0_1266,
inference(avatar_split_clause,[],[f917,f35091]) ).
fof(f35091,plain,
( spl0_1266
<=> ! [X5,X9,X7,X14,X6] :
( ~ class_Ring__and__Field_Opordered__semiring(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(X9,X5),X14))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f917,axiom,
! [X6,X9,X7,X14,X5] :
( ~ class_Ring__and__Field_Opordered__semiring(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(X9,X5),X14))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__mono_0) ).
fof(f35089,plain,
spl0_1265,
inference(avatar_split_clause,[],[f701,f35087]) ).
fof(f35087,plain,
( spl0_1265
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f701,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__eq_9) ).
fof(f35085,plain,
spl0_1264,
inference(avatar_split_clause,[],[f700,f35083]) ).
fof(f35083,plain,
( spl0_1264
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f700,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__divide__eq_9) ).
fof(f35081,plain,
spl0_1263,
inference(avatar_split_clause,[],[f689,f35079]) ).
fof(f35079,plain,
( spl0_1263
<=> ! [X5,X9,X7,X14,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),X14))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f689,axiom,
! [X6,X9,X7,X14,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),X14))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__strict__mono_0) ).
fof(f35077,plain,
spl0_1262,
inference(avatar_split_clause,[],[f672,f35075]) ).
fof(f35075,plain,
( spl0_1262
<=> ! [X5,X9,X7,X14,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),X14))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f672,axiom,
! [X6,X9,X7,X14,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),X14))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__strict__mono_H_0) ).
fof(f35073,plain,
spl0_1261,
inference(avatar_split_clause,[],[f665,f35071]) ).
fof(f35071,plain,
( spl0_1261
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f665,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__eq_8) ).
fof(f35069,plain,
spl0_1260,
inference(avatar_split_clause,[],[f664,f35067]) ).
fof(f35067,plain,
( spl0_1260
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f664,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__eq_9) ).
fof(f35065,plain,
spl0_1259,
inference(avatar_split_clause,[],[f663,f35063]) ).
fof(f35063,plain,
( spl0_1259
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f663,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__divide__eq_8) ).
fof(f35061,plain,
spl0_1258,
inference(avatar_split_clause,[],[f662,f35059]) ).
fof(f35059,plain,
( spl0_1258
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f662,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__divide__eq_9) ).
fof(f35057,plain,
spl0_1257,
inference(avatar_split_clause,[],[f638,f35055]) ).
fof(f35055,plain,
( spl0_1257
<=> ! [X5,X9,X7,X14,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),X14))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f638,axiom,
! [X6,X9,X7,X14,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),X14))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__less__imp__less_0) ).
fof(f35053,plain,
spl0_1256,
inference(avatar_split_clause,[],[f637,f35051]) ).
fof(f35051,plain,
( spl0_1256
<=> ! [X5,X6,X7,X14,X9] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(X9,X5),X14))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f637,axiom,
! [X6,X9,X7,X14,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(X9,X5),X14))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__le__imp__less_0) ).
fof(f35049,plain,
spl0_1255,
inference(avatar_split_clause,[],[f547,f35047]) ).
fof(f35047,plain,
( spl0_1255
<=> ! [X11,X8,X12,X5,X16] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X8,X5),X16))
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X8))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X16),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X12),X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f547,axiom,
! [X11,X8,X16,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X8,X5),X16))
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X8))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X16),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X12),X8))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_frac__le_0) ).
fof(f35045,plain,
spl0_1254,
inference(avatar_split_clause,[],[f262,f35043]) ).
fof(f35043,plain,
( spl0_1254
<=> ! [X11,X8,X12,X5,X16] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X8,X5),X16))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X8))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X16),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X12),X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f262,axiom,
! [X11,X8,X16,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X8,X5),X16))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X8))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X16),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X12),X8))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_frac__less2_0) ).
fof(f35041,plain,
spl0_1253,
inference(avatar_split_clause,[],[f139,f35039]) ).
fof(f35039,plain,
( spl0_1253
<=> ! [X11,X8,X12,X5,X16] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X8,X5),X16))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X8))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X16),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X12),X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f139,axiom,
! [X11,X8,X16,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X8,X5),X16))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X8))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X16),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X12),X8))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_frac__less_0) ).
fof(f35037,plain,
spl0_1252,
inference(avatar_split_clause,[],[f90,f35035]) ).
fof(f35035,plain,
( spl0_1252
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f90,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__eq_8) ).
fof(f35033,plain,
spl0_1251,
inference(avatar_split_clause,[],[f89,f35031]) ).
fof(f35031,plain,
( spl0_1251
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f89,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__divide__eq_8) ).
fof(f34404,plain,
spl0_1250,
inference(avatar_split_clause,[],[f1223,f34402]) ).
fof(f34402,plain,
( spl0_1250
<=> ! [X10,X32,X20,X5,X25] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Ominus__class_Ominus(X5)),X10),X32,X20,X5,X5)),X25) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),X25)),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X32),X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f1223,axiom,
! [X10,X5,X25,X32,X20] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Ominus__class_Ominus(X5)),X10),X32,X20,X5,X5)),X25) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),X25)),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X32),X25)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__subtractf_0) ).
fof(f34400,plain,
spl0_1249,
inference(avatar_split_clause,[],[f1151,f34398]) ).
fof(f34398,plain,
( spl0_1249
<=> ! [X10,X32,X20,X5,X25] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Oplus__class_Oplus(X5)),X10),X32,X20,X5,X5)),X25) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),X25)),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X32),X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f1151,axiom,
! [X10,X5,X25,X32,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Oplus__class_Oplus(X5)),X10),X32,X20,X5,X5)),X25) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),X25)),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X32),X25)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__addf_0) ).
fof(f34396,plain,
( ~ spl0_1246
| spl0_1247
| ~ spl0_1248
| ~ spl0_323
| ~ spl0_644 ),
inference(avatar_split_clause,[],[f9272,f9060,f3220,f34393,f34389,f34385]) ).
fof(f34385,plain,
( spl0_1246
<=> class_Lattices_Obounded__lattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f34389,plain,
( spl0_1247
<=> v_n = v_i ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f34393,plain,
( spl0_1248
<=> v_n = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f3220,plain,
( spl0_323
<=> ! [X25,X5,X26] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Orderings_Obot__class_Obot(X5) = X25
| c_Orderings_Obot__class_Obot(X5) != c_Lattices_Oupper__semilattice__class_Osup(X25,X26,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f9060,plain,
( spl0_644
<=> v_n = c_Lattices_Oupper__semilattice__class_Osup(v_i,v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f9272,plain,
( v_n != c_Orderings_Obot__class_Obot(tc_nat)
| v_n = v_i
| ~ class_Lattices_Obounded__lattice(tc_nat)
| ~ spl0_323
| ~ spl0_644 ),
inference(inner_rewriting,[],[f9263]) ).
fof(f9263,plain,
( v_n != c_Orderings_Obot__class_Obot(tc_nat)
| v_i = c_Orderings_Obot__class_Obot(tc_nat)
| ~ class_Lattices_Obounded__lattice(tc_nat)
| ~ spl0_323
| ~ spl0_644 ),
inference(superposition,[],[f3221,f9062]) ).
fof(f9062,plain,
( v_n = c_Lattices_Oupper__semilattice__class_Osup(v_i,v_n,tc_nat)
| ~ spl0_644 ),
inference(avatar_component_clause,[],[f9060]) ).
fof(f3221,plain,
( ! [X26,X5,X25] :
( c_Orderings_Obot__class_Obot(X5) != c_Lattices_Oupper__semilattice__class_Osup(X25,X26,X5)
| c_Orderings_Obot__class_Obot(X5) = X25
| ~ class_Lattices_Obounded__lattice(X5) )
| ~ spl0_323 ),
inference(avatar_component_clause,[],[f3220]) ).
fof(f34383,plain,
spl0_1245,
inference(avatar_split_clause,[],[f959,f34381]) ).
fof(f34381,plain,
( spl0_1245
<=> ! [X5,X42,X14,X6,X9,X7] :
( ~ class_Ring__and__Field_Oring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X6)),X42)),X14) = X9
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f959,axiom,
! [X6,X9,X7,X14,X5,X42] :
( ~ class_Ring__and__Field_Oring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X6)),X42)),X14) = X9
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X14) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_eq__add__iff2_0) ).
fof(f34379,plain,
spl0_1244,
inference(avatar_split_clause,[],[f903,f34377]) ).
fof(f34377,plain,
( spl0_1244
<=> ! [X5,X6,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f903,axiom,
! [X2,X1,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__diff__inverse_0) ).
fof(f34375,plain,
spl0_1243,
inference(avatar_split_clause,[],[f706,f34373]) ).
fof(f34373,plain,
( spl0_1243
<=> ! [X5,X9,X7,X14,X6] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| X6 = X7
| X9 = X14
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X14)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X14)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f706,axiom,
! [X6,X9,X7,X14,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| X6 = X7
| X9 = X14
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X14)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X14)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__ringb_Onoteq__reduce_0) ).
fof(f34371,plain,
spl0_1242,
inference(avatar_split_clause,[],[f640,f34369]) ).
fof(f34369,plain,
( spl0_1242
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f640,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__strict__left__mono_0) ).
fof(f34367,plain,
spl0_1241,
inference(avatar_split_clause,[],[f639,f34365]) ).
fof(f34365,plain,
( spl0_1241
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f639,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__strict__left__mono__neg_0) ).
fof(f34363,plain,
spl0_1240,
inference(avatar_split_clause,[],[f260,f34361]) ).
fof(f34361,plain,
( spl0_1240
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f260,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__left__mono_0) ).
fof(f34359,plain,
( ~ spl0_1239
| ~ spl0_304
| ~ spl0_324
| ~ spl0_492
| spl0_1238 ),
inference(avatar_split_clause,[],[f34354,f34348,f5080,f3224,f3114,f34356]) ).
fof(f5080,plain,
( spl0_492
<=> ! [X6,X25,X5] : c_Set_Oinsert(X6,X25,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X25,tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f34348,plain,
( spl0_1238
<=> hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f34354,plain,
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) != hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Set_Oinsert(v_i,c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_nat))
| ~ spl0_304
| ~ spl0_324
| ~ spl0_492
| spl0_1238 ),
inference(forward_demodulation,[],[f34353,f3116]) ).
fof(f34353,plain,
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) != hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Set_Oinsert(v_i,c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_nat))
| ~ spl0_324
| ~ spl0_492
| spl0_1238 ),
inference(forward_demodulation,[],[f34352,f6320]) ).
fof(f6320,plain,
( ! [X8,X9,X7] : c_Lattices_Oupper__semilattice__class_Osup(X9,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_bool)),X8),tc_fun(X8,tc_bool)) = c_Set_Oinsert(X7,X9,X8)
| ~ spl0_324
| ~ spl0_492 ),
inference(superposition,[],[f5081,f3225]) ).
fof(f5081,plain,
( ! [X6,X5,X25] : c_Set_Oinsert(X6,X25,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X25,tc_fun(X5,tc_bool))
| ~ spl0_492 ),
inference(avatar_component_clause,[],[f5080]) ).
fof(f34352,plain,
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) != hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_fun(tc_nat,tc_bool)))
| ~ spl0_324
| spl0_1238 ),
inference(forward_demodulation,[],[f34350,f3225]) ).
fof(f34350,plain,
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) != hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool)))
| spl0_1238 ),
inference(avatar_component_clause,[],[f34348]) ).
fof(f34351,plain,
~ spl0_1238,
inference(avatar_split_clause,[],[f1312,f34348]) ).
fof(f1312,axiom,
hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_SetInterval_Oord__class_OatLeastLessThan(v_i,v_n,tc_nat)) != hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n))),hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),tc_nat,tc_nat,tc_nat),v_i)))),tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat))),v_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_i,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_i,v_n,tc_nat),tc_fun(tc_nat,tc_bool))),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_conjecture_0) ).
fof(f34242,plain,
spl0_1237,
inference(avatar_split_clause,[],[f1144,f34240]) ).
fof(f34240,plain,
( spl0_1237
<=> ! [X5,X10,X11,X32,X20,X29,X1] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OLIM(X10,X11,X29,X5,X20)
| ~ c_Lim_OLIM(X32,X11,X1,X5,X20)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X32,X5,X20,X20),X11,hAPP(hAPP(c_HOL_Ominus__class_Ominus(X20),X29),X1),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f1144,axiom,
! [X10,X29,X11,X1,X5,X32,X20] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OLIM(X10,X11,X29,X5,X20)
| ~ c_Lim_OLIM(X32,X11,X1,X5,X20)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X32,X5,X20,X20),X11,hAPP(hAPP(c_HOL_Ominus__class_Ominus(X20),X29),X1),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__diff_0) ).
fof(f34238,plain,
spl0_1236,
inference(avatar_split_clause,[],[f1135,f34236]) ).
fof(f34236,plain,
( spl0_1236
<=> ! [X5,X10,X32,X20,X22,X6,X21] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Lim_OLIM(X10,X6,X21,X5,X20)
| ~ c_Lim_OLIM(X32,X6,X22,X5,X20)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X10),X32,X5,X20,X20),X6,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X21),X22),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f1135,axiom,
! [X21,X10,X6,X5,X22,X32,X20] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Lim_OLIM(X10,X6,X21,X5,X20)
| ~ c_Lim_OLIM(X32,X6,X22,X5,X20)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X10),X32,X5,X20,X20),X6,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X21),X22),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__mult_0) ).
fof(f34234,plain,
spl0_1235,
inference(avatar_split_clause,[],[f865,f34232]) ).
fof(f34232,plain,
( spl0_1235
<=> ! [X5,X10,X32,X20,X22,X6,X21] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OLIM(X10,X6,X21,X5,X20)
| ~ c_Lim_OLIM(X32,X6,X22,X5,X20)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oplus__class_Oplus(X20)),X10),X32,X5,X20,X20),X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X21),X22),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f865,axiom,
! [X21,X10,X6,X5,X22,X32,X20] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OLIM(X10,X6,X21,X5,X20)
| ~ c_Lim_OLIM(X32,X6,X22,X5,X20)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oplus__class_Oplus(X20)),X10),X32,X5,X20,X20),X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X21),X22),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__add_0) ).
fof(f34190,plain,
( spl0_1234
| ~ spl0_138
| ~ spl0_304
| ~ spl0_336
| ~ spl0_1233 ),
inference(avatar_split_clause,[],[f34186,f34181,f3434,f3114,f2186,f34188]) ).
fof(f34188,plain,
( spl0_1234
<=> ! [X2,X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2))),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f34181,plain,
( spl0_1233
<=> ! [X2,X0] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_FFT__Mirabelle_Oroot(X2))),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f34186,plain,
( ! [X2,X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2))),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X2)) )
| ~ spl0_138
| ~ spl0_304
| ~ spl0_336
| ~ spl0_1233 ),
inference(forward_demodulation,[],[f34185,f3685]) ).
fof(f34185,plain,
( ! [X2,X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_FFT__Mirabelle_Oroot(X2))),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X2)) )
| ~ spl0_304
| ~ spl0_1233 ),
inference(forward_demodulation,[],[f34184,f3116]) ).
fof(f34184,plain,
( ! [X2,X0] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X2))
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_FFT__Mirabelle_Oroot(X2))),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ spl0_304
| ~ spl0_1233 ),
inference(forward_demodulation,[],[f34182,f3116]) ).
fof(f34182,plain,
( ! [X2,X0] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_FFT__Mirabelle_Oroot(X2))),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ spl0_1233 ),
inference(avatar_component_clause,[],[f34181]) ).
fof(f34183,plain,
spl0_1233,
inference(avatar_split_clause,[],[f760,f34181]) ).
fof(f760,axiom,
! [X2,X0] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_FFT__Mirabelle_Oroot(X2))),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_root__summation__inv_0) ).
fof(f34126,plain,
( spl0_1232
| ~ spl0_304
| ~ spl0_1230 ),
inference(avatar_split_clause,[],[f34118,f34115,f3114,f34124]) ).
fof(f34124,plain,
( spl0_1232
<=> ! [X5,X0,X10] :
( c_Series_Osuminf(X10,X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat))),c_Series_Osuminf(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X5))
| ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f34115,plain,
( spl0_1230
<=> ! [X5,X0,X10] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5)
| c_Series_Osuminf(X10,X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))),c_Series_Osuminf(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f34118,plain,
( ! [X10,X0,X5] :
( c_Series_Osuminf(X10,X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat))),c_Series_Osuminf(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X5))
| ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5) )
| ~ spl0_304
| ~ spl0_1230 ),
inference(forward_demodulation,[],[f34116,f3116]) ).
fof(f34116,plain,
( ! [X10,X0,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5)
| c_Series_Osuminf(X10,X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))),c_Series_Osuminf(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X5)) )
| ~ spl0_1230 ),
inference(avatar_component_clause,[],[f34115]) ).
fof(f34122,plain,
( spl0_1231
| ~ spl0_304
| ~ spl0_1229 ),
inference(avatar_split_clause,[],[f34113,f34110,f3114,f34120]) ).
fof(f34120,plain,
( spl0_1231
<=> ! [X5,X0,X10] :
( c_Series_Osuminf(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),c_Series_Osuminf(X10,X5)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat)))
| ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f34110,plain,
( spl0_1229
<=> ! [X5,X0,X10] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5)
| c_Series_Osuminf(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),c_Series_Osuminf(X10,X5)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f34113,plain,
( ! [X10,X0,X5] :
( c_Series_Osuminf(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),c_Series_Osuminf(X10,X5)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat)))
| ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5) )
| ~ spl0_304
| ~ spl0_1229 ),
inference(forward_demodulation,[],[f34111,f3116]) ).
fof(f34111,plain,
( ! [X10,X0,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5)
| c_Series_Osuminf(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),c_Series_Osuminf(X10,X5)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))) )
| ~ spl0_1229 ),
inference(avatar_component_clause,[],[f34110]) ).
fof(f34117,plain,
spl0_1230,
inference(avatar_split_clause,[],[f1095,f34115]) ).
fof(f1095,axiom,
! [X10,X0,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5)
| c_Series_Osuminf(X10,X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))),c_Series_Osuminf(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_suminf__split__initial__segment_0) ).
fof(f34112,plain,
spl0_1229,
inference(avatar_split_clause,[],[f1007,f34110]) ).
fof(f1007,axiom,
! [X10,X0,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5)
| c_Series_Osuminf(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),c_Series_Osuminf(X10,X5)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_suminf__minus__initial__segment_0) ).
fof(f32533,plain,
spl0_1228,
inference(avatar_split_clause,[],[f1187,f32531]) ).
fof(f32531,plain,
( spl0_1228
<=> ! [X5,X10,X20,X6,X32] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Lim_OLIM(X10,X6,c_HOL_Ozero__class_Ozero(X20),X5,X20)
| ~ c_Lim_OLIM(X32,X6,c_HOL_Ozero__class_Ozero(X20),X5,X20)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X10),X32,X5,X20,X20),X6,c_HOL_Ozero__class_Ozero(X20),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f1187,axiom,
! [X10,X6,X5,X32,X20] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Lim_OLIM(X10,X6,c_HOL_Ozero__class_Ozero(X20),X5,X20)
| ~ c_Lim_OLIM(X32,X6,c_HOL_Ozero__class_Ozero(X20),X5,X20)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X10),X32,X5,X20,X20),X6,c_HOL_Ozero__class_Ozero(X20),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__mult__zero_0) ).
fof(f32529,plain,
spl0_1227,
inference(avatar_split_clause,[],[f1143,f32527]) ).
fof(f32527,plain,
( spl0_1227
<=> ! [X38,X10,X20,X6,X5,X32,X7] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Limits_Otendsto(X10,X6,X38,X5,X20)
| ~ c_Limits_Otendsto(X32,X7,X38,X5,X20)
| c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X32,X5,X20,X20),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X20),X6),X7),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f1143,axiom,
! [X38,X10,X6,X7,X5,X32,X20] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Limits_Otendsto(X10,X6,X38,X5,X20)
| ~ c_Limits_Otendsto(X32,X7,X38,X5,X20)
| c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X32,X5,X20,X20),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X20),X6),X7),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_tendsto__diff_0) ).
fof(f32488,plain,
spl0_1226,
inference(avatar_split_clause,[],[f1134,f32486]) ).
fof(f32486,plain,
( spl0_1226
<=> ! [X38,X10,X20,X6,X5,X32,X7] :
( ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Limits_Otendsto(X10,X6,X38,X5,X20)
| ~ c_Limits_Otendsto(X32,X7,X38,X5,X20)
| c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X10),X32,X5,X20,X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X6),X7),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f1134,axiom,
! [X38,X10,X6,X7,X5,X32,X20] :
( ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Limits_Otendsto(X10,X6,X38,X5,X20)
| ~ c_Limits_Otendsto(X32,X7,X38,X5,X20)
| c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X10),X32,X5,X20,X20),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X6),X7),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult_Otendsto_0) ).
fof(f32484,plain,
spl0_1225,
inference(avatar_split_clause,[],[f1098,f32482]) ).
fof(f32482,plain,
( spl0_1225
<=> ! [X5,X10,X20,X6,X32] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OLIM(X10,X6,c_HOL_Ozero__class_Ozero(X20),X5,X20)
| ~ c_Lim_OLIM(X32,X6,c_HOL_Ozero__class_Ozero(X20),X5,X20)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oplus__class_Oplus(X20)),X10),X32,X5,X20,X20),X6,c_HOL_Ozero__class_Ozero(X20),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f1098,axiom,
! [X10,X6,X5,X32,X20] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OLIM(X10,X6,c_HOL_Ozero__class_Ozero(X20),X5,X20)
| ~ c_Lim_OLIM(X32,X6,c_HOL_Ozero__class_Ozero(X20),X5,X20)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oplus__class_Oplus(X20)),X10),X32,X5,X20,X20),X6,c_HOL_Ozero__class_Ozero(X20),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__add__zero_0) ).
fof(f32480,plain,
spl0_1224,
inference(avatar_split_clause,[],[f957,f32478]) ).
fof(f32478,plain,
( spl0_1224
<=> ! [X5,X42,X7,X6,X9] :
( ~ class_Ring__and__Field_Oring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X42)),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f957,axiom,
! [X6,X9,X7,X5,X42] :
( ~ class_Ring__and__Field_Oring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X42)),X9)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_eq__add__iff1_1) ).
fof(f32476,plain,
spl0_1223,
inference(avatar_split_clause,[],[f869,f32474]) ).
fof(f32474,plain,
( spl0_1223
<=> ! [X38,X10,X20,X6,X5,X32,X7] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Limits_Otendsto(X10,X6,X38,X5,X20)
| ~ c_Limits_Otendsto(X32,X7,X38,X5,X20)
| c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oplus__class_Oplus(X20)),X10),X32,X5,X20,X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X6),X7),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f869,axiom,
! [X38,X10,X6,X7,X5,X32,X20] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Limits_Otendsto(X10,X6,X38,X5,X20)
| ~ c_Limits_Otendsto(X32,X7,X38,X5,X20)
| c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oplus__class_Oplus(X20)),X10),X32,X5,X20,X20),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X20),X6),X7),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_tendsto__add_0) ).
fof(f32472,plain,
spl0_1222,
inference(avatar_split_clause,[],[f829,f32470]) ).
fof(f32470,plain,
( spl0_1222
<=> ! [X5,X42,X7,X6,X9] :
( ~ class_Ring__and__Field_Osemiring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X42)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f829,axiom,
! [X6,X9,X7,X5,X42] :
( ~ class_Ring__and__Field_Osemiring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X42)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X42)),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X42)),X9) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_combine__common__factor_0) ).
fof(f32468,plain,
spl0_1221,
inference(avatar_split_clause,[],[f755,f32466]) ).
fof(f32466,plain,
( spl0_1221
<=> ! [X5,X6,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f755,axiom,
! [X2,X1,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__diff__rev__if_0) ).
fof(f32464,plain,
spl0_1220,
inference(avatar_split_clause,[],[f654,f32462]) ).
fof(f32462,plain,
( spl0_1220
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f654,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__eq_1) ).
fof(f32460,plain,
spl0_1219,
inference(avatar_split_clause,[],[f653,f32458]) ).
fof(f32458,plain,
( spl0_1219
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f653,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__eq_4) ).
fof(f32456,plain,
spl0_1218,
inference(avatar_split_clause,[],[f652,f32454]) ).
fof(f32454,plain,
( spl0_1218
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f652,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__eq_5) ).
fof(f32452,plain,
spl0_1217,
inference(avatar_split_clause,[],[f651,f32450]) ).
fof(f32450,plain,
( spl0_1217
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f651,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__eq_7) ).
fof(f32418,plain,
spl0_1216,
inference(avatar_split_clause,[],[f650,f32416]) ).
fof(f32416,plain,
( spl0_1216
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f650,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__divide__eq_1) ).
fof(f32414,plain,
spl0_1215,
inference(avatar_split_clause,[],[f649,f32412]) ).
fof(f32412,plain,
( spl0_1215
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f649,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__divide__eq_4) ).
fof(f32410,plain,
spl0_1214,
inference(avatar_split_clause,[],[f648,f32408]) ).
fof(f32408,plain,
( spl0_1214
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f648,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__divide__eq_5) ).
fof(f32406,plain,
spl0_1213,
inference(avatar_split_clause,[],[f647,f32404]) ).
fof(f32404,plain,
( spl0_1213
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f647,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__divide__eq_7) ).
fof(f32402,plain,
spl0_1212,
inference(avatar_split_clause,[],[f597,f32400]) ).
fof(f32400,plain,
( spl0_1212
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f597,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__divide__eq_4) ).
fof(f32398,plain,
spl0_1211,
inference(avatar_split_clause,[],[f596,f32396]) ).
fof(f32396,plain,
( spl0_1211
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)))
| hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f596,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)))
| hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__divide__eq_1) ).
fof(f32394,plain,
spl0_1210,
inference(avatar_split_clause,[],[f595,f32392]) ).
fof(f32392,plain,
( spl0_1210
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f595,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__eq_4) ).
fof(f32390,plain,
spl0_1209,
inference(avatar_split_clause,[],[f594,f32388]) ).
fof(f32388,plain,
( spl0_1209
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f594,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__eq_1) ).
fof(f32386,plain,
spl0_1208,
inference(avatar_split_clause,[],[f201,f32384]) ).
fof(f32384,plain,
( spl0_1208
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f201,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__divide__eq_7) ).
fof(f32382,plain,
spl0_1207,
inference(avatar_split_clause,[],[f200,f32380]) ).
fof(f32380,plain,
( spl0_1207
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f200,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__divide__eq_5) ).
fof(f32378,plain,
( spl0_1206
| ~ spl0_630
| ~ spl0_1130 ),
inference(avatar_split_clause,[],[f31873,f28431,f8869,f32375]) ).
fof(f32375,plain,
( spl0_1206
<=> v_n = c_Lattices_Oupper__semilattice__class_Osup(v_n,v_i,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f8869,plain,
( spl0_630
<=> v_i = c_Lattices_Olower__semilattice__class_Oinf(v_i,v_n,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f28431,plain,
( spl0_1130
<=> ! [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_1130])]) ).
fof(f31873,plain,
( v_n = c_Lattices_Oupper__semilattice__class_Osup(v_n,v_i,tc_nat)
| ~ spl0_630
| ~ spl0_1130 ),
inference(superposition,[],[f28432,f8871]) ).
fof(f8871,plain,
( v_i = c_Lattices_Olower__semilattice__class_Oinf(v_i,v_n,tc_nat)
| ~ spl0_630 ),
inference(avatar_component_clause,[],[f8869]) ).
fof(f28432,plain,
( ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_nat),tc_nat) = X1
| ~ spl0_1130 ),
inference(avatar_component_clause,[],[f28431]) ).
fof(f32373,plain,
spl0_1205,
inference(avatar_split_clause,[],[f199,f32371]) ).
fof(f32371,plain,
( spl0_1205
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f199,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__eq_7) ).
fof(f32369,plain,
spl0_1204,
inference(avatar_split_clause,[],[f198,f32367]) ).
fof(f32367,plain,
( spl0_1204
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f198,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__eq_5) ).
fof(f32011,plain,
( spl0_1203
| ~ spl0_304
| ~ spl0_1200 ),
inference(avatar_split_clause,[],[f31866,f31863,f3114,f32009]) ).
fof(f32009,plain,
( spl0_1203
<=> ! [X37,X10,X0,X5] :
( c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X37),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat))),X5)
| ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(X10,X37,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f31863,plain,
( spl0_1200
<=> ! [X37,X10,X0,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(X10,X37,X5)
| c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X37),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f31866,plain,
( ! [X10,X0,X37,X5] :
( c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X37),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat))),X5)
| ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(X10,X37,X5) )
| ~ spl0_304
| ~ spl0_1200 ),
inference(forward_demodulation,[],[f31864,f3116]) ).
fof(f31864,plain,
( ! [X10,X0,X37,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(X10,X37,X5)
| c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X37),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))),X5) )
| ~ spl0_1200 ),
inference(avatar_component_clause,[],[f31863]) ).
fof(f32003,plain,
( spl0_1202
| ~ spl0_304
| ~ spl0_1198 ),
inference(avatar_split_clause,[],[f31857,f31854,f3114,f32001]) ).
fof(f32001,plain,
( spl0_1202
<=> ! [X5,X7,X6,X2] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| X6 = X7
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f31854,plain,
( spl0_1198
<=> ! [X5,X7,X6,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| X6 = X7
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f31857,plain,
( ! [X2,X6,X7,X5] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| X6 = X7
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2) )
| ~ spl0_304
| ~ spl0_1198 ),
inference(forward_demodulation,[],[f31855,f3116]) ).
fof(f31855,plain,
( ! [X2,X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| X6 = X7
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2) )
| ~ spl0_1198 ),
inference(avatar_component_clause,[],[f31854]) ).
fof(f31908,plain,
spl0_1201,
inference(avatar_split_clause,[],[f1484,f31906]) ).
fof(f31906,plain,
( spl0_1201
<=> ! [X28,X4,X3,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4))),X28)),X1)
| ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f1484,plain,
! [X3,X28,X1,X4] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4))),X28)),X1)
| ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3)) ),
inference(forward_demodulation,[],[f211,f444]) ).
fof(f444,axiom,
! [X3,X28,X0,X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)),X28)),X0),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_left__add__mult__distrib_0) ).
fof(f211,axiom,
! [X3,X28,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X3))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X28)),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__eq__add__iff1_1) ).
fof(f31865,plain,
spl0_1200,
inference(avatar_split_clause,[],[f1175,f31863]) ).
fof(f1175,axiom,
! [X10,X0,X37,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(X10,X37,X5)
| c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X37),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sums__split__initial__segment_0) ).
fof(f31861,plain,
spl0_1199,
inference(avatar_split_clause,[],[f1173,f31859]) ).
fof(f31859,plain,
( spl0_1199
<=> ! [X5,X6,X10,X20,X29,X2] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ class_Power_Opower(X20)
| ~ c_Lim_OLIM(X10,X6,X29,X5,X20)
| c_Lim_OLIM(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(tc_nat,X20),X5),c_Power_Opower__class_Opower(X20)),X10),X5,tc_nat,X20),X2),X6,hAPP(hAPP(c_Power_Opower__class_Opower(X20),X29),X2),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f1173,axiom,
! [X2,X10,X29,X6,X5,X20] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ class_Power_Opower(X20)
| ~ c_Lim_OLIM(X10,X6,X29,X5,X20)
| c_Lim_OLIM(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(tc_nat,X20),X5),c_Power_Opower__class_Opower(X20)),X10),X5,tc_nat,X20),X2),X6,hAPP(hAPP(c_Power_Opower__class_Opower(X20),X29),X2),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__power_0) ).
fof(f31856,plain,
spl0_1198,
inference(avatar_split_clause,[],[f1110,f31854]) ).
fof(f1110,axiom,
! [X2,X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| X6 = X7
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__eq__imp__eq__base_0) ).
fof(f31852,plain,
spl0_1197,
inference(avatar_split_clause,[],[f401,f31850]) ).
fof(f31850,plain,
( spl0_1197
<=> ! [X9,X7,X14,X6] :
( X6 = X7
| X9 = X14
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X7),X14)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),X14)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X7),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f401,axiom,
! [X6,X9,X7,X14] :
( X6 = X7
| X9 = X14
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X7),X14)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X6),X14)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X7),X9)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_natgb_Onoteq__reduce_0) ).
fof(f31747,plain,
( spl0_1196
| ~ spl0_304
| ~ spl0_1189 ),
inference(avatar_split_clause,[],[f31042,f31039,f3114,f31745]) ).
fof(f31745,plain,
( spl0_1196
<=> ! [X5,X7,X6,X2] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f31039,plain,
( spl0_1189
<=> ! [X5,X7,X6,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f31042,plain,
( ! [X2,X6,X7,X5] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2))) )
| ~ spl0_304
| ~ spl0_1189 ),
inference(forward_demodulation,[],[f31040,f3116]) ).
fof(f31040,plain,
( ! [X2,X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2))) )
| ~ spl0_1189 ),
inference(avatar_component_clause,[],[f31039]) ).
fof(f31066,plain,
spl0_1195,
inference(avatar_split_clause,[],[f1237,f31064]) ).
fof(f31064,plain,
( spl0_1195
<=> ! [X32,X20,X12,X5,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X32),X25)),X12) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Otimes__class_Otimes(X5)),X32),X20,X5,X5),X12)),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f1237,axiom,
! [X5,X25,X32,X12,X20] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X32),X25)),X12) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Otimes__class_Otimes(X5)),X32),X20,X5,X5),X12)),X25) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left_Osetsum_0) ).
fof(f31062,plain,
spl0_1194,
inference(avatar_split_clause,[],[f1236,f31060]) ).
fof(f31060,plain,
( spl0_1194
<=> ! [X10,X13,X5,X25,X20] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),X25)),X13) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Otimes__class_Otimes(X5)),X10),X20,X5,X5),X13)),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f1236,axiom,
! [X10,X5,X25,X13,X20] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),X25)),X13) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Otimes__class_Otimes(X5)),X10),X20,X5,X5),X13)),X25) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__left__distrib_0) ).
fof(f31058,plain,
spl0_1193,
inference(avatar_split_clause,[],[f1150,f31056]) ).
fof(f31056,plain,
( spl0_1193
<=> ! [X10,X13,X5,X25,X20] :
( ~ class_Ring__and__Field_Ofield(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),X25)),X13) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Oinverse__class_Odivide(X5)),X10),X20,X5,X5),X13)),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f1150,axiom,
! [X10,X5,X25,X13,X20] :
( ~ class_Ring__and__Field_Ofield(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),X25)),X13) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Oinverse__class_Odivide(X5)),X10),X20,X5,X5),X13)),X25) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__divide__distrib_0) ).
fof(f31054,plain,
spl0_1192,
inference(avatar_split_clause,[],[f1149,f31052]) ).
fof(f31052,plain,
( spl0_1192
<=> ! [X32,X20,X12,X5,X25] :
( ~ class_RealVector_Oreal__normed__field(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X32),X25)),X12) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Oinverse__class_Odivide(X5)),X32),X20,X5,X5),X12)),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f1149,axiom,
! [X5,X25,X32,X12,X20] :
( ~ class_RealVector_Oreal__normed__field(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X32),X25)),X12) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Oinverse__class_Odivide(X5)),X32),X20,X5,X5),X12)),X25) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_Osetsum_0) ).
fof(f31050,plain,
spl0_1191,
inference(avatar_split_clause,[],[f956,f31048]) ).
fof(f31048,plain,
( spl0_1191
<=> ! [X5,X35,X7,X6] :
( ~ class_Ring__and__Field_Oring(X5)
| ~ class_Int_Onumber(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),c_Int_Onumber__class_Onumber__of(X35,X5)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_Int_Onumber__class_Onumber__of(X35,X5))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),c_Int_Onumber__class_Onumber__of(X35,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f956,axiom,
! [X6,X7,X5,X35] :
( ~ class_Ring__and__Field_Oring(X5)
| ~ class_Int_Onumber(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),c_Int_Onumber__class_Onumber__of(X35,X5)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_Int_Onumber__class_Onumber__of(X35,X5))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),c_Int_Onumber__class_Onumber__of(X35,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_left__diff__distrib__number__of_0) ).
fof(f31046,plain,
spl0_1190,
inference(avatar_split_clause,[],[f955,f31044]) ).
fof(f31044,plain,
( spl0_1190
<=> ! [X5,X35,X7,X9] :
( ~ class_Ring__and__Field_Oring(X5)
| ~ class_Int_Onumber(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X35,X5)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X35,X5)),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X35,X5)),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f955,axiom,
! [X9,X7,X5,X35] :
( ~ class_Ring__and__Field_Oring(X5)
| ~ class_Int_Onumber(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X35,X5)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X9)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X35,X5)),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X35,X5)),X9)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_right__diff__distrib__number__of_0) ).
fof(f31041,plain,
spl0_1189,
inference(avatar_split_clause,[],[f863,f31039]) ).
fof(f863,axiom,
! [X2,X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__strict__mono_0) ).
fof(f31037,plain,
spl0_1188,
inference(avatar_split_clause,[],[f757,f31035]) ).
fof(f31035,plain,
( spl0_1188
<=> ! [X12,X5,X2,X39] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| ~ hBOOL(hAPP(c_lessequals(X39,tc_nat),X2))
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X2)),X39)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X39))),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f757,axiom,
! [X2,X39,X5,X12] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| ~ hBOOL(hAPP(c_lessequals(X39,tc_nat),X2))
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X2)),X39)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X39))),X12) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_lemma__realpow__diff_0) ).
fof(f31033,plain,
spl0_1187,
inference(avatar_split_clause,[],[f753,f31031]) ).
fof(f31031,plain,
( spl0_1187
<=> ! [X5,X18,X7,X6,X19] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| ~ c_SEQ_OLIMSEQ(X19,X7,X5)
| c_HOL_Ozero__class_Ozero(X5) = X7
| c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oinverse__class_Odivide(X5)),X18),X19,tc_nat,X5,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f753,axiom,
! [X18,X6,X19,X7,X5] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| ~ c_SEQ_OLIMSEQ(X19,X7,X5)
| c_HOL_Ozero__class_Ozero(X5) = X7
| c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oinverse__class_Odivide(X5)),X18),X19,tc_nat,X5,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__divide_0) ).
fof(f31029,plain,
spl0_1186,
inference(avatar_split_clause,[],[f516,f31027]) ).
fof(f31027,plain,
( spl0_1186
<=> ! [X5,X35,X7,X6] :
( ~ class_Ring__and__Field_Osemiring(X5)
| ~ class_Int_Onumber(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),c_Int_Onumber__class_Onumber__of(X35,X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_Int_Onumber__class_Onumber__of(X35,X5))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),c_Int_Onumber__class_Onumber__of(X35,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f516,axiom,
! [X6,X7,X5,X35] :
( ~ class_Ring__and__Field_Osemiring(X5)
| ~ class_Int_Onumber(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),c_Int_Onumber__class_Onumber__of(X35,X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_Int_Onumber__class_Onumber__of(X35,X5))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),c_Int_Onumber__class_Onumber__of(X35,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_left__distrib__number__of_0) ).
fof(f31024,plain,
spl0_1185,
inference(avatar_split_clause,[],[f444,f31022]) ).
fof(f31022,plain,
( spl0_1185
<=> ! [X4,X0,X3,X28] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X28)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X28)),X0)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)),X28)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f31020,plain,
spl0_1184,
inference(avatar_split_clause,[],[f423,f31018]) ).
fof(f31018,plain,
( spl0_1184
<=> ! [X5,X35,X7,X9] :
( ~ class_Ring__and__Field_Osemiring(X5)
| ~ class_Int_Onumber(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X35,X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X35,X5)),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X35,X5)),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f423,axiom,
! [X9,X7,X5,X35] :
( ~ class_Ring__and__Field_Osemiring(X5)
| ~ class_Int_Onumber(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X35,X5)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X35,X5)),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X35,X5)),X9)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_right__distrib__number__of_0) ).
fof(f31016,plain,
spl0_1183,
inference(avatar_split_clause,[],[f357,f31014]) ).
fof(f31014,plain,
( spl0_1183
<=> ! [X5,X6,X2,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X30))
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X30),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f357,axiom,
! [X2,X6,X5,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X30))
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X30),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__decreasing_0) ).
fof(f31012,plain,
spl0_1182,
inference(avatar_split_clause,[],[f356,f31010]) ).
fof(f31010,plain,
( spl0_1182
<=> ! [X5,X6,X2,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X30))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X30),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f356,axiom,
! [X2,X6,X5,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X30))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X30),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__strict__decreasing_0) ).
fof(f31008,plain,
spl0_1181,
inference(avatar_split_clause,[],[f14,f31006]) ).
fof(f31006,plain,
( spl0_1181
<=> ! [X10,X5,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1))
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat))),hAPP(X10,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f14,axiom,
! [X2,X10,X1,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1))
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat))),hAPP(X10,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__op__ivl__Suc_1) ).
fof(f30886,plain,
( spl0_1180
| ~ spl0_282
| ~ spl0_1087 ),
inference(avatar_split_clause,[],[f30665,f26698,f2962,f30884]) ).
fof(f30884,plain,
( spl0_1180
<=> ! [X4] :
( c_Orderings_Obot__class_Obot(tc_nat) != X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f26698,plain,
( spl0_1087
<=> ! [X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X4) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f30665,plain,
( ! [X4] :
( c_Orderings_Obot__class_Obot(tc_nat) != X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
| ~ spl0_282
| ~ spl0_1087 ),
inference(superposition,[],[f2963,f26699]) ).
fof(f26699,plain,
( ! [X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X4) = X4
| ~ spl0_1087 ),
inference(avatar_component_clause,[],[f26698]) ).
fof(f30857,plain,
spl0_1179,
inference(avatar_split_clause,[],[f1145,f30855]) ).
fof(f30855,plain,
( spl0_1179
<=> ! [X10,X32,X11,X5,X15,X23] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ c_Deriv_Oderiv(X32,X11,X23,X5)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Ominus__class_Ominus(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X15),X23),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f1145,axiom,
! [X10,X11,X15,X5,X32,X23] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ c_Deriv_Oderiv(X32,X11,X23,X5)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Ominus__class_Ominus(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X15),X23),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__diff_0) ).
fof(f30853,plain,
spl0_1178,
inference(avatar_split_clause,[],[f1131,f30851]) ).
fof(f30851,plain,
( spl0_1178
<=> ! [X10,X32,X20,X5,X25] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| c_Finite__Set_Osetprod(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Otimes__class_Otimes(X5)),X10),X32,X20,X5,X5),X25,X20,X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Finite__Set_Osetprod(X10,X25,X20,X5)),c_Finite__Set_Osetprod(X32,X25,X20,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f1131,axiom,
! [X10,X5,X25,X32,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| c_Finite__Set_Osetprod(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X20),c_HOL_Otimes__class_Otimes(X5)),X10),X32,X20,X5,X5),X25,X20,X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Finite__Set_Osetprod(X10,X25,X20,X5)),c_Finite__Set_Osetprod(X32,X25,X20,X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setprod__timesf_0) ).
fof(f30849,plain,
spl0_1177,
inference(avatar_split_clause,[],[f1126,f30847]) ).
fof(f30847,plain,
( spl0_1177
<=> ! [X5,X6,X20,X12,X29,X32] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Lim_OLIM(X32,X6,X29,X5,X20)
| c_Lim_OLIM(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X32),X5,X20,X20),X12),X6,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X29),X12),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f1126,axiom,
! [X29,X6,X5,X12,X32,X20] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Lim_OLIM(X32,X6,X29,X5,X20)
| c_Lim_OLIM(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X32),X5,X20,X20),X12),X6,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X29),X12),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left_OLIM_0) ).
fof(f30845,plain,
spl0_1176,
inference(avatar_split_clause,[],[f1100,f30843]) ).
fof(f30843,plain,
( spl0_1176
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f1100,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__Suc__less_0) ).
fof(f30841,plain,
spl0_1175,
inference(avatar_split_clause,[],[f867,f30839]) ).
fof(f30839,plain,
( spl0_1175
<=> ! [X10,X32,X11,X5,X15,X23] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ c_Deriv_Oderiv(X32,X11,X23,X5)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oplus__class_Oplus(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X15),X23),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f867,axiom,
! [X10,X11,X15,X5,X32,X23] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ c_Deriv_Oderiv(X32,X11,X23,X5)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oplus__class_Oplus(X5)),X10),X32,X5,X5,X5),X11,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X15),X23),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__add_0) ).
fof(f30652,plain,
spl0_1174,
inference(avatar_split_clause,[],[f849,f30650]) ).
fof(f30650,plain,
( spl0_1174
<=> ! [X5,X6,X20,X12,X29,X32] :
( ~ class_RealVector_Oreal__normed__field(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OLIM(X32,X6,X29,X5,X20)
| c_Lim_OLIM(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oinverse__class_Odivide(X20)),X32),X5,X20,X20),X12),X6,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X20),X29),X12),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f849,axiom,
! [X29,X6,X5,X12,X32,X20] :
( ~ class_RealVector_Oreal__normed__field(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OLIM(X32,X6,X29,X5,X20)
| c_Lim_OLIM(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oinverse__class_Odivide(X20)),X32),X5,X20,X20),X12),X6,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X20),X29),X12),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_OLIM_0) ).
fof(f30648,plain,
spl0_1173,
inference(avatar_split_clause,[],[f827,f30646]) ).
fof(f30646,plain,
( spl0_1173
<=> ! [X11,X12,X5,X16] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f827,axiom,
! [X11,X16,X5,X12] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__ringb_Oadd__mul__solve_1) ).
fof(f30644,plain,
spl0_1172,
inference(avatar_split_clause,[],[f818,f30642]) ).
fof(f30642,plain,
( spl0_1172
<=> ! [X16,X11,X12,X5,X8] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X16),X8)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f818,axiom,
! [X11,X8,X16,X5,X12] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X16),X8)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X8)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__frac__frac_0) ).
fof(f30640,plain,
spl0_1171,
inference(avatar_split_clause,[],[f761,f30638]) ).
fof(f30638,plain,
( spl0_1171
<=> ! [X18,X5,X19] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X18,X5)
| ~ c_Series_Osummable(X19,X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),c_Series_Osuminf(X18,X5)),c_Series_Osuminf(X19,X5)) = c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X18),X19,tc_nat,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f761,axiom,
! [X18,X19,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X18,X5)
| ~ c_Series_Osummable(X19,X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),c_Series_Osuminf(X18,X5)),c_Series_Osuminf(X19,X5)) = c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X18),X19,tc_nat,X5,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_suminf__diff_0) ).
fof(f30636,plain,
spl0_1170,
inference(avatar_split_clause,[],[f44,f30634]) ).
fof(f30634,plain,
( spl0_1170
<=> ! [X18,X5,X19] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X18,X5)
| ~ c_Series_Osummable(X19,X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Series_Osuminf(X18,X5)),c_Series_Osuminf(X19,X5)) = c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oplus__class_Oplus(X5)),X18),X19,tc_nat,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f44,axiom,
! [X18,X19,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X18,X5)
| ~ c_Series_Osummable(X19,X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Series_Osuminf(X18,X5)),c_Series_Osuminf(X19,X5)) = c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oplus__class_Oplus(X5)),X18),X19,tc_nat,X5,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_suminf__add_0) ).
fof(f30592,plain,
( spl0_1169
| ~ spl0_304
| ~ spl0_1168 ),
inference(avatar_split_clause,[],[f29547,f29543,f3114,f30590]) ).
fof(f30590,plain,
( spl0_1169
<=> ! [X2,X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f29543,plain,
( spl0_1168
<=> ! [X2,X0] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f29547,plain,
( ! [X2,X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X2,tc_nat))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X2)) )
| ~ spl0_304
| ~ spl0_1168 ),
inference(forward_demodulation,[],[f29546,f3116]) ).
fof(f29546,plain,
( ! [X2,X0] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X2))
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) )
| ~ spl0_304
| ~ spl0_1168 ),
inference(forward_demodulation,[],[f29544,f3116]) ).
fof(f29544,plain,
( ! [X2,X0] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) )
| ~ spl0_1168 ),
inference(avatar_component_clause,[],[f29543]) ).
fof(f29545,plain,
spl0_1168,
inference(avatar_split_clause,[],[f1163,f29543]) ).
fof(f1163,axiom,
! [X2,X0] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X0))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_root__summation_0) ).
fof(f29541,plain,
spl0_1167,
inference(avatar_split_clause,[],[f939,f29539]) ).
fof(f29539,plain,
( spl0_1167
<=> ! [X11,X8,X12,X5,X16] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| c_HOL_Ozero__class_Ozero(X5) = X16
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X8),X12)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X8),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f939,axiom,
! [X11,X8,X16,X5,X12] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| c_HOL_Ozero__class_Ozero(X5) = X16
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X8),X12)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X8),X16) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_frac__eq__eq_1) ).
fof(f29537,plain,
spl0_1166,
inference(avatar_split_clause,[],[f938,f29535]) ).
fof(f29535,plain,
( spl0_1166
<=> ! [X11,X8,X12,X5,X16] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| c_HOL_Ozero__class_Ozero(X5) = X16
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X8),X16)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X8),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f938,axiom,
! [X11,X8,X16,X5,X12] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| c_HOL_Ozero__class_Ozero(X5) = X16
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X8),X16)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X8),X12) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_frac__eq__eq_0) ).
fof(f29533,plain,
spl0_1165,
inference(avatar_split_clause,[],[f844,f29531]) ).
fof(f29531,plain,
( spl0_1165
<=> ! [X5,X7,X6,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| X6 = X7
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Suc,X2)) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),hAPP(c_Suc,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f844,axiom,
! [X2,X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| X6 = X7
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Suc,X2)) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),hAPP(c_Suc,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__inject__base_0) ).
fof(f29529,plain,
spl0_1164,
inference(avatar_split_clause,[],[f767,f29527]) ).
fof(f29527,plain,
( spl0_1164
<=> ! [X10,X5,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(X10,X1)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f767,axiom,
! [X2,X10,X1,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(X10,X1)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,tc_nat))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__add__nat__ivl__singleton_0) ).
fof(f29525,plain,
spl0_1163,
inference(avatar_split_clause,[],[f659,f29523]) ).
fof(f29523,plain,
( spl0_1163
<=> ! [X11,X12,X5,X16] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X16),X12))),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12)),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f659,axiom,
! [X11,X16,X5,X12] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X16),X12))),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12)),X16) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__frac__num_0) ).
fof(f29521,plain,
spl0_1162,
inference(avatar_split_clause,[],[f658,f29519]) ).
fof(f29519,plain,
( spl0_1162
<=> ! [X11,X12,X5,X16] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X16),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X16),X12))),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f658,axiom,
! [X11,X16,X5,X12] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X16),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X16),X12))),X12) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__num__frac_0) ).
fof(f29517,plain,
spl0_1161,
inference(avatar_split_clause,[],[f493,f29515]) ).
fof(f29515,plain,
( spl0_1161
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f493,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__eq_2) ).
fof(f29513,plain,
spl0_1160,
inference(avatar_split_clause,[],[f492,f29511]) ).
fof(f29511,plain,
( spl0_1160
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f492,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__eq_3) ).
fof(f29509,plain,
( spl0_1159
| ~ spl0_774
| ~ spl0_821 ),
inference(avatar_split_clause,[],[f23416,f14441,f13870,f29507]) ).
fof(f29507,plain,
( spl0_1159
<=> ! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_Int_Oint),tc_Int_Oint) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f13870,plain,
( spl0_774
<=> ! [X9,X8] : c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_Int_Oint),tc_Int_Oint) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f14441,plain,
( spl0_821
<=> ! [X9,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_Int_Oint) = c_Lattices_Oupper__semilattice__class_Osup(X9,X8,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f23416,plain,
( ! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_Int_Oint),tc_Int_Oint) = X1
| ~ spl0_774
| ~ spl0_821 ),
inference(superposition,[],[f13871,f14442]) ).
fof(f14442,plain,
( ! [X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_Int_Oint) = c_Lattices_Oupper__semilattice__class_Osup(X9,X8,tc_Int_Oint)
| ~ spl0_821 ),
inference(avatar_component_clause,[],[f14441]) ).
fof(f13871,plain,
( ! [X8,X9] : c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_Int_Oint),tc_Int_Oint) = X8
| ~ spl0_774 ),
inference(avatar_component_clause,[],[f13870]) ).
fof(f29505,plain,
spl0_1158,
inference(avatar_split_clause,[],[f491,f29503]) ).
fof(f29503,plain,
( spl0_1158
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f491,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__divide__eq_2) ).
fof(f29501,plain,
spl0_1157,
inference(avatar_split_clause,[],[f490,f29499]) ).
fof(f29499,plain,
( spl0_1157
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f490,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__divide__eq_3) ).
fof(f29497,plain,
spl0_1156,
inference(avatar_split_clause,[],[f160,f29495]) ).
fof(f29495,plain,
( spl0_1156
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f160,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__divide__eq_3) ).
fof(f29493,plain,
spl0_1155,
inference(avatar_split_clause,[],[f159,f29491]) ).
fof(f29491,plain,
( spl0_1155
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f159,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__divide__eq_2) ).
fof(f29489,plain,
spl0_1154,
inference(avatar_split_clause,[],[f158,f29487]) ).
fof(f29487,plain,
( spl0_1154
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f158,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__eq_3) ).
fof(f29485,plain,
spl0_1153,
inference(avatar_split_clause,[],[f157,f29483]) ).
fof(f29483,plain,
( spl0_1153
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f157,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__eq_2) ).
fof(f29126,plain,
( spl0_1152
| ~ spl0_769
| ~ spl0_810 ),
inference(avatar_split_clause,[],[f23326,f14394,f13794,f29124]) ).
fof(f29124,plain,
( spl0_1152
<=> ! [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_1152])]) ).
fof(f13794,plain,
( spl0_769
<=> ! [X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_bool),tc_bool) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f14394,plain,
( spl0_810
<=> ! [X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f23326,plain,
( ! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_bool),tc_bool) = X1
| ~ spl0_769
| ~ spl0_810 ),
inference(superposition,[],[f13795,f14395]) ).
fof(f14395,plain,
( ! [X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_bool)
| ~ spl0_810 ),
inference(avatar_component_clause,[],[f14394]) ).
fof(f13795,plain,
( ! [X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_bool),tc_bool) = X6
| ~ spl0_769 ),
inference(avatar_component_clause,[],[f13794]) ).
fof(f29005,plain,
spl0_1151,
inference(avatar_split_clause,[],[f1491,f29003]) ).
fof(f29003,plain,
( spl0_1151
<=> ! [X2,X0,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X0)))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f1491,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X0)))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X2)) ),
inference(forward_demodulation,[],[f1074,f1069]) ).
fof(f1069,axiom,
! [X3,X0,X4] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X0)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__diff__left_0) ).
fof(f1074,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X2))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X0)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Nat_Odiff__diff__eq_0) ).
fof(f29001,plain,
spl0_1150,
inference(avatar_split_clause,[],[f1253,f28999]) ).
fof(f28999,plain,
( spl0_1150
<=> ! [X51,X53,X50,X5,X52] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X50),X53)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X51),X52)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X50),X51)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X53),X52)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f1253,axiom,
! [X50,X51,X52,X53,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X50),X53)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X51),X52)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X50),X51)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X53),X52)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f28997,plain,
spl0_1149,
inference(avatar_split_clause,[],[f1127,f28995]) ).
fof(f28995,plain,
( spl0_1149
<=> ! [X38,X20,X12,X6,X5,X32] :
( ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Limits_Otendsto(X32,X6,X38,X5,X20)
| c_Limits_Otendsto(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X32),X5,X20,X20),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X6),X12),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f1127,axiom,
! [X38,X6,X5,X12,X32,X20] :
( ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Limits_Otendsto(X32,X6,X38,X5,X20)
| c_Limits_Otendsto(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X32),X5,X20,X20),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X6),X12),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left_Otendsto_0) ).
fof(f28993,plain,
spl0_1148,
inference(avatar_split_clause,[],[f1101,f28991]) ).
fof(f28991,plain,
( spl0_1148
<=> ! [X5,X10,X20,X0,X6,X21] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ class_RealVector_Ometric__space(X20)
| ~ c_Lim_OLIM(X10,X6,X21,X5,X20)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X5,X20,X5),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(X5),X5,X5,X5),X0)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X0),X21,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f1101,axiom,
! [X21,X10,X0,X6,X5,X20] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ class_RealVector_Ometric__space(X20)
| ~ c_Lim_OLIM(X10,X6,X21,X5,X20)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X5,X20,X5),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(X5),X5,X5,X5),X0)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X0),X21,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__offset_0) ).
fof(f28989,plain,
( spl0_1147
| ~ spl0_767
| ~ spl0_807 ),
inference(avatar_split_clause,[],[f23232,f14213,f13466,f28987]) ).
fof(f28987,plain,
( spl0_1147
<=> ! [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_1147])]) ).
fof(f14213,plain,
( spl0_807
<=> ! [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_807])]) ).
fof(f23232,plain,
( ! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X1,tc_nat),tc_nat) = X1
| ~ spl0_767
| ~ spl0_807 ),
inference(superposition,[],[f13467,f14214]) ).
fof(f14214,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_nat)
| ~ spl0_807 ),
inference(avatar_component_clause,[],[f14213]) ).
fof(f28985,plain,
spl0_1146,
inference(avatar_split_clause,[],[f1097,f28983]) ).
fof(f28983,plain,
( spl0_1146
<=> ! [X10,X11,X5,X32] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Odifferentiable(X10,X11,X5)
| ~ c_Deriv_Odifferentiable(X32,X11,X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(X32,X11)
| c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),X10),X32,X5,X5,X5),X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f1097,axiom,
! [X10,X11,X5,X32] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Odifferentiable(X10,X11,X5)
| ~ c_Deriv_Odifferentiable(X32,X11,X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(X32,X11)
| c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),X10),X32,X5,X5,X5),X11,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_differentiable__divide_0) ).
fof(f28981,plain,
spl0_1145,
inference(avatar_split_clause,[],[f859,f28979]) ).
fof(f28979,plain,
( spl0_1145
<=> ! [X5,X6,X7,X14,X9] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X9),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f859,axiom,
! [X6,X9,X7,X14,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X9),X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Deriv_Oadd__diff__add_0) ).
fof(f28977,plain,
spl0_1144,
inference(avatar_split_clause,[],[f848,f28975]) ).
fof(f28975,plain,
( spl0_1144
<=> ! [X38,X20,X12,X6,X5,X32] :
( ~ class_RealVector_Oreal__normed__field(X20)
| ~ c_Limits_Otendsto(X32,X6,X38,X5,X20)
| c_Limits_Otendsto(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oinverse__class_Odivide(X20)),X32),X5,X20,X20),X12),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X20),X6),X12),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f848,axiom,
! [X38,X6,X5,X12,X32,X20] :
( ~ class_RealVector_Oreal__normed__field(X20)
| ~ c_Limits_Otendsto(X32,X6,X38,X5,X20)
| c_Limits_Otendsto(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oinverse__class_Odivide(X20)),X32),X5,X20,X20),X12),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X20),X6),X12),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_Otendsto_0) ).
fof(f28973,plain,
spl0_1143,
inference(avatar_split_clause,[],[f842,f28971]) ).
fof(f28971,plain,
( spl0_1143
<=> ! [X5,X7,X6,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Suc,X2)),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),hAPP(c_Suc,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f842,axiom,
! [X2,X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Suc,X2)),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),hAPP(c_Suc,X2)))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__le__imp__le__base_0) ).
fof(f28969,plain,
spl0_1142,
inference(avatar_split_clause,[],[f702,f28967]) ).
fof(f28967,plain,
( spl0_1142
<=> ! [X5,X31,X10,X20,X6,X29,X32] :
( ~ class_RealVector_Ometric__space(X20)
| ~ class_RealVector_Ometric__space(X31)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OLIM(X10,X6,X29,X31,X5)
| ~ c_Lim_OLIM(X32,X29,hAPP(X32,X29),X5,X20)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X5,X20,X31),X32),X10),X6,hAPP(X32,X29),X31,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f702,axiom,
! [X31,X10,X29,X6,X5,X32,X20] :
( ~ class_RealVector_Ometric__space(X20)
| ~ class_RealVector_Ometric__space(X31)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OLIM(X10,X6,X29,X31,X5)
| ~ c_Lim_OLIM(X32,X29,hAPP(X32,X29),X5,X20)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X5,X20,X31),X32),X10),X6,hAPP(X32,X29),X31,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__compose_0) ).
fof(f28965,plain,
spl0_1141,
inference(avatar_split_clause,[],[f172,f28963]) ).
fof(f28963,plain,
( spl0_1141
<=> ! [X5,X6,X7,X14,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f172,axiom,
! [X6,X9,X7,X14,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f28883,plain,
( spl0_1140
| ~ spl0_677
| ~ spl0_766 ),
inference(avatar_split_clause,[],[f21702,f13263,f9800,f28881]) ).
fof(f28881,plain,
( spl0_1140
<=> ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_Int_Oint),tc_Int_Oint) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f9800,plain,
( spl0_677
<=> ! [X9,X8] : c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(X9,X8,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f13263,plain,
( spl0_766
<=> ! [X9,X8] : c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_Int_Oint),tc_Int_Oint) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f21702,plain,
( ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_Int_Oint),tc_Int_Oint) = X1
| ~ spl0_677
| ~ spl0_766 ),
inference(superposition,[],[f13264,f9801]) ).
fof(f9801,plain,
( ! [X8,X9] : c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(X9,X8,tc_Int_Oint)
| ~ spl0_677 ),
inference(avatar_component_clause,[],[f9800]) ).
fof(f13264,plain,
( ! [X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_Int_Oint),tc_Int_Oint) = X8
| ~ spl0_766 ),
inference(avatar_component_clause,[],[f13263]) ).
fof(f28614,plain,
( spl0_1139
| ~ spl0_666
| ~ spl0_762 ),
inference(avatar_split_clause,[],[f21628,f12863,f9756,f28612]) ).
fof(f28612,plain,
( spl0_1139
<=> ! [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_1139])]) ).
fof(f9756,plain,
( spl0_666
<=> ! [X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f12863,plain,
( spl0_762
<=> ! [X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_bool),tc_bool) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f21628,plain,
( ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_bool),tc_bool) = X1
| ~ spl0_666
| ~ spl0_762 ),
inference(superposition,[],[f12864,f9757]) ).
fof(f9757,plain,
( ! [X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_bool)
| ~ spl0_666 ),
inference(avatar_component_clause,[],[f9756]) ).
fof(f12864,plain,
( ! [X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_bool),tc_bool) = X6
| ~ spl0_762 ),
inference(avatar_component_clause,[],[f12863]) ).
fof(f28465,plain,
spl0_1138,
inference(avatar_split_clause,[],[f1184,f28463]) ).
fof(f28463,plain,
( spl0_1138
<=> ! [X5,X10,X9,X20,X6] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Lim_OLIM(X10,X6,c_HOL_Ozero__class_Ozero(X20),X5,X20)
| c_Lim_OLIM(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X10),X5,X20,X20),X9),X6,c_HOL_Ozero__class_Ozero(X20),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f1184,axiom,
! [X10,X6,X9,X5,X20] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Lim_OLIM(X10,X6,c_HOL_Ozero__class_Ozero(X20),X5,X20)
| c_Lim_OLIM(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X10),X5,X20,X20),X9),X6,c_HOL_Ozero__class_Ozero(X20),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__mult__left__zero_0) ).
fof(f28461,plain,
spl0_1137,
inference(avatar_split_clause,[],[f1167,f28459]) ).
fof(f28459,plain,
( spl0_1137
<=> ! [X5,X18,X7,X6,X19] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| ~ c_SEQ_OLIMSEQ(X19,X7,X5)
| c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X18),X19,tc_nat,X5,X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f1167,axiom,
! [X18,X6,X19,X7,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| ~ c_SEQ_OLIMSEQ(X19,X7,X5)
| c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X18),X19,tc_nat,X5,X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__diff_0) ).
fof(f28457,plain,
spl0_1136,
inference(avatar_split_clause,[],[f1164,f28455]) ).
fof(f28455,plain,
( spl0_1136
<=> ! [X5,X18,X7,X6,X19] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(X18,X6,X5)
| ~ c_Series_Osums(X19,X7,X5)
| c_Series_Osums(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X18),X19,tc_nat,X5,X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f1164,axiom,
! [X18,X6,X19,X7,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(X18,X6,X5)
| ~ c_Series_Osums(X19,X7,X5)
| c_Series_Osums(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X18),X19,tc_nat,X5,X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sums__diff_0) ).
fof(f28453,plain,
spl0_1135,
inference(avatar_split_clause,[],[f1154,f28451]) ).
fof(f28451,plain,
( spl0_1135
<=> ! [X5,X18,X7,X6,X19] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| ~ c_SEQ_OLIMSEQ(X19,X7,X5)
| c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X18),X19,tc_nat,X5,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f1154,axiom,
! [X18,X6,X19,X7,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| ~ c_SEQ_OLIMSEQ(X19,X7,X5)
| c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X18),X19,tc_nat,X5,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__mult_0) ).
fof(f28449,plain,
spl0_1134,
inference(avatar_split_clause,[],[f1146,f28447]) ).
fof(f28447,plain,
( spl0_1134
<=> ! [X5,X10,X20,X6,X32] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Lim_OisCont(X10,X6,X5,X20)
| ~ c_Lim_OisCont(X32,X6,X5,X20)
| c_Lim_OisCont(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X32,X5,X20,X20),X6,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f1146,axiom,
! [X10,X6,X5,X32,X20] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Lim_OisCont(X10,X6,X5,X20)
| ~ c_Lim_OisCont(X32,X6,X5,X20)
| c_Lim_OisCont(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X32,X5,X20,X20),X6,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_isCont__diff_0) ).
fof(f28445,plain,
spl0_1133,
inference(avatar_split_clause,[],[f1130,f28443]) ).
fof(f28443,plain,
( spl0_1133
<=> ! [X5,X10,X20,X6,X32] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Lim_OisCont(X10,X6,X5,X20)
| ~ c_Lim_OisCont(X32,X6,X5,X20)
| c_Lim_OisCont(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X10),X32,X5,X20,X20),X6,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f1130,axiom,
! [X10,X6,X5,X32,X20] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Lim_OisCont(X10,X6,X5,X20)
| ~ c_Lim_OisCont(X32,X6,X5,X20)
| c_Lim_OisCont(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X10),X32,X5,X20,X20),X6,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_isCont__mult_0) ).
fof(f28441,plain,
spl0_1132,
inference(avatar_split_clause,[],[f1096,f28439]) ).
fof(f28439,plain,
( spl0_1132
<=> ! [X5,X20,X12,X6,X32] :
( ~ class_RealVector_Oreal__normed__field(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OLIM(X32,X6,c_HOL_Ozero__class_Ozero(X20),X5,X20)
| c_Lim_OLIM(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oinverse__class_Odivide(X20)),X32),X5,X20,X20),X12),X6,c_HOL_Ozero__class_Ozero(X20),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f1096,axiom,
! [X6,X5,X12,X32,X20] :
( ~ class_RealVector_Oreal__normed__field(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OLIM(X32,X6,c_HOL_Ozero__class_Ozero(X20),X5,X20)
| c_Lim_OLIM(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oinverse__class_Odivide(X20)),X32),X5,X20,X20),X12),X6,c_HOL_Ozero__class_Ozero(X20),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_OLIM__zero_0) ).
fof(f28437,plain,
spl0_1131,
inference(avatar_split_clause,[],[f1065,f28435]) ).
fof(f28435,plain,
( spl0_1131
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f1065,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__diff__iff_0) ).
fof(f28433,plain,
( spl0_1130
| ~ spl0_655
| ~ spl0_751 ),
inference(avatar_split_clause,[],[f20674,f12818,f9712,f28431]) ).
fof(f12818,plain,
( spl0_751
<=> ! [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_751])]) ).
fof(f20674,plain,
( ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X1,tc_nat),tc_nat) = X1
| ~ spl0_655
| ~ spl0_751 ),
inference(superposition,[],[f12819,f9713]) ).
fof(f12819,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_751 ),
inference(avatar_component_clause,[],[f12818]) ).
fof(f28429,plain,
spl0_1129,
inference(avatar_split_clause,[],[f1018,f28427]) ).
fof(f28427,plain,
( spl0_1129
<=> ! [X5,X18,X7,X6,X19] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| ~ c_SEQ_OLIMSEQ(X19,X7,X5)
| c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oplus__class_Oplus(X5)),X18),X19,tc_nat,X5,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f1018,axiom,
! [X18,X6,X19,X7,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| ~ c_SEQ_OLIMSEQ(X19,X7,X5)
| c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oplus__class_Oplus(X5)),X18),X19,tc_nat,X5,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__add_0) ).
fof(f28425,plain,
spl0_1128,
inference(avatar_split_clause,[],[f1016,f28423]) ).
fof(f28423,plain,
( spl0_1128
<=> ! [X5,X18,X7,X6,X19] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(X18,X6,X5)
| ~ c_Series_Osums(X19,X7,X5)
| c_Series_Osums(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oplus__class_Oplus(X5)),X18),X19,tc_nat,X5,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f1016,axiom,
! [X18,X6,X19,X7,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(X18,X6,X5)
| ~ c_Series_Osums(X19,X7,X5)
| c_Series_Osums(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oplus__class_Oplus(X5)),X18),X19,tc_nat,X5,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sums__add_0) ).
fof(f28421,plain,
spl0_1127,
inference(avatar_split_clause,[],[f969,f28419]) ).
fof(f28419,plain,
( spl0_1127
<=> ! [X5,X7,X6,X2] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X7
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7)),X2) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f969,axiom,
! [X2,X6,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X7
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7)),X2) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nonzero__power__divide_0) ).
fof(f28417,plain,
spl0_1126,
inference(avatar_split_clause,[],[f868,f28415]) ).
fof(f28415,plain,
( spl0_1126
<=> ! [X5,X10,X20,X6,X32] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Lim_OisCont(X10,X6,X5,X20)
| ~ c_Lim_OisCont(X32,X6,X5,X20)
| c_Lim_OisCont(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oplus__class_Oplus(X20)),X10),X32,X5,X20,X20),X6,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f868,axiom,
! [X10,X6,X5,X32,X20] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Lim_OisCont(X10,X6,X5,X20)
| ~ c_Lim_OisCont(X32,X6,X5,X20)
| c_Lim_OisCont(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oplus__class_Oplus(X20)),X10),X32,X5,X20,X20),X6,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_isCont__add_0) ).
fof(f28413,plain,
spl0_1125,
inference(avatar_split_clause,[],[f803,f28411]) ).
fof(f28411,plain,
( spl0_1125
<=> ! [X5,X11,X13,X14,X9] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| X9 = X14
| c_HOL_Ozero__class_Ozero(X5) = X13
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X13),X9)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X13),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f803,axiom,
! [X11,X9,X14,X5,X13] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| X9 = X14
| c_HOL_Ozero__class_Ozero(X5) = X13
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X13),X9)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X13),X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(f28409,plain,
spl0_1124,
inference(avatar_split_clause,[],[f657,f28407]) ).
fof(f28407,plain,
( spl0_1124
<=> ! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X11),X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f657,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X11),X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left__le__one__le_0) ).
fof(f28405,plain,
spl0_1123,
inference(avatar_split_clause,[],[f656,f28403]) ).
fof(f28403,plain,
( spl0_1123
<=> ! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12),X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f656,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12),X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right__le__one__le_0) ).
fof(f28401,plain,
spl0_1122,
inference(avatar_split_clause,[],[f574,f28399]) ).
fof(f28399,plain,
( spl0_1122
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f574,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__diff__iff_0) ).
fof(f28390,plain,
( spl0_1121
| ~ spl0_295
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f4493,f4423,f3046,f28387]) ).
fof(f28387,plain,
( spl0_1121
<=> c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),v_i),v_n) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f3046,plain,
( spl0_295
<=> hBOOL(hAPP(c_lessequals(v_i,tc_nat),v_n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f4493,plain,
( c_Orderings_Obot__class_Obot(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),v_i),v_n)
| ~ spl0_295
| ~ spl0_411 ),
inference(resolution,[],[f4424,f3048]) ).
fof(f3048,plain,
( hBOOL(hAPP(c_lessequals(v_i,tc_nat),v_n))
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f3046]) ).
fof(f27293,plain,
spl0_1120,
inference(avatar_split_clause,[],[f1186,f27291]) ).
fof(f27291,plain,
( spl0_1120
<=> ! [X5,X6,X10,X20,X29] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Lim_OLIM(X10,X6,X29,X5,X20)
| c_Lim_OLIM(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X5,X20,X20),X29),X6,c_HOL_Ozero__class_Ozero(X20),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f1186,axiom,
! [X10,X29,X6,X5,X20] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Lim_OLIM(X10,X6,X29,X5,X20)
| c_Lim_OLIM(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X5,X20,X20),X29),X6,c_HOL_Ozero__class_Ozero(X20),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__zero_0) ).
fof(f27289,plain,
spl0_1119,
inference(avatar_split_clause,[],[f1185,f27287]) ).
fof(f27287,plain,
( spl0_1119
<=> ! [X5,X6,X10,X20,X29] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ class_RealVector_Ometric__space(X5)
| c_Lim_OLIM(X10,X6,X29,X5,X20)
| ~ c_Lim_OLIM(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X5,X20,X20),X29),X6,c_HOL_Ozero__class_Ozero(X20),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f1185,axiom,
! [X10,X29,X6,X5,X20] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ class_RealVector_Ometric__space(X5)
| c_Lim_OLIM(X10,X6,X29,X5,X20)
| ~ c_Lim_OLIM(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X5,X20,X20),X29),X6,c_HOL_Ozero__class_Ozero(X20),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__zero__iff_0) ).
fof(f27285,plain,
spl0_1118,
inference(avatar_split_clause,[],[f1176,f27283]) ).
fof(f27283,plain,
( spl0_1118
<=> ! [X5,X18,X6,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ class_Power_Opower(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| c_SEQ_OLIMSEQ(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(tc_nat,X5),tc_nat),c_Power_Opower__class_Opower(X5)),X18),tc_nat,tc_nat,X5),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X1),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f1176,axiom,
! [X18,X1,X6,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ class_Power_Opower(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| c_SEQ_OLIMSEQ(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(tc_nat,X5),tc_nat),c_Power_Opower__class_Opower(X5)),X18),tc_nat,tc_nat,X5),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X1),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__pow_0) ).
fof(f27281,plain,
spl0_1117,
inference(avatar_split_clause,[],[f1094,f27279]) ).
fof(f27279,plain,
( spl0_1117
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| c_SetInterval_Oord__class_OatLeastLessThan(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X0),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X0),tc_nat),tc_fun(tc_nat,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f1094,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| c_SetInterval_Oord__class_OatLeastLessThan(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X0),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X0),tc_nat),tc_fun(tc_nat,tc_bool)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_atLeastLessThan__add__Un_0) ).
fof(f27277,plain,
spl0_1116,
inference(avatar_split_clause,[],[f850,f27275]) ).
fof(f27275,plain,
( spl0_1116
<=> ! [X10,X9,X11,X5,X15] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| c_Deriv_Oderiv(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),X10),X5,X5,X5),X9),X11,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X15),X9),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f850,axiom,
! [X10,X11,X9,X15,X5] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| c_Deriv_Oderiv(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oinverse__class_Odivide(X5)),X10),X5,X5,X5),X9),X11,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X15),X9),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__cdivide_0) ).
fof(f27273,plain,
spl0_1115,
inference(avatar_split_clause,[],[f759,f27271]) ).
fof(f27271,plain,
( spl0_1115
<=> ! [X9,X5,X10] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_Series_Osummable(X10,X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Series_Osuminf(X10,X5)),X9) = c_Series_Osuminf(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X10),tc_nat,X5,X5),X9),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f759,axiom,
! [X10,X9,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_Series_Osummable(X10,X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Series_Osuminf(X10,X5)),X9) = c_Series_Osuminf(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X10),tc_nat,X5,X5),X9),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_suminf__mult2_0) ).
fof(f27269,plain,
spl0_1114,
inference(avatar_split_clause,[],[f678,f27267]) ).
fof(f27267,plain,
( spl0_1114
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f678,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__eq_0) ).
fof(f27265,plain,
( ~ spl0_34
| ~ spl0_1113
| ~ spl0_337
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f3688,f3534,f3438,f27262,f1666]) ).
fof(f27262,plain,
( spl0_1113
<=> hBOOL(hAPP(c_lessequals(v_n,tc_nat),c_Orderings_Obot__class_Obot(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f3534,plain,
( spl0_359
<=> hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),v_n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f3688,plain,
( ~ hBOOL(hAPP(c_lessequals(v_n,tc_nat),c_Orderings_Obot__class_Obot(tc_nat)))
| ~ class_Orderings_Opreorder(tc_nat)
| ~ spl0_337
| ~ spl0_359 ),
inference(resolution,[],[f3439,f3536]) ).
fof(f3536,plain,
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),v_n))
| ~ spl0_359 ),
inference(avatar_component_clause,[],[f3534]) ).
fof(f27260,plain,
spl0_1112,
inference(avatar_split_clause,[],[f676,f27258]) ).
fof(f27258,plain,
( spl0_1112
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f676,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__divide__eq_0) ).
fof(f27256,plain,
spl0_1111,
inference(avatar_split_clause,[],[f544,f27254]) ).
fof(f27254,plain,
( spl0_1111
<=> ! [X18,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Series_Osummable(X18,X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_Series_Osuminf(X18,X5)),X12) = c_Series_Osuminf(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oinverse__class_Odivide(X5)),X18),tc_nat,X5,X5),X12),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f544,axiom,
! [X18,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Series_Osummable(X18,X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_Series_Osuminf(X18,X5)),X12) = c_Series_Osuminf(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oinverse__class_Odivide(X5)),X18),tc_nat,X5,X5),X12),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_Osuminf_0) ).
fof(f27252,plain,
spl0_1110,
inference(avatar_split_clause,[],[f261,f27250]) ).
fof(f27250,plain,
( spl0_1110
<=> ! [X4,X0,X1] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X4))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0))),X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f261,axiom,
! [X0,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X4))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0))),X1) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__Suc__diff__eq2_0) ).
fof(f27248,plain,
spl0_1109,
inference(avatar_split_clause,[],[f219,f27246]) ).
fof(f27246,plain,
( spl0_1109
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6))
| hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f219,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),X6))
| hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__eq_0) ).
fof(f27244,plain,
spl0_1108,
inference(avatar_split_clause,[],[f217,f27242]) ).
fof(f27242,plain,
( spl0_1108
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f217,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__divide__eq_0) ).
fof(f27240,plain,
spl0_1107,
inference(avatar_split_clause,[],[f132,f27238]) ).
fof(f27238,plain,
( spl0_1107
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f132,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__right__mono__neg_0) ).
fof(f27236,plain,
spl0_1106,
inference(avatar_split_clause,[],[f131,f27234]) ).
fof(f27234,plain,
( spl0_1106
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f131,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__right__mono_0) ).
fof(f27232,plain,
spl0_1105,
inference(avatar_split_clause,[],[f60,f27230]) ).
fof(f27230,plain,
( spl0_1105
<=> ! [X4,X0,X1] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X4))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0))) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0)),hAPP(c_Suc,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f60,axiom,
! [X0,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X4))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0))) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0)),hAPP(c_Suc,X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__Suc__diff__eq1_0) ).
fof(f27042,plain,
( spl0_1104
| ~ spl0_304
| ~ spl0_1099 ),
inference(avatar_split_clause,[],[f26750,f26746,f3114,f27040]) ).
fof(f27040,plain,
( spl0_1104
<=> ! [X5,X0,X10] :
( c_HOL_Ozero__class_Ozero(X5) != hAPP(X10,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OgreaterThanLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f26746,plain,
( spl0_1099
<=> ! [X5,X0,X10] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OgreaterThanLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Ozero__class_Ozero(X5) != hAPP(X10,c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f26750,plain,
( ! [X10,X0,X5] :
( c_HOL_Ozero__class_Ozero(X5) != hAPP(X10,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OgreaterThanLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) )
| ~ spl0_304
| ~ spl0_1099 ),
inference(forward_demodulation,[],[f26749,f3116]) ).
fof(f26749,plain,
( ! [X10,X0,X5] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OgreaterThanLessThan(c_Orderings_Obot__class_Obot(tc_nat),X0,tc_nat))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Ozero__class_Ozero(X5) != hAPP(X10,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_304
| ~ spl0_1099 ),
inference(forward_demodulation,[],[f26747,f3116]) ).
fof(f26747,plain,
( ! [X10,X0,X5] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OgreaterThanLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Ozero__class_Ozero(X5) != hAPP(X10,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_1099 ),
inference(avatar_component_clause,[],[f26746]) ).
fof(f27027,plain,
( ~ spl0_47
| spl0_1103
| ~ spl0_253
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f3396,f2896,f2689,f27025,f1731]) ).
fof(f27025,plain,
( spl0_1103
<=> ! [X3] : hBOOL(hAPP(c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f2896,plain,
( spl0_272
<=> ! [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_272])]) ).
fof(f3396,plain,
( ! [X3] :
( hBOOL(hAPP(c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),X3))
| ~ class_Lattices_Olattice(tc_bool) )
| ~ spl0_253
| ~ spl0_272 ),
inference(superposition,[],[f2690,f2897]) ).
fof(f2897,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
| ~ spl0_272 ),
inference(avatar_component_clause,[],[f2896]) ).
fof(f26841,plain,
( spl0_1102
| ~ spl0_304
| ~ spl0_1085 ),
inference(avatar_split_clause,[],[f26692,f26689,f3114,f26839]) ).
fof(f26839,plain,
( spl0_1102
<=> ! [X2,X0,X14] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X14))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X2))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f26689,plain,
( spl0_1085
<=> ! [X2,X0,X14] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X14))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X2))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f26692,plain,
( ! [X2,X0,X14] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X14))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X2))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X0) )
| ~ spl0_304
| ~ spl0_1085 ),
inference(forward_demodulation,[],[f26690,f3116]) ).
fof(f26690,plain,
( ! [X2,X0,X14] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X14))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X2))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X0) )
| ~ spl0_1085 ),
inference(avatar_component_clause,[],[f26689]) ).
fof(f26837,plain,
( spl0_1101
| ~ spl0_304
| ~ spl0_1084 ),
inference(avatar_split_clause,[],[f26687,f26682,f3114,f26835]) ).
fof(f26835,plain,
( spl0_1101
<=> ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f26682,plain,
( spl0_1084
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f26687,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X1)) )
| ~ spl0_304
| ~ spl0_1084 ),
inference(forward_demodulation,[],[f26686,f3116]) ).
fof(f26686,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X1))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_304
| ~ spl0_1084 ),
inference(forward_demodulation,[],[f26685,f3116]) ).
fof(f26685,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_304
| ~ spl0_1084 ),
inference(forward_demodulation,[],[f26683,f3116]) ).
fof(f26683,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_1084 ),
inference(avatar_component_clause,[],[f26682]) ).
fof(f26757,plain,
( spl0_1100
| ~ spl0_304
| ~ spl0_1082 ),
inference(avatar_split_clause,[],[f26676,f26671,f3114,f26755]) ).
fof(f26755,plain,
( spl0_1100
<=> ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f26671,plain,
( spl0_1082
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f26676,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2)) )
| ~ spl0_304
| ~ spl0_1082 ),
inference(forward_demodulation,[],[f26675,f3116]) ).
fof(f26675,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_304
| ~ spl0_1082 ),
inference(forward_demodulation,[],[f26674,f3116]) ).
fof(f26674,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_304
| ~ spl0_1082 ),
inference(forward_demodulation,[],[f26672,f3116]) ).
fof(f26672,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_1082 ),
inference(avatar_component_clause,[],[f26671]) ).
fof(f26748,plain,
spl0_1099,
inference(avatar_split_clause,[],[f1490,f26746]) ).
fof(f1490,plain,
! [X10,X0,X5] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OgreaterThanLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Ozero__class_Ozero(X5) != hAPP(X10,c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(forward_demodulation,[],[f1192,f1119]) ).
fof(f1119,axiom,
! [X28,X29] : c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X29),X28,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X28,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_atLeastSucLessThan__greaterThanLessThan_0) ).
fof(f1192,axiom,
! [X10,X0,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Ozero__class_Ozero(X5) != hAPP(X10,c_HOL_Ozero__class_Ozero(tc_nat))
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__shift__lb__Suc0__0__upt_0) ).
fof(f26744,plain,
( spl0_1098
| ~ spl0_194
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3168,f3114,f2433,f26742]) ).
fof(f26742,plain,
( spl0_1098
<=> ! [X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X5),c_Orderings_Obot__class_Obot(tc_nat)) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f3168,plain,
( ! [X5] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X5),c_Orderings_Obot__class_Obot(tc_nat)) = X5
| ~ spl0_194
| ~ spl0_304 ),
inference(superposition,[],[f2434,f3116]) ).
fof(f26740,plain,
spl0_1097,
inference(avatar_split_clause,[],[f1479,f26738]) ).
fof(f26738,plain,
( spl0_1097
<=> ! [X10,X5,X2,X1] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc)),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,hAPP(c_Suc,X2),tc_nat))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f1479,plain,
! [X2,X10,X1,X5] :
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc)),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,hAPP(c_Suc,X2),tc_nat))
| ~ class_OrderedGroup_Ocomm__monoid__add(X5) ),
inference(forward_demodulation,[],[f1177,f1119]) ).
fof(f1177,axiom,
! [X2,X10,X1,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X1),hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc)),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__shift__bounds__Suc__ivl_0) ).
fof(f26736,plain,
spl0_1096,
inference(avatar_split_clause,[],[f1226,f26734]) ).
fof(f26734,plain,
( spl0_1096
<=> ! [X32,X11,X5,X25,X20] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X32),X25)) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(hAPP(c_COMBB(X5,X5,X20),hAPP(c_HOL_Otimes__class_Otimes(X5),X11)),X32)),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f1226,axiom,
! [X11,X5,X25,X32,X20] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X32),X25)) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(hAPP(c_COMBB(X5,X5,X20),hAPP(c_HOL_Otimes__class_Otimes(X5),X11)),X32)),X25) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right_Osetsum_0) ).
fof(f26732,plain,
spl0_1095,
inference(avatar_split_clause,[],[f1225,f26730]) ).
fof(f26730,plain,
( spl0_1095
<=> ! [X10,X13,X5,X25,X20] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X13),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),X25)) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(hAPP(c_COMBB(X5,X5,X20),hAPP(c_HOL_Otimes__class_Otimes(X5),X13)),X10)),X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f1225,axiom,
! [X10,X5,X25,X13,X20] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X13),hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),X25)) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),hAPP(hAPP(c_COMBB(X5,X5,X20),hAPP(c_HOL_Otimes__class_Otimes(X5),X13)),X10)),X25) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__right__distrib_0) ).
fof(f26728,plain,
spl0_1094,
inference(avatar_split_clause,[],[f1172,f26726]) ).
fof(f26726,plain,
( spl0_1094
<=> ! [X5,X10,X20,X6,X2] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ class_Power_Opower(X20)
| ~ c_Lim_OisCont(X10,X6,X5,X20)
| c_Lim_OisCont(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(tc_nat,X20),X5),c_Power_Opower__class_Opower(X20)),X10),X5,tc_nat,X20),X2),X6,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f1172,axiom,
! [X2,X10,X6,X5,X20] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ class_Power_Opower(X20)
| ~ c_Lim_OisCont(X10,X6,X5,X20)
| c_Lim_OisCont(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(tc_nat,X20),X5),c_Power_Opower__class_Opower(X20)),X10),X5,tc_nat,X20),X2),X6,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_isCont__power_0) ).
fof(f26724,plain,
spl0_1093,
inference(avatar_split_clause,[],[f1147,f26722]) ).
fof(f26722,plain,
( spl0_1093
<=> ! [X38,X10,X20,X5,X32] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Limits_OZfun(X10,X38,X5,X20)
| ~ c_Limits_OZfun(X32,X38,X5,X20)
| c_Limits_OZfun(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X32,X5,X20,X20),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f1147,axiom,
! [X38,X10,X5,X32,X20] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Limits_OZfun(X10,X38,X5,X20)
| ~ c_Limits_OZfun(X32,X38,X5,X20)
| c_Limits_OZfun(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X32,X5,X20,X20),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Zfun__diff_0) ).
fof(f26720,plain,
spl0_1092,
inference(avatar_split_clause,[],[f1132,f26718]) ).
fof(f26718,plain,
( spl0_1092
<=> ! [X38,X10,X20,X5,X32] :
( ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Limits_OZfun(X10,X38,X5,X20)
| ~ c_Limits_OZfun(X32,X38,X5,X20)
| c_Limits_OZfun(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X10),X32,X5,X20,X20),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f1132,axiom,
! [X38,X10,X5,X32,X20] :
( ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Limits_OZfun(X10,X38,X5,X20)
| ~ c_Limits_OZfun(X32,X38,X5,X20)
| c_Limits_OZfun(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X10),X32,X5,X20,X20),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Zfun__mult_0) ).
fof(f26716,plain,
spl0_1091,
inference(avatar_split_clause,[],[f929,f26714]) ).
fof(f26714,plain,
( spl0_1091
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) = X7
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f929,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) = X7
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nonzero__inverse__mult__distrib_0) ).
fof(f26712,plain,
spl0_1090,
inference(avatar_split_clause,[],[f920,f26710]) ).
fof(f26710,plain,
( spl0_1090
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f920,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel__right__disj_0) ).
fof(f26708,plain,
spl0_1089,
inference(avatar_split_clause,[],[f919,f26706]) ).
fof(f26706,plain,
( spl0_1089
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f919,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel__left__disj_0) ).
fof(f26704,plain,
spl0_1088,
inference(avatar_split_clause,[],[f910,f26702]) ).
fof(f26702,plain,
( spl0_1088
<=> ! [X5,X7,X6,X2] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7)),X2) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f910,axiom,
! [X2,X6,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7)),X2) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__divide_0) ).
fof(f26700,plain,
( spl0_1087
| ~ spl0_187
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3167,f3114,f2404,f26698]) ).
fof(f3167,plain,
( ! [X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X4) = X4
| ~ spl0_187
| ~ spl0_304 ),
inference(superposition,[],[f2405,f3116]) ).
fof(f26696,plain,
spl0_1086,
inference(avatar_split_clause,[],[f866,f26694]) ).
fof(f26694,plain,
( spl0_1086
<=> ! [X38,X10,X20,X5,X32] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Limits_OZfun(X10,X38,X5,X20)
| ~ c_Limits_OZfun(X32,X38,X5,X20)
| c_Limits_OZfun(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oplus__class_Oplus(X20)),X10),X32,X5,X20,X20),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f866,axiom,
! [X38,X10,X5,X32,X20] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Limits_OZfun(X10,X38,X5,X20)
| ~ c_Limits_OZfun(X32,X38,X5,X20)
| c_Limits_OZfun(c_COMBS(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oplus__class_Oplus(X20)),X10),X32,X5,X20,X20),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Zfun__add_0) ).
fof(f26691,plain,
spl0_1085,
inference(avatar_split_clause,[],[f766,f26689]) ).
fof(f766,axiom,
! [X2,X0,X14] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X14))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X2))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X14),X0)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_root__cancel_0) ).
fof(f26684,plain,
spl0_1084,
inference(avatar_split_clause,[],[f717,f26682]) ).
fof(f717,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_one__le__mult__iff_2) ).
fof(f26680,plain,
spl0_1083,
inference(avatar_split_clause,[],[f267,f26678]) ).
fof(f26678,plain,
( spl0_1083
<=> ! [X5,X31,X10,X20,X6,X29,X32] :
( ~ class_RealVector_Ometric__space(X20)
| ~ class_RealVector_Ometric__space(X31)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OisCont(X32,X29,X5,X20)
| ~ c_Lim_OLIM(X10,X6,X29,X31,X5)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X5,X20,X31),X32),X10),X6,hAPP(X32,X29),X31,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f267,axiom,
! [X31,X10,X29,X6,X5,X32,X20] :
( ~ class_RealVector_Ometric__space(X20)
| ~ class_RealVector_Ometric__space(X31)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OisCont(X32,X29,X5,X20)
| ~ c_Lim_OLIM(X10,X6,X29,X31,X5)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X5,X20,X31),X32),X10),X6,hAPP(X32,X29),X31,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_isCont__LIM__compose_0) ).
fof(f26673,plain,
spl0_1082,
inference(avatar_split_clause,[],[f202,f26671]) ).
fof(f202,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_one__less__mult_0) ).
fof(f26669,plain,
spl0_1081,
inference(avatar_split_clause,[],[f9,f26667]) ).
fof(f26667,plain,
( spl0_1081
<=> ! [X2,X5,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatMost(hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatMost(X2,tc_nat))),hAPP(X10,hAPP(c_Suc,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f9,axiom,
! [X2,X10,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatMost(hAPP(c_Suc,X2),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatMost(X2,tc_nat))),hAPP(X10,hAPP(c_Suc,X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__atMost__Suc_0) ).
fof(f26597,plain,
( spl0_1080
| ~ spl0_186
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3166,f3114,f2400,f26595]) ).
fof(f26595,plain,
( spl0_1080
<=> ! [X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_Orderings_Obot__class_Obot(tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f26593,plain,
( spl0_1079
| ~ spl0_304
| ~ spl0_1074 ),
inference(avatar_split_clause,[],[f23514,f23511,f3114,f26591]) ).
fof(f26591,plain,
( spl0_1079
<=> ! [X5,X18,X11,X29] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X29))
| ~ class_RealVector_Ometric__space(X5)
| ~ c_SEQ_OLIMSEQ(X18,X11,X5)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X18),hAPP(c_COMBC(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_nat,tc_nat),X29)),X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f23511,plain,
( spl0_1074
<=> ! [X5,X18,X11,X29] :
( ~ class_RealVector_Ometric__space(X5)
| ~ c_SEQ_OLIMSEQ(X18,X11,X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X29))
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X18),hAPP(c_COMBC(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_nat,tc_nat),X29)),X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f23514,plain,
( ! [X29,X11,X18,X5] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X29))
| ~ class_RealVector_Ometric__space(X5)
| ~ c_SEQ_OLIMSEQ(X18,X11,X5)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X18),hAPP(c_COMBC(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_nat,tc_nat),X29)),X11,X5) )
| ~ spl0_304
| ~ spl0_1074 ),
inference(forward_demodulation,[],[f23512,f3116]) ).
fof(f23512,plain,
( ! [X29,X11,X18,X5] :
( ~ class_RealVector_Ometric__space(X5)
| ~ c_SEQ_OLIMSEQ(X18,X11,X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X29))
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X18),hAPP(c_COMBC(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_nat,tc_nat),X29)),X11,X5) )
| ~ spl0_1074 ),
inference(avatar_component_clause,[],[f23511]) ).
fof(f26207,plain,
( spl0_1078
| ~ spl0_184
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3165,f3114,f2392,f26205]) ).
fof(f26205,plain,
( spl0_1078
<=> ! [X2] : hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),hAPP(c_Suc,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f3165,plain,
( ! [X2] : hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),hAPP(c_Suc,X2)))
| ~ spl0_184
| ~ spl0_304 ),
inference(superposition,[],[f2393,f3116]) ).
fof(f23526,plain,
spl0_1077,
inference(avatar_split_clause,[],[f1168,f23524]) ).
fof(f23524,plain,
( spl0_1077
<=> ! [X5,X10,X7,X6] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OLIMSEQ(X10,X6,X5)
| c_SEQ_OLIMSEQ(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X10),tc_nat,X5,X5),X7),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f1168,axiom,
! [X10,X6,X7,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OLIMSEQ(X10,X6,X5)
| c_SEQ_OLIMSEQ(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X10),tc_nat,X5,X5),X7),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__diff__const_0) ).
fof(f23522,plain,
spl0_1076,
inference(avatar_split_clause,[],[f1162,f23520]) ).
fof(f23520,plain,
( spl0_1076
<=> ! [X5,X9,X10,X6] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_Series_Osums(X10,X6,X5)
| c_Series_Osums(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X10),tc_nat,X5,X5),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f1162,axiom,
! [X10,X6,X9,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_Series_Osums(X10,X6,X5)
| c_Series_Osums(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X10),tc_nat,X5,X5),X9),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sums__mult2_0) ).
fof(f23518,plain,
spl0_1075,
inference(avatar_split_clause,[],[f1157,f23516]) ).
fof(f23516,plain,
( spl0_1075
<=> ! [X5,X18,X12,X6] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| c_SEQ_OLIMSEQ(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X18),tc_nat,X5,X5),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X12),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f1157,axiom,
! [X18,X6,X5,X12] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| c_SEQ_OLIMSEQ(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X18),tc_nat,X5,X5),X12),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X12),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left_OLIMSEQ_0) ).
fof(f23513,plain,
spl0_1074,
inference(avatar_split_clause,[],[f1083,f23511]) ).
fof(f1083,axiom,
! [X29,X11,X18,X5] :
( ~ class_RealVector_Ometric__space(X5)
| ~ c_SEQ_OLIMSEQ(X18,X11,X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X29))
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X18),hAPP(c_COMBC(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_nat,tc_nat),X29)),X11,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__linear_0) ).
fof(f23509,plain,
spl0_1073,
inference(avatar_split_clause,[],[f1027,f23507]) ).
fof(f23507,plain,
( spl0_1073
<=> ! [X5,X10,X7,X6] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OLIMSEQ(X10,X6,X5)
| c_SEQ_OLIMSEQ(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oplus__class_Oplus(X5)),X10),tc_nat,X5,X5),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f1027,axiom,
! [X10,X6,X7,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OLIMSEQ(X10,X6,X5)
| c_SEQ_OLIMSEQ(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oplus__class_Oplus(X5)),X10),tc_nat,X5,X5),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__add__const_0) ).
fof(f23505,plain,
spl0_1072,
inference(avatar_split_clause,[],[f1025,f23503]) ).
fof(f23503,plain,
( spl0_1072
<=> ! [X5,X18,X12,X6] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Series_Osums(X18,X6,X5)
| c_Series_Osums(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oinverse__class_Odivide(X5)),X18),tc_nat,X5,X5),X12),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X12),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f1025,axiom,
! [X18,X6,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Series_Osums(X18,X6,X5)
| c_Series_Osums(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oinverse__class_Odivide(X5)),X18),tc_nat,X5,X5),X12),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X12),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_Osums_0) ).
fof(f23501,plain,
spl0_1071,
inference(avatar_split_clause,[],[f1022,f23499]) ).
fof(f23499,plain,
( spl0_1071
<=> ! [X5,X18,X12,X6] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| c_SEQ_OLIMSEQ(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oinverse__class_Odivide(X5)),X18),tc_nat,X5,X5),X12),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X12),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f1022,axiom,
! [X18,X6,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| c_SEQ_OLIMSEQ(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oinverse__class_Odivide(X5)),X18),tc_nat,X5,X5),X12),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X12),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_OLIMSEQ_0) ).
fof(f23497,plain,
spl0_1070,
inference(avatar_split_clause,[],[f1008,f23495]) ).
fof(f23495,plain,
( spl0_1070
<=> ! [X5,X28,X29,X1] :
( ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X29,X5),X1))
| ~ hBOOL(hAPP(c_lessequals(X1,X5),X28))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X29,X1,X5),c_SetInterval_Oord__class_OatLeastLessThan(X1,X28,X5),tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X29,X28,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f1008,axiom,
! [X28,X29,X1,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X29,X5),X1))
| ~ hBOOL(hAPP(c_lessequals(X1,X5),X28))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(X29,X1,X5),c_SetInterval_Oord__class_OatLeastLessThan(X1,X28,X5),tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X29,X28,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_ivl__disj__un_I17_J_0) ).
fof(f23493,plain,
spl0_1069,
inference(avatar_split_clause,[],[f963,f23491]) ).
fof(f23491,plain,
( spl0_1069
<=> ! [X5,X7,X6,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f963,axiom,
! [X2,X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__mono_0) ).
fof(f23489,plain,
spl0_1068,
inference(avatar_split_clause,[],[f946,f23487]) ).
fof(f23487,plain,
( spl0_1068
<=> ! [X5,X6,X11,X20,X29,X32] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Lim_OLIM(X32,X6,X29,X5,X20)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X20,X20,X5),hAPP(c_HOL_Otimes__class_Otimes(X20),X11)),X32),X6,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X11),X29),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f946,axiom,
! [X29,X11,X6,X5,X32,X20] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Lim_OLIM(X32,X6,X29,X5,X20)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X20,X20,X5),hAPP(c_HOL_Otimes__class_Otimes(X20),X11)),X32),X6,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X11),X29),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right_OLIM_0) ).
fof(f23485,plain,
spl0_1067,
inference(avatar_split_clause,[],[f942,f23483]) ).
fof(f23483,plain,
( spl0_1067
<=> ! [X10,X32,X11,X5,X15,X23] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ c_Deriv_Oderiv(X32,hAPP(X10,X11),X23,X5)
| c_Deriv_Oderiv(hAPP(hAPP(c_COMBB(X5,X5,X5),X32),X10),X11,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X23),X15),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f942,axiom,
! [X10,X11,X15,X5,X32,X23] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ c_Deriv_Oderiv(X32,hAPP(X10,X11),X23,X5)
| c_Deriv_Oderiv(hAPP(hAPP(c_COMBB(X5,X5,X5),X32),X10),X11,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X23),X15),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__chain_H_0) ).
fof(f23481,plain,
spl0_1066,
inference(avatar_split_clause,[],[f937,f23479]) ).
fof(f23479,plain,
( spl0_1066
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f937,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel__right__disj_2) ).
fof(f23477,plain,
spl0_1065,
inference(avatar_split_clause,[],[f936,f23475]) ).
fof(f23475,plain,
( spl0_1065
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f936,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel__right__disj_1) ).
fof(f23473,plain,
spl0_1064,
inference(avatar_split_clause,[],[f935,f23471]) ).
fof(f23471,plain,
( spl0_1064
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f935,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel__left__disj_2) ).
fof(f23469,plain,
spl0_1063,
inference(avatar_split_clause,[],[f934,f23467]) ).
fof(f23467,plain,
( spl0_1063
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f934,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel__left__disj_1) ).
fof(f23465,plain,
spl0_1062,
inference(avatar_split_clause,[],[f845,f23463]) ).
fof(f23463,plain,
( spl0_1062
<=> ! [X5,X7,X6,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f845,axiom,
! [X2,X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__less__imp__less__base_0) ).
fof(f23415,plain,
spl0_1061,
inference(avatar_split_clause,[],[f802,f23413]) ).
fof(f23413,plain,
( spl0_1061
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_lessequals(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f802,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_lessequals(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right__mono__neg_0) ).
fof(f23411,plain,
spl0_1060,
inference(avatar_split_clause,[],[f801,f23409]) ).
fof(f23409,plain,
( spl0_1060
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_lessequals(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f801,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_lessequals(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left__mono__neg_0) ).
fof(f23407,plain,
spl0_1059,
inference(avatar_split_clause,[],[f800,f23405]) ).
fof(f23405,plain,
( spl0_1059
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Omult__mono(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f800,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Omult__mono(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right__mono_0) ).
fof(f23403,plain,
spl0_1058,
inference(avatar_split_clause,[],[f799,f23401]) ).
fof(f23401,plain,
( spl0_1058
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Omult__mono(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f799,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Omult__mono(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left__mono_0) ).
fof(f23399,plain,
spl0_1057,
inference(avatar_split_clause,[],[f798,f23397]) ).
fof(f23397,plain,
( spl0_1057
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Omult__mono1(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f798,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Omult__mono1(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__mono1_0) ).
fof(f23395,plain,
spl0_1056,
inference(avatar_split_clause,[],[f782,f23393]) ).
fof(f23393,plain,
( spl0_1056
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = X9
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f782,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = X9
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__divide__mult__cancel__right_0) ).
fof(f23391,plain,
spl0_1055,
inference(avatar_split_clause,[],[f781,f23389]) ).
fof(f23389,plain,
( spl0_1055
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = X9
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f781,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = X9
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__divide__mult__cancel__left_0) ).
fof(f23387,plain,
spl0_1054,
inference(avatar_split_clause,[],[f780,f23385]) ).
fof(f23385,plain,
( spl0_1054
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f780,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__strict__left__mono__comm_0) ).
fof(f23383,plain,
spl0_1053,
inference(avatar_split_clause,[],[f778,f23381]) ).
fof(f23381,plain,
( spl0_1053
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f778,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel__right__disj_4) ).
fof(f23379,plain,
spl0_1052,
inference(avatar_split_clause,[],[f777,f23377]) ).
fof(f23377,plain,
( spl0_1052
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f777,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__strict__right__mono_0) ).
fof(f23321,plain,
spl0_1051,
inference(avatar_split_clause,[],[f776,f23319]) ).
fof(f23319,plain,
( spl0_1051
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f776,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__strict__right__mono__neg_0) ).
fof(f23317,plain,
spl0_1050,
inference(avatar_split_clause,[],[f773,f23315]) ).
fof(f23315,plain,
( spl0_1050
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f773,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__strict__left__mono_0) ).
fof(f23313,plain,
spl0_1049,
inference(avatar_split_clause,[],[f772,f23311]) ).
fof(f23311,plain,
( spl0_1049
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f772,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__strict__left__mono__neg_0) ).
fof(f23309,plain,
spl0_1048,
inference(avatar_split_clause,[],[f771,f23307]) ).
fof(f23307,plain,
( spl0_1048
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f771,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel__left__pos_1) ).
fof(f23305,plain,
spl0_1047,
inference(avatar_split_clause,[],[f770,f23303]) ).
fof(f23303,plain,
( spl0_1047
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f770,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel__left__pos_0) ).
fof(f23301,plain,
spl0_1046,
inference(avatar_split_clause,[],[f768,f23299]) ).
fof(f23299,plain,
( spl0_1046
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f768,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel__left__neg_0) ).
fof(f23297,plain,
spl0_1045,
inference(avatar_split_clause,[],[f765,f23295]) ).
fof(f23295,plain,
( spl0_1045
<=> ! [X5,X29,X28,X1] :
( ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X1,X5),X28))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X29,X5),X1))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X1,X5),c_SetInterval_Oord__class_OatLeastLessThan(X1,X28,X5),tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X28,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f765,axiom,
! [X28,X29,X1,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X1,X5),X28))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X29,X5),X1))
| c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X1,X5),c_SetInterval_Oord__class_OatLeastLessThan(X1,X28,X5),tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X28,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_ivl__disj__un_I15_J_0) ).
fof(f23293,plain,
spl0_1044,
inference(avatar_split_clause,[],[f695,f23291]) ).
fof(f23291,plain,
( spl0_1044
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f695,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__cancel__left__neg_0) ).
fof(f23289,plain,
spl0_1043,
inference(avatar_split_clause,[],[f694,f23287]) ).
fof(f23287,plain,
( spl0_1043
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f694,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__cancel__left__neg_1) ).
fof(f23285,plain,
spl0_1042,
inference(avatar_split_clause,[],[f693,f23283]) ).
fof(f23283,plain,
( spl0_1042
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f693,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__cancel__left__pos_0) ).
fof(f23227,plain,
spl0_1041,
inference(avatar_split_clause,[],[f692,f23225]) ).
fof(f23225,plain,
( spl0_1041
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f692,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__cancel__left__pos_1) ).
fof(f23223,plain,
spl0_1040,
inference(avatar_split_clause,[],[f691,f23221]) ).
fof(f23221,plain,
( spl0_1040
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f691,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left__le__imp__le_0) ).
fof(f23219,plain,
spl0_1039,
inference(avatar_split_clause,[],[f690,f23217]) ).
fof(f23217,plain,
( spl0_1039
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f690,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right__le__imp__le_0) ).
fof(f23215,plain,
spl0_1038,
inference(avatar_split_clause,[],[f687,f23213]) ).
fof(f23213,plain,
( spl0_1038
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__semiring(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f687,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left__less__imp__less_0) ).
fof(f23211,plain,
spl0_1037,
inference(avatar_split_clause,[],[f686,f23209]) ).
fof(f23209,plain,
( spl0_1037
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__semiring(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f686,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right__less__imp__less_0) ).
fof(f23207,plain,
spl0_1036,
inference(avatar_split_clause,[],[f685,f23205]) ).
fof(f23205,plain,
( spl0_1036
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f685,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__imp__less__left_0) ).
fof(f23203,plain,
spl0_1035,
inference(avatar_split_clause,[],[f684,f23201]) ).
fof(f23201,plain,
( spl0_1035
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f684,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__imp__less__right_0) ).
fof(f23199,plain,
spl0_1034,
inference(avatar_split_clause,[],[f674,f23197]) ).
fof(f23197,plain,
( spl0_1034
<=> ! [X11,X12,X5,X16] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X16),X12)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12),X5),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f674,axiom,
! [X11,X16,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X16),X12)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12),X5),X16)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__imp__div__pos__less_0) ).
fof(f23195,plain,
spl0_1033,
inference(avatar_split_clause,[],[f673,f23193]) ).
fof(f23193,plain,
( spl0_1033
<=> ! [X11,X12,X5,X16] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X16),X12),X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X16,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f673,axiom,
! [X11,X16,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X16),X12),X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X16,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__imp__less__div__pos_0) ).
fof(f23191,plain,
spl0_1032,
inference(avatar_split_clause,[],[f632,f23189]) ).
fof(f23189,plain,
( spl0_1032
<=> ! [X5,X10,X20,X6,X21] :
( ~ class_RealVector_Oreal__normed__div__algebra(X20)
| ~ class_RealVector_Ometric__space(X5)
| c_HOL_Ozero__class_Ozero(X20) = X21
| ~ c_Lim_OLIM(X10,X6,X21,X5,X20)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X20,X20,X5),c_HOL_Oinverse__class_Oinverse(X20)),X10),X6,hAPP(c_HOL_Oinverse__class_Oinverse(X20),X21),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f632,axiom,
! [X21,X10,X6,X5,X20] :
( ~ class_RealVector_Oreal__normed__div__algebra(X20)
| ~ class_RealVector_Ometric__space(X5)
| c_HOL_Ozero__class_Ozero(X20) = X21
| ~ c_Lim_OLIM(X10,X6,X21,X5,X20)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X20,X20,X5),c_HOL_Oinverse__class_Oinverse(X20)),X10),X6,hAPP(c_HOL_Oinverse__class_Oinverse(X20),X21),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__inverse_0) ).
fof(f23169,plain,
spl0_1031,
inference(avatar_split_clause,[],[f586,f23167]) ).
fof(f23167,plain,
( spl0_1031
<=> ! [X11,X12,X5,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f586,axiom,
! [X11,X7,X5,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X12))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__strict__increasing__iff_1) ).
fof(f23165,plain,
spl0_1030,
inference(avatar_split_clause,[],[f585,f23163]) ).
fof(f23163,plain,
( spl0_1030
<=> ! [X11,X12,X5,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f585,axiom,
! [X11,X7,X5,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X12))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__strict__increasing__iff_0) ).
fof(f23161,plain,
spl0_1029,
inference(avatar_split_clause,[],[f215,f23159]) ).
fof(f23159,plain,
( spl0_1029
<=> ! [X11,X12,X5,X16] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| ~ hBOOL(hAPP(c_lessequals(X11,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X16),X12)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12),X5),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f215,axiom,
! [X11,X16,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| ~ hBOOL(hAPP(c_lessequals(X11,X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X16),X12)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12),X5),X16)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__imp__div__pos__le_0) ).
fof(f23157,plain,
spl0_1028,
inference(avatar_split_clause,[],[f214,f23155]) ).
fof(f23155,plain,
( spl0_1028
<=> ! [X11,X12,X5,X16] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X16),X12),X5),X11))
| hBOOL(hAPP(c_lessequals(X16,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f214,axiom,
! [X11,X16,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X16),X12),X5),X11))
| hBOOL(hAPP(c_lessequals(X16,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__imp__le__div__pos_0) ).
fof(f23153,plain,
spl0_1027,
inference(avatar_split_clause,[],[f207,f23151]) ).
fof(f23151,plain,
( spl0_1027
<=> ! [X5,X6,X2,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X30))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X30))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f207,axiom,
! [X2,X6,X5,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X30))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X30))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__increasing_0) ).
fof(f23149,plain,
spl0_1026,
inference(avatar_split_clause,[],[f180,f23147]) ).
fof(f23147,plain,
( spl0_1026
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f180,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__strict__right__mono__neg_0) ).
fof(f23145,plain,
spl0_1025,
inference(avatar_split_clause,[],[f179,f23143]) ).
fof(f23143,plain,
( spl0_1025
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f179,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__strict__right__mono_0) ).
fof(f23141,plain,
spl0_1024,
inference(avatar_split_clause,[],[f171,f23139]) ).
fof(f23139,plain,
( spl0_1024
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Oone__class_Oone(X5)),c_HOL_Oone__class_Oone(X5))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f171,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Oone__class_Oone(X5)),c_HOL_Oone__class_Oone(X5))))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__half__sum_0) ).
fof(f23137,plain,
spl0_1023,
inference(avatar_split_clause,[],[f170,f23135]) ).
fof(f23135,plain,
( spl0_1023
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Oone__class_Oone(X5)),c_HOL_Oone__class_Oone(X5))),X5),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f170,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Oone__class_Oone(X5)),c_HOL_Oone__class_Oone(X5))),X5),X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_gt__half__sum_0) ).
fof(f23133,plain,
spl0_1022,
inference(avatar_split_clause,[],[f147,f23131]) ).
fof(f23131,plain,
( spl0_1022
<=> ! [X11,X12,X5,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,tc_nat),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f147,axiom,
! [X11,X7,X5,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,tc_nat),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X12))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__increasing__iff_1) ).
fof(f23111,plain,
spl0_1021,
inference(avatar_split_clause,[],[f146,f23109]) ).
fof(f23109,plain,
( spl0_1021
<=> ! [X11,X12,X5,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_lessequals(X11,tc_nat),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f146,axiom,
! [X11,X7,X5,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_lessequals(X11,tc_nat),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X12))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__increasing__iff_0) ).
fof(f21909,plain,
( spl0_1020
| ~ spl0_304
| ~ spl0_974 ),
inference(avatar_split_clause,[],[f21496,f21493,f3114,f21907]) ).
fof(f21907,plain,
( spl0_1020
<=> ! [X11,X13,X14,X9] :
( c_Orderings_Obot__class_Obot(tc_nat) = X13
| X9 = X14
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X13),X9)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X13),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f21493,plain,
( spl0_974
<=> ! [X11,X13,X14,X9] :
( X9 = X14
| c_HOL_Ozero__class_Ozero(tc_nat) = X13
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X13),X9)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X13),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f21496,plain,
( ! [X11,X9,X14,X13] :
( c_Orderings_Obot__class_Obot(tc_nat) = X13
| X9 = X14
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X13),X9)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X13),X14)) )
| ~ spl0_304
| ~ spl0_974 ),
inference(forward_demodulation,[],[f21494,f3116]) ).
fof(f21494,plain,
( ! [X11,X9,X14,X13] :
( X9 = X14
| c_HOL_Ozero__class_Ozero(tc_nat) = X13
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X13),X9)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X13),X14)) )
| ~ spl0_974 ),
inference(avatar_component_clause,[],[f21493]) ).
fof(f21766,plain,
spl0_1019,
inference(avatar_split_clause,[],[f1296,f21764]) ).
fof(f21764,plain,
( spl0_1019
<=> ! [X6,X40,X7,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X40)),X7) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X40),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f1296,axiom,
! [X40,X6,X7,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X40)),X7) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X40),X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult_Odiff__left_0) ).
fof(f21762,plain,
spl0_1018,
inference(avatar_split_clause,[],[f1295,f21760]) ).
fof(f21760,plain,
( spl0_1018
<=> ! [X5,X41,X7,X6] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X41)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f1295,axiom,
! [X41,X6,X7,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X7),X41)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X41)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult_Odiff__right_0) ).
fof(f21758,plain,
spl0_1017,
inference(avatar_split_clause,[],[f1235,f21756]) ).
fof(f21756,plain,
( spl0_1017
<=> ! [X48,X11,X12,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12)),X48) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X48)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),X48)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f1235,axiom,
! [X48,X11,X5,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12)),X48) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X48)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X12),X48)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Opwr__mul_0) ).
fof(f21754,plain,
spl0_1016,
inference(avatar_split_clause,[],[f1234,f21752]) ).
fof(f21752,plain,
( spl0_1016
<=> ! [X5,X7,X6,X2] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f1234,axiom,
! [X2,X6,X7,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X7),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__mult__distrib_0) ).
fof(f21750,plain,
spl0_1015,
inference(avatar_split_clause,[],[f1190,f21748]) ).
fof(f21748,plain,
( spl0_1015
<=> ! [X10,X21,X5,X32] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OLIMSEQ(X10,X21,X5)
| c_SEQ_OLIMSEQ(X32,X21,X5)
| ~ c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X10),X32,tc_nat,X5,X5),c_HOL_Ozero__class_Ozero(X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f1190,axiom,
! [X21,X10,X5,X32] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OLIMSEQ(X10,X21,X5)
| c_SEQ_OLIMSEQ(X32,X21,X5)
| ~ c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X10),X32,tc_nat,X5,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__diff__approach__zero2_0) ).
fof(f21746,plain,
spl0_1014,
inference(avatar_split_clause,[],[f1189,f21744]) ).
fof(f21744,plain,
( spl0_1014
<=> ! [X32,X10,X5,X21] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OLIMSEQ(X32,X21,X5)
| c_SEQ_OLIMSEQ(X10,X21,X5)
| ~ c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X10),X32,tc_nat,X5,X5),c_HOL_Ozero__class_Ozero(X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f1189,axiom,
! [X21,X10,X5,X32] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OLIMSEQ(X32,X21,X5)
| c_SEQ_OLIMSEQ(X10,X21,X5)
| ~ c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X10),X32,tc_nat,X5,X5),c_HOL_Ozero__class_Ozero(X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__diff__approach__zero_0) ).
fof(f21742,plain,
spl0_1013,
inference(avatar_split_clause,[],[f985,f21740]) ).
fof(f21740,plain,
( spl0_1013
<=> ! [X48,X11,X5,X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X39)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X48)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X39),X48)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f985,axiom,
! [X39,X48,X11,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X39)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X48)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X39),X48)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Omul__pwr_0) ).
fof(f21738,plain,
spl0_1012,
inference(avatar_split_clause,[],[f980,f21736]) ).
fof(f21736,plain,
( spl0_1012
<=> ! [X5,X6,X2,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f980,axiom,
! [X2,X1,X6,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__add_0) ).
fof(f21734,plain,
spl0_1011,
inference(avatar_split_clause,[],[f870,f21732]) ).
fof(f21732,plain,
( spl0_1011
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f870,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__less__power__Suc_0) ).
fof(f21700,plain,
spl0_1010,
inference(avatar_split_clause,[],[f857,f21698]) ).
fof(f21698,plain,
( spl0_1010
<=> ! [X5,X11,X12,X36] :
( ~ class_RealVector_Oreal__normed__field(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X12)),X36) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X36)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X12),X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f857,axiom,
! [X11,X36,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X12)),X36) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X36)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X12),X36)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_Odiff_0) ).
fof(f21696,plain,
spl0_1009,
inference(avatar_split_clause,[],[f856,f21694]) ).
fof(f21694,plain,
( spl0_1009
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Ofield(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X9) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X9)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f856,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X9) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X9)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__divide__distrib_0) ).
fof(f21692,plain,
spl0_1008,
inference(avatar_split_clause,[],[f817,f21690]) ).
fof(f21690,plain,
( spl0_1008
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f817,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f21688,plain,
spl0_1007,
inference(avatar_split_clause,[],[f816,f21686]) ).
fof(f21686,plain,
( spl0_1007
<=> ! [X17,X11,X12,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X17),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X17),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f816,axiom,
! [X11,X17,X5,X12] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X17),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X17),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X17),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right_Oadd_0) ).
fof(f21684,plain,
spl0_1006,
inference(avatar_split_clause,[],[f814,f21682]) ).
fof(f21682,plain,
( spl0_1006
<=> ! [X5,X11,X12,X36] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12)),X36) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X36)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f814,axiom,
! [X11,X36,X5,X12] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12)),X36) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X36)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X36)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left_Oadd_0) ).
fof(f21680,plain,
spl0_1005,
inference(avatar_split_clause,[],[f812,f21678]) ).
fof(f21678,plain,
( spl0_1005
<=> ! [X5,X11,X12,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X12),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f812,axiom,
! [X11,X16,X5,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X12),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Omul__d_0) ).
fof(f21676,plain,
spl0_1004,
inference(avatar_split_clause,[],[f811,f21674]) ).
fof(f21674,plain,
( spl0_1004
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f811,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_comm__semiring__class_Odistrib_0) ).
fof(f21672,plain,
spl0_1003,
inference(avatar_split_clause,[],[f725,f21670]) ).
fof(f21670,plain,
( spl0_1003
<=> ! [X5,X6,X7,X14,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X9,X5),X14))
| ~ hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9)))
| hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f725,axiom,
! [X6,X9,X7,X14,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X9,X5),X14))
| ~ hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9)))
| hBOOL(hAPP(c_lessequals(X6,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__add__right__mono_0) ).
fof(f21668,plain,
spl0_1002,
inference(avatar_split_clause,[],[f709,f21666]) ).
fof(f21666,plain,
( spl0_1002
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f709,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel__left__disj_3) ).
fof(f21664,plain,
spl0_1001,
inference(avatar_split_clause,[],[f708,f21662]) ).
fof(f21662,plain,
( spl0_1001
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f708,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel__right__disj_3) ).
fof(f21626,plain,
spl0_1000,
inference(avatar_split_clause,[],[f703,f21624]) ).
fof(f21624,plain,
( spl0_1000
<=> ! [X5,X31,X10,X20,X6,X32] :
( ~ class_RealVector_Ometric__space(X31)
| ~ class_RealVector_Ometric__space(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OisCont(X10,X6,X5,X20)
| ~ c_Lim_OisCont(X32,hAPP(X10,X6),X20,X31)
| c_Lim_OisCont(hAPP(hAPP(c_COMBB(X20,X31,X5),X32),X10),X6,X5,X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f703,axiom,
! [X31,X10,X6,X5,X32,X20] :
( ~ class_RealVector_Ometric__space(X31)
| ~ class_RealVector_Ometric__space(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OisCont(X10,X6,X5,X20)
| ~ c_Lim_OisCont(X32,hAPP(X10,X6),X20,X31)
| c_Lim_OisCont(hAPP(hAPP(c_COMBB(X20,X31,X5),X32),X10),X6,X5,X31) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_isCont__o2_0) ).
fof(f21622,plain,
spl0_999,
inference(avatar_split_clause,[],[f636,f21620]) ).
fof(f21620,plain,
( spl0_999
<=> ! [X5,X7,X9,X8] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ class_Int_Onumber(X5)
| c_HOL_Ozero__class_Ozero(X5) = X9
| c_Int_Onumber__class_Onumber__of(X8,X5) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X8,X5)),X9) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f636,axiom,
! [X8,X9,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ class_Int_Onumber(X5)
| c_HOL_Ozero__class_Ozero(X5) = X9
| c_Int_Onumber__class_Onumber__of(X8,X5) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Int_Onumber__class_Onumber__of(X8,X5)),X9) = X7 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__eq__eq__number__of_0) ).
fof(f21618,plain,
spl0_998,
inference(avatar_split_clause,[],[f546,f21616]) ).
fof(f21616,plain,
( spl0_998
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f546,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__divide__iff_5) ).
fof(f21614,plain,
spl0_997,
inference(avatar_split_clause,[],[f545,f21612]) ).
fof(f21612,plain,
( spl0_997
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f545,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__divide__iff_4) ).
fof(f21610,plain,
spl0_996,
inference(avatar_split_clause,[],[f536,f21608]) ).
fof(f21608,plain,
( spl0_996
<=> ! [X5,X9,X7,X14,X6] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),X14))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f536,axiom,
! [X6,X9,X7,X14,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),X14))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__strict__mono_0) ).
fof(f21606,plain,
spl0_995,
inference(avatar_split_clause,[],[f498,f21604]) ).
fof(f21604,plain,
( spl0_995
<=> ! [X5,X9,X7,X14,X6] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),X14))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f498,axiom,
! [X6,X9,X7,X14,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X9,X5),X14))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__le__less__mono_0) ).
fof(f21602,plain,
spl0_994,
inference(avatar_split_clause,[],[f497,f21600]) ).
fof(f21600,plain,
( spl0_994
<=> ! [X5,X6,X7,X14,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X9,X5),X14))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f497,axiom,
! [X6,X9,X7,X14,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X9,X5),X14))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__less__le__mono_0) ).
fof(f21598,plain,
spl0_993,
inference(avatar_split_clause,[],[f495,f21596]) ).
fof(f21596,plain,
( spl0_993
<=> ! [X5,X11,X12,X36] :
( ~ class_RealVector_Oreal__normed__field(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12)),X36) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X36)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X12),X36)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f495,axiom,
! [X11,X36,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12)),X36) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X36)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X12),X36)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_Oadd_0) ).
fof(f21594,plain,
spl0_992,
inference(avatar_split_clause,[],[f494,f21592]) ).
fof(f21592,plain,
( spl0_992
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Ofield(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X9)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f494,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X9)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__divide__distrib_0) ).
fof(f21590,plain,
spl0_991,
inference(avatar_split_clause,[],[f475,f21588]) ).
fof(f21588,plain,
( spl0_991
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f475,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__0__iff_0) ).
fof(f21560,plain,
spl0_990,
inference(avatar_split_clause,[],[f474,f21558]) ).
fof(f21558,plain,
( spl0_990
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f474,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__0__iff_1) ).
fof(f21556,plain,
spl0_989,
inference(avatar_split_clause,[],[f473,f21554]) ).
fof(f21554,plain,
( spl0_989
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f473,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__0__iff_2) ).
fof(f21552,plain,
spl0_988,
inference(avatar_split_clause,[],[f472,f21550]) ).
fof(f21550,plain,
( spl0_988
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f472,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__0__iff_3) ).
fof(f21548,plain,
spl0_987,
inference(avatar_split_clause,[],[f421,f21546]) ).
fof(f21546,plain,
( spl0_987
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f421,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__divide__iff_0) ).
fof(f21544,plain,
spl0_986,
inference(avatar_split_clause,[],[f420,f21542]) ).
fof(f21542,plain,
( spl0_986
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f420,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__divide__iff_1) ).
fof(f21540,plain,
spl0_985,
inference(avatar_split_clause,[],[f419,f21538]) ).
fof(f21538,plain,
( spl0_985
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f419,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__divide__iff_2) ).
fof(f21536,plain,
spl0_984,
inference(avatar_split_clause,[],[f418,f21534]) ).
fof(f21534,plain,
( spl0_984
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f418,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__divide__iff_3) ).
fof(f21532,plain,
spl0_983,
inference(avatar_split_clause,[],[f373,f21530]) ).
fof(f21530,plain,
( spl0_983
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f373,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__0__iff_3) ).
fof(f21528,plain,
spl0_982,
inference(avatar_split_clause,[],[f372,f21526]) ).
fof(f21526,plain,
( spl0_982
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f372,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__0__iff_2) ).
fof(f21524,plain,
spl0_981,
inference(avatar_split_clause,[],[f371,f21522]) ).
fof(f21522,plain,
( spl0_981
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f371,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__0__iff_1) ).
fof(f21520,plain,
( spl0_980
| ~ spl0_655
| ~ spl0_968 ),
inference(avatar_split_clause,[],[f21448,f21159,f9712,f21518]) ).
fof(f21518,plain,
( spl0_980
<=> ! [X1] : c_Orderings_Obot__class_Obot(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f21159,plain,
( spl0_968
<=> ! [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_968])]) ).
fof(f21448,plain,
( ! [X1] : c_Orderings_Obot__class_Obot(tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_655
| ~ spl0_968 ),
inference(superposition,[],[f21160,f9713]) ).
fof(f21160,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_968 ),
inference(avatar_component_clause,[],[f21159]) ).
fof(f21516,plain,
spl0_979,
inference(avatar_split_clause,[],[f370,f21514]) ).
fof(f21514,plain,
( spl0_979
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f370,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__0__iff_0) ).
fof(f21512,plain,
spl0_978,
inference(avatar_split_clause,[],[f336,f21510]) ).
fof(f21510,plain,
( spl0_978
<=> ! [X5,X9,X7,X14,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(X9,X5),X14))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f336,axiom,
! [X6,X9,X7,X14,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(X9,X5),X14))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X14))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__mono_0) ).
fof(f21508,plain,
spl0_977,
inference(avatar_split_clause,[],[f325,f21506]) ).
fof(f21506,plain,
( spl0_977
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Suc,X2)),X5),c_HOL_Oone__class_Oone(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f325,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Suc,X2)),X5),c_HOL_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__Suc__less__one_0) ).
fof(f21504,plain,
spl0_976,
inference(avatar_split_clause,[],[f229,f21502]) ).
fof(f21502,plain,
( spl0_976
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f229,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__0__iff_4) ).
fof(f21500,plain,
spl0_975,
inference(avatar_split_clause,[],[f228,f21498]) ).
fof(f21498,plain,
( spl0_975
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f228,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__0__iff_5) ).
fof(f21495,plain,
spl0_974,
inference(avatar_split_clause,[],[f22,f21493]) ).
fof(f22,axiom,
! [X11,X9,X14,X13] :
( X9 = X14
| c_HOL_Ozero__class_Ozero(tc_nat) = X13
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X13),X9)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X13),X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_natgb_Oadd__scale__eq__noteq_0) ).
fof(f21491,plain,
spl0_973,
inference(avatar_split_clause,[],[f18,f21489]) ).
fof(f21489,plain,
( spl0_973
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f18,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__divide__iff_0) ).
fof(f21487,plain,
spl0_972,
inference(avatar_split_clause,[],[f17,f21485]) ).
fof(f21485,plain,
( spl0_972
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f17,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__divide__iff_1) ).
fof(f21483,plain,
spl0_971,
inference(avatar_split_clause,[],[f16,f21481]) ).
fof(f21481,plain,
( spl0_971
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f16,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__divide__iff_2) ).
fof(f21479,plain,
spl0_970,
inference(avatar_split_clause,[],[f15,f21477]) ).
fof(f21477,plain,
( spl0_970
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f15,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__divide__iff_3) ).
fof(f21212,plain,
( spl0_969
| ~ spl0_304
| ~ spl0_961 ),
inference(avatar_split_clause,[],[f20381,f20378,f3114,f21210]) ).
fof(f21210,plain,
( spl0_969
<=> ! [X5,X10] :
( c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X10),hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),tc_nat,X5,X5),X5) = hAPP(X10,c_Orderings_Obot__class_Obot(tc_nat))
| ~ class_RealVector_Oreal__normed__algebra__1(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f20378,plain,
( spl0_961
<=> ! [X5,X10] :
( ~ class_RealVector_Oreal__normed__algebra__1(X5)
| hAPP(X10,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X10),hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),tc_nat,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f20381,plain,
( ! [X10,X5] :
( c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X10),hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),tc_nat,X5,X5),X5) = hAPP(X10,c_Orderings_Obot__class_Obot(tc_nat))
| ~ class_RealVector_Oreal__normed__algebra__1(X5) )
| ~ spl0_304
| ~ spl0_961 ),
inference(forward_demodulation,[],[f20379,f3116]) ).
fof(f20379,plain,
( ! [X10,X5] :
( ~ class_RealVector_Oreal__normed__algebra__1(X5)
| hAPP(X10,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X10),hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),tc_nat,X5,X5),X5) )
| ~ spl0_961 ),
inference(avatar_component_clause,[],[f20378]) ).
fof(f21161,plain,
( spl0_968
| ~ spl0_751
| ~ spl0_859 ),
inference(avatar_split_clause,[],[f20677,f14911,f12818,f21159]) ).
fof(f14911,plain,
( spl0_859
<=> ! [X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f20677,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_751
| ~ spl0_859 ),
inference(superposition,[],[f12819,f14912]) ).
fof(f14912,plain,
( ! [X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat) = X1
| ~ spl0_859 ),
inference(avatar_component_clause,[],[f14911]) ).
fof(f21132,plain,
( spl0_967
| ~ spl0_304
| ~ spl0_952 ),
inference(avatar_split_clause,[],[f20344,f20340,f3114,f21130]) ).
fof(f21130,plain,
( spl0_967
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f20340,plain,
( spl0_952
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f20344,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_304
| ~ spl0_952 ),
inference(forward_demodulation,[],[f20343,f3116]) ).
fof(f20343,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_304
| ~ spl0_952 ),
inference(forward_demodulation,[],[f20341,f3116]) ).
fof(f20341,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_952 ),
inference(avatar_component_clause,[],[f20340]) ).
fof(f21128,plain,
( spl0_966
| ~ spl0_304
| ~ spl0_951 ),
inference(avatar_split_clause,[],[f20338,f20334,f3114,f21126]) ).
fof(f21126,plain,
( spl0_966
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f20334,plain,
( spl0_951
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f20338,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1))) )
| ~ spl0_304
| ~ spl0_951 ),
inference(forward_demodulation,[],[f20337,f3116]) ).
fof(f20337,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1))) )
| ~ spl0_304
| ~ spl0_951 ),
inference(forward_demodulation,[],[f20335,f3116]) ).
fof(f20335,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1))) )
| ~ spl0_951 ),
inference(avatar_component_clause,[],[f20334]) ).
fof(f20464,plain,
( spl0_965
| ~ spl0_304
| ~ spl0_947 ),
inference(avatar_split_clause,[],[f20251,f20248,f3114,f20462]) ).
fof(f20462,plain,
( spl0_965
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f20248,plain,
( spl0_947
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f20251,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) )
| ~ spl0_304
| ~ spl0_947 ),
inference(forward_demodulation,[],[f20249,f3116]) ).
fof(f20249,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) )
| ~ spl0_947 ),
inference(avatar_component_clause,[],[f20248]) ).
fof(f20460,plain,
( spl0_964
| ~ spl0_304
| ~ spl0_946 ),
inference(avatar_split_clause,[],[f20246,f20243,f3114,f20458]) ).
fof(f20458,plain,
( spl0_964
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f20243,plain,
( spl0_946
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f20246,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) )
| ~ spl0_304
| ~ spl0_946 ),
inference(forward_demodulation,[],[f20244,f3116]) ).
fof(f20244,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) )
| ~ spl0_946 ),
inference(avatar_component_clause,[],[f20243]) ).
fof(f20456,plain,
( spl0_963
| ~ spl0_304
| ~ spl0_945 ),
inference(avatar_split_clause,[],[f20241,f20238,f3114,f20454]) ).
fof(f20454,plain,
( spl0_963
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f20238,plain,
( spl0_945
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f20241,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) )
| ~ spl0_304
| ~ spl0_945 ),
inference(forward_demodulation,[],[f20239,f3116]) ).
fof(f20239,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) )
| ~ spl0_945 ),
inference(avatar_component_clause,[],[f20238]) ).
fof(f20452,plain,
( spl0_962
| ~ spl0_304
| ~ spl0_944 ),
inference(avatar_split_clause,[],[f20236,f20233,f3114,f20450]) ).
fof(f20450,plain,
( spl0_962
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f20233,plain,
( spl0_944
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f20236,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) )
| ~ spl0_304
| ~ spl0_944 ),
inference(forward_demodulation,[],[f20234,f3116]) ).
fof(f20234,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) )
| ~ spl0_944 ),
inference(avatar_component_clause,[],[f20233]) ).
fof(f20380,plain,
spl0_961,
inference(avatar_split_clause,[],[f1195,f20378]) ).
fof(f1195,axiom,
! [X10,X5] :
( ~ class_RealVector_Oreal__normed__algebra__1(X5)
| hAPP(X10,c_HOL_Ozero__class_Ozero(tc_nat)) = c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X10),hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),tc_nat,X5,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_powser__zero_0) ).
fof(f20376,plain,
spl0_960,
inference(avatar_split_clause,[],[f1170,f20374]) ).
fof(f20374,plain,
( spl0_960
<=> ! [X6,X10,X20,X5,X26] : c_Set_Ovimage(X10,c_Set_Oinsert(X6,X26,X20),X5,X20) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X10,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),X5,X20),c_Set_Ovimage(X10,X26,X5,X20),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f1170,axiom,
! [X10,X6,X26,X5,X20] : c_Set_Ovimage(X10,c_Set_Oinsert(X6,X26,X20),X5,X20) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X10,c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20),X5,X20),c_Set_Ovimage(X10,X26,X5,X20),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_vimage__insert_0) ).
fof(f20372,plain,
spl0_959,
inference(avatar_split_clause,[],[f1148,f20370]) ).
fof(f20370,plain,
( spl0_959
<=> ! [X10,X11,X5,X32] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Odifferentiable(X10,X11,X5)
| ~ c_Deriv_Odifferentiable(X32,X11,X5)
| c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Ominus__class_Ominus(X5)),X10),X32,X5,X5,X5),X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f1148,axiom,
! [X10,X11,X5,X32] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Odifferentiable(X10,X11,X5)
| ~ c_Deriv_Odifferentiable(X32,X11,X5)
| c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Ominus__class_Ominus(X5)),X10),X32,X5,X5,X5),X11,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_differentiable__diff_0) ).
fof(f20368,plain,
spl0_958,
inference(avatar_split_clause,[],[f1133,f20366]) ).
fof(f20366,plain,
( spl0_958
<=> ! [X10,X11,X5,X32] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Odifferentiable(X10,X11,X5)
| ~ c_Deriv_Odifferentiable(X32,X11,X5)
| c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Otimes__class_Otimes(X5)),X10),X32,X5,X5,X5),X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f1133,axiom,
! [X10,X11,X5,X32] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Odifferentiable(X10,X11,X5)
| ~ c_Deriv_Odifferentiable(X32,X11,X5)
| c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Otimes__class_Otimes(X5)),X10),X32,X5,X5,X5),X11,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_differentiable__mult_0) ).
fof(f20364,plain,
spl0_957,
inference(avatar_split_clause,[],[f1103,f20362]) ).
fof(f20362,plain,
( spl0_957
<=> ! [X38,X10,X20,X6,X5] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| c_Limits_Otendsto(X10,X6,X38,X5,X20)
| ~ c_Limits_OZfun(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X5,X20,X20),X6),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f1103,axiom,
! [X38,X10,X6,X5,X20] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| c_Limits_Otendsto(X10,X6,X38,X5,X20)
| ~ c_Limits_OZfun(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X5,X20,X20),X6),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_tendsto__Zfun__iff_1) ).
fof(f20360,plain,
spl0_956,
inference(avatar_split_clause,[],[f1102,f20358]) ).
fof(f20358,plain,
( spl0_956
<=> ! [X38,X10,X20,X6,X5] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Limits_Otendsto(X10,X6,X38,X5,X20)
| c_Limits_OZfun(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X5,X20,X20),X6),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f1102,axiom,
! [X38,X10,X6,X5,X20] :
( ~ class_RealVector_Oreal__normed__vector(X20)
| ~ c_Limits_Otendsto(X10,X6,X38,X5,X20)
| c_Limits_OZfun(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Ominus__class_Ominus(X20)),X10),X5,X20,X20),X6),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_tendsto__Zfun__iff_0) ).
fof(f20356,plain,
spl0_955,
inference(avatar_split_clause,[],[f945,f20354]) ).
fof(f20354,plain,
( spl0_955
<=> ! [X38,X11,X20,X6,X5,X32] :
( ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Limits_Otendsto(X32,X6,X38,X5,X20)
| c_Limits_Otendsto(hAPP(hAPP(c_COMBB(X20,X20,X5),hAPP(c_HOL_Otimes__class_Otimes(X20),X11)),X32),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X11),X6),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f945,axiom,
! [X38,X11,X6,X5,X32,X20] :
( ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Limits_Otendsto(X32,X6,X38,X5,X20)
| c_Limits_Otendsto(hAPP(hAPP(c_COMBB(X20,X20,X5),hAPP(c_HOL_Otimes__class_Otimes(X20),X11)),X32),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X20),X11),X6),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right_Otendsto_0) ).
fof(f20352,plain,
spl0_954,
inference(avatar_split_clause,[],[f864,f20350]) ).
fof(f20350,plain,
( spl0_954
<=> ! [X10,X11,X5,X32] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Odifferentiable(X10,X11,X5)
| ~ c_Deriv_Odifferentiable(X32,X11,X5)
| c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oplus__class_Oplus(X5)),X10),X32,X5,X5,X5),X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f864,axiom,
! [X10,X11,X5,X32] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Odifferentiable(X10,X11,X5)
| ~ c_Deriv_Odifferentiable(X32,X11,X5)
| c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),X5),c_HOL_Oplus__class_Oplus(X5)),X10),X32,X5,X5,X5),X11,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_differentiable__sum_0) ).
fof(f20348,plain,
spl0_953,
inference(avatar_split_clause,[],[f635,f20346]) ).
fof(f20346,plain,
( spl0_953
<=> ! [X5,X38,X10,X20,X6] :
( ~ class_RealVector_Oreal__normed__div__algebra(X20)
| c_HOL_Ozero__class_Ozero(X20) = X6
| ~ c_Limits_Otendsto(X10,X6,X38,X5,X20)
| c_Limits_Otendsto(hAPP(hAPP(c_COMBB(X20,X20,X5),c_HOL_Oinverse__class_Oinverse(X20)),X10),hAPP(c_HOL_Oinverse__class_Oinverse(X20),X6),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f635,axiom,
! [X38,X10,X6,X5,X20] :
( ~ class_RealVector_Oreal__normed__div__algebra(X20)
| c_HOL_Ozero__class_Ozero(X20) = X6
| ~ c_Limits_Otendsto(X10,X6,X38,X5,X20)
| c_Limits_Otendsto(hAPP(hAPP(c_COMBB(X20,X20,X5),c_HOL_Oinverse__class_Oinverse(X20)),X10),hAPP(c_HOL_Oinverse__class_Oinverse(X20),X6),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_tendsto__inverse_0) ).
fof(f20342,plain,
spl0_952,
inference(avatar_split_clause,[],[f569,f20340]) ).
fof(f569,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_n__less__m__mult__n_0) ).
fof(f20336,plain,
spl0_951,
inference(avatar_split_clause,[],[f568,f20334]) ).
fof(f568,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_n__less__n__mult__m_0) ).
fof(f20332,plain,
spl0_950,
inference(avatar_split_clause,[],[f559,f20330]) ).
fof(f20330,plain,
( spl0_950
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X4))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f559,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X4))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__diff__assoc_0) ).
fof(f20259,plain,
spl0_949,
inference(avatar_split_clause,[],[f558,f20257]) ).
fof(f20257,plain,
( spl0_949
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X4))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X3)),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f558,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X4))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X3)),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0)),X3) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__diff__assoc2_0) ).
fof(f20255,plain,
spl0_948,
inference(avatar_split_clause,[],[f515,f20253]) ).
fof(f20253,plain,
( spl0_948
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X4))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f515,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X4))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0)),X4) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__diff__right_0) ).
fof(f20250,plain,
spl0_947,
inference(avatar_split_clause,[],[f487,f20248]) ).
fof(f487,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel2_2) ).
fof(f20245,plain,
spl0_946,
inference(avatar_split_clause,[],[f486,f20243]) ).
fof(f486,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel1_2) ).
fof(f20240,plain,
spl0_945,
inference(avatar_split_clause,[],[f431,f20238]) ).
fof(f431,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__cancel2_0) ).
fof(f20235,plain,
spl0_944,
inference(avatar_split_clause,[],[f429,f20233]) ).
fof(f429,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__mult__le__cancel1_0) ).
fof(f20231,plain,
spl0_943,
inference(avatar_split_clause,[],[f264,f20229]) ).
fof(f20229,plain,
( spl0_943
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X6)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f264,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X6)),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__one__over_0) ).
fof(f20227,plain,
spl0_942,
inference(avatar_split_clause,[],[f107,f20225]) ).
fof(f20225,plain,
( spl0_942
<=> ! [X12,X5,X11] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = X11
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f107,axiom,
! [X11,X5,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = X11
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__nonneg__eq__0__iff_0) ).
fof(f20223,plain,
spl0_941,
inference(avatar_split_clause,[],[f106,f20221]) ).
fof(f20221,plain,
( spl0_941
<=> ! [X11,X5,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f106,axiom,
! [X11,X5,X12] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__nonneg__eq__0__iff_1) ).
fof(f17382,plain,
( spl0_940
| ~ spl0_304
| ~ spl0_888 ),
inference(avatar_split_clause,[],[f15495,f15492,f3114,f17380]) ).
fof(f17380,plain,
( spl0_940
<=> ! [X6,X2,X5] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f15492,plain,
( spl0_888
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f15495,plain,
( ! [X2,X6,X5] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) )
| ~ spl0_304
| ~ spl0_888 ),
inference(forward_demodulation,[],[f15493,f3116]) ).
fof(f15493,plain,
( ! [X2,X6,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) )
| ~ spl0_888 ),
inference(avatar_component_clause,[],[f15492]) ).
fof(f15900,plain,
spl0_939,
inference(avatar_split_clause,[],[f1129,f15898]) ).
fof(f15898,plain,
( spl0_939
<=> ! [X38,X10,X20,X6,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Limits_OZfun(X10,X38,X5,X20)
| c_Limits_OZfun(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X10),X5,X20,X20),X6),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f1129,axiom,
! [X38,X10,X6,X5,X20] :
( ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Limits_OZfun(X10,X38,X5,X20)
| c_Limits_OZfun(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Otimes__class_Otimes(X20)),X10),X5,X20,X20),X6),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Zfun__mult__left_0) ).
fof(f15896,plain,
spl0_938,
inference(avatar_split_clause,[],[f1123,f15894]) ).
fof(f15894,plain,
( spl0_938
<=> ! [X5,X10,X9,X20,X6] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Lim_OLIM(X10,X6,c_HOL_Ozero__class_Ozero(X20),X5,X20)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X20,X20,X5),hAPP(c_HOL_Otimes__class_Otimes(X20),X9)),X10),X6,c_HOL_Ozero__class_Ozero(X20),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f1123,axiom,
! [X10,X6,X9,X5,X20] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Lim_OLIM(X10,X6,c_HOL_Ozero__class_Ozero(X20),X5,X20)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X20,X20,X5),hAPP(c_HOL_Otimes__class_Otimes(X20),X9)),X10),X6,c_HOL_Ozero__class_Ozero(X20),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__mult__right__zero_0) ).
fof(f15892,plain,
spl0_937,
inference(avatar_split_clause,[],[f1081,f15890]) ).
fof(f15890,plain,
( spl0_937
<=> ! [X5,X27,X25,X26] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),X25,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X26,X25,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X27,X25,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f1081,axiom,
! [X26,X27,X5,X25] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),X25,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X26,X25,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X27,X25,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Int__Un__distrib2_0) ).
fof(f15888,plain,
spl0_936,
inference(avatar_split_clause,[],[f1080,f15886]) ).
fof(f1080,axiom,
! [X26,X27,X5,X25] : c_Lattices_Olower__semilattice__class_Oinf(X25,c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Int__Un__distrib_0) ).
fof(f15823,plain,
spl0_935,
inference(avatar_split_clause,[],[f1079,f15821]) ).
fof(f1079,axiom,
! [X26,X27,X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),X25,tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X26,X25,tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X27,X25,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Un__Int__distrib2_0) ).
fof(f15819,plain,
spl0_934,
inference(avatar_split_clause,[],[f1078,f15817]) ).
fof(f1078,axiom,
! [X26,X27,X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Un__Int__distrib_0) ).
fof(f15815,plain,
spl0_933,
inference(avatar_split_clause,[],[f1073,f15813]) ).
fof(f15813,plain,
( spl0_933
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f1073,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__mult__distrib2_0) ).
fof(f15811,plain,
spl0_932,
inference(avatar_split_clause,[],[f1072,f15809]) ).
fof(f15809,plain,
( spl0_932
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f1072,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__mult__distrib_0) ).
fof(f15807,plain,
spl0_931,
inference(avatar_split_clause,[],[f1070,f15805]) ).
fof(f15805,plain,
( spl0_931
<=> ! [X2,X0,X1] :
( X1 = X2
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X2))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f1070,axiom,
! [X2,X0,X1] :
( X1 = X2
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X2))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_eq__diff__iff_0) ).
fof(f15803,plain,
spl0_930,
inference(avatar_split_clause,[],[f1058,f15801]) ).
fof(f15801,plain,
( spl0_930
<=> ! [X29,X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X29))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X29),X2),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X29),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f1058,axiom,
! [X2,X29,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X29))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X29),X2),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X29),X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__less__mono2_0) ).
fof(f15799,plain,
spl0_929,
inference(avatar_split_clause,[],[f928,f15797]) ).
fof(f15797,plain,
( spl0_929
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f928,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__nonneg__nonpos2_0) ).
fof(f15795,plain,
spl0_928,
inference(avatar_split_clause,[],[f924,f15793]) ).
fof(f15793,plain,
( spl0_928
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f924,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_split__mult__neg__le_0) ).
fof(f15791,plain,
spl0_927,
inference(avatar_split_clause,[],[f923,f15789]) ).
fof(f15789,plain,
( spl0_927
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f923,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__0__iff_5) ).
fof(f15787,plain,
spl0_926,
inference(avatar_split_clause,[],[f922,f15785]) ).
fof(f15785,plain,
( spl0_926
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f922,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__0__iff_4) ).
fof(f15743,plain,
spl0_925,
inference(avatar_split_clause,[],[f916,f15741]) ).
fof(f15741,plain,
( spl0_925
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f916,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__mult__iff_3) ).
fof(f15739,plain,
spl0_924,
inference(avatar_split_clause,[],[f915,f15737]) ).
fof(f15737,plain,
( spl0_924
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f915,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__mult__iff_2) ).
fof(f15735,plain,
spl0_923,
inference(avatar_split_clause,[],[f914,f15733]) ).
fof(f15733,plain,
( spl0_923
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f914,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__mult__iff_1) ).
fof(f15731,plain,
spl0_922,
inference(avatar_split_clause,[],[f913,f15729]) ).
fof(f15729,plain,
( spl0_922
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f913,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__mult__iff_0) ).
fof(f15727,plain,
spl0_921,
inference(avatar_split_clause,[],[f912,f15725]) ).
fof(f15725,plain,
( spl0_921
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f912,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__nonneg__nonneg_0) ).
fof(f15723,plain,
spl0_920,
inference(avatar_split_clause,[],[f911,f15721]) ).
fof(f15721,plain,
( spl0_920
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f911,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__mult__iff_5) ).
fof(f15719,plain,
spl0_919,
inference(avatar_split_clause,[],[f851,f15717]) ).
fof(f15717,plain,
( spl0_919
<=> ! [X38,X20,X12,X5,X32] :
( ~ class_RealVector_Oreal__normed__field(X20)
| ~ c_Limits_OZfun(X32,X38,X5,X20)
| c_Limits_OZfun(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oinverse__class_Odivide(X20)),X32),X5,X20,X20),X12),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f851,axiom,
! [X38,X5,X12,X32,X20] :
( ~ class_RealVector_Oreal__normed__field(X20)
| ~ c_Limits_OZfun(X32,X38,X5,X20)
| c_Limits_OZfun(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X20,tc_fun(X20,X20),X5),c_HOL_Oinverse__class_Odivide(X20)),X32),X5,X20,X20),X12),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_OZfun_0) ).
fof(f15715,plain,
spl0_918,
inference(avatar_split_clause,[],[f810,f15713]) ).
fof(f15713,plain,
( spl0_918
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f810,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__mult__iff_4) ).
fof(f15711,plain,
spl0_917,
inference(avatar_split_clause,[],[f808,f15709]) ).
fof(f15709,plain,
( spl0_917
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f808,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__nonpos__nonpos_0) ).
fof(f15707,plain,
spl0_916,
inference(avatar_split_clause,[],[f806,f15705]) ).
fof(f15705,plain,
( spl0_916
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f806,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_split__mult__pos__le_0) ).
fof(f15655,plain,
spl0_915,
inference(avatar_split_clause,[],[f797,f15653]) ).
fof(f15653,plain,
( spl0_915
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f797,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__pos__neg2_0) ).
fof(f15651,plain,
spl0_914,
inference(avatar_split_clause,[],[f796,f15649]) ).
fof(f15649,plain,
( spl0_914
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f796,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__pos__neg_0) ).
fof(f15647,plain,
spl0_913,
inference(avatar_split_clause,[],[f794,f15645]) ).
fof(f15645,plain,
( spl0_913
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f794,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__0__iff_3) ).
fof(f15643,plain,
spl0_912,
inference(avatar_split_clause,[],[f793,f15641]) ).
fof(f15641,plain,
( spl0_912
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f793,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__0__iff_2) ).
fof(f15639,plain,
spl0_911,
inference(avatar_split_clause,[],[f792,f15637]) ).
fof(f15637,plain,
( spl0_911
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f792,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__0__iff_1) ).
fof(f15635,plain,
spl0_910,
inference(avatar_split_clause,[],[f791,f15633]) ).
fof(f15633,plain,
( spl0_910
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f791,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__0__iff_0) ).
fof(f15631,plain,
spl0_909,
inference(avatar_split_clause,[],[f786,f15629]) ).
fof(f15629,plain,
( spl0_909
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f786,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__mult__pos2_0) ).
fof(f15627,plain,
spl0_908,
inference(avatar_split_clause,[],[f785,f15625]) ).
fof(f15625,plain,
( spl0_908
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f785,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__mult__pos_0) ).
fof(f15623,plain,
spl0_907,
inference(avatar_split_clause,[],[f784,f15621]) ).
fof(f15621,plain,
( spl0_907
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f784,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__pos__pos_0) ).
fof(f15619,plain,
spl0_906,
inference(avatar_split_clause,[],[f783,f15617]) ).
fof(f15617,plain,
( spl0_906
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f783,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__neg__neg_0) ).
fof(f15575,plain,
spl0_905,
inference(avatar_split_clause,[],[f727,f15573]) ).
fof(f15573,plain,
( spl0_905
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f727,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__nonpos__nonpos_0) ).
fof(f15571,plain,
spl0_904,
inference(avatar_split_clause,[],[f699,f15569]) ).
fof(f15569,plain,
( spl0_904
<=> ! [X12,X5,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Ozero__class_Ozero(X5) = X11
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f699,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Ozero__class_Ozero(X5) = X11
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sum__squares__gt__zero__iff_1) ).
fof(f15567,plain,
spl0_903,
inference(avatar_split_clause,[],[f698,f15565]) ).
fof(f15565,plain,
( spl0_903
<=> ! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f698,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sum__squares__gt__zero__iff_2) ).
fof(f15563,plain,
spl0_902,
inference(avatar_split_clause,[],[f697,f15561]) ).
fof(f15561,plain,
( spl0_902
<=> ! [X12,X5,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Ozero__class_Ozero(X5) = X11
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f697,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Ozero__class_Ozero(X5) = X11
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sum__squares__le__zero__iff_0) ).
fof(f15559,plain,
spl0_901,
inference(avatar_split_clause,[],[f696,f15557]) ).
fof(f15557,plain,
( spl0_901
<=> ! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f696,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sum__squares__le__zero__iff_1) ).
fof(f15555,plain,
spl0_900,
inference(avatar_split_clause,[],[f681,f15553]) ).
fof(f15553,plain,
( spl0_900
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5))),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f681,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5))),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sum__squares__le__zero__iff_2) ).
fof(f15551,plain,
spl0_899,
inference(avatar_split_clause,[],[f671,f15549]) ).
fof(f15549,plain,
( spl0_899
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f671,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5))))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sum__squares__gt__zero__iff_0) ).
fof(f15547,plain,
spl0_898,
inference(avatar_split_clause,[],[f633,f15545]) ).
fof(f15545,plain,
( spl0_898
<=> ! [X5,X10,X20,X6] :
( ~ class_RealVector_Oreal__normed__div__algebra(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OisCont(X10,X6,X5,X20)
| hAPP(X10,X6) = c_HOL_Ozero__class_Ozero(X20)
| c_Lim_OisCont(hAPP(hAPP(c_COMBB(X20,X20,X5),c_HOL_Oinverse__class_Oinverse(X20)),X10),X6,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f633,axiom,
! [X10,X6,X5,X20] :
( ~ class_RealVector_Oreal__normed__div__algebra(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OisCont(X10,X6,X5,X20)
| hAPP(X10,X6) = c_HOL_Ozero__class_Ozero(X20)
| c_Lim_OisCont(hAPP(hAPP(c_COMBB(X20,X20,X5),c_HOL_Oinverse__class_Oinverse(X20)),X10),X6,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_isCont__inverse_0) ).
fof(f15543,plain,
spl0_897,
inference(avatar_split_clause,[],[f605,f15541]) ).
fof(f15541,plain,
( spl0_897
<=> ! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f605,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__pos__neg_0) ).
fof(f15539,plain,
spl0_896,
inference(avatar_split_clause,[],[f604,f15537]) ).
fof(f15537,plain,
( spl0_896
<=> ! [X12,X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f604,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__neg__pos_0) ).
fof(f15523,plain,
spl0_895,
inference(avatar_split_clause,[],[f542,f15521]) ).
fof(f15521,plain,
( spl0_895
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f542,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_one__less__inverse__iff_2) ).
fof(f15519,plain,
spl0_894,
inference(avatar_split_clause,[],[f535,f15517]) ).
fof(f15517,plain,
( spl0_894
<=> ! [X4,X0,X29,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),X4))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X29))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X29))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f535,axiom,
! [X3,X0,X29,X4] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),X4))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X29))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X29))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__less__mono_0) ).
fof(f15515,plain,
spl0_893,
inference(avatar_split_clause,[],[f526,f15513]) ).
fof(f15513,plain,
( spl0_893
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f526,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__pos__pos_0) ).
fof(f15511,plain,
spl0_892,
inference(avatar_split_clause,[],[f496,f15509]) ).
fof(f15509,plain,
( spl0_892
<=> ! [X2,X5,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f496,axiom,
! [X2,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X1),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__1__mult_0) ).
fof(f15507,plain,
spl0_891,
inference(avatar_split_clause,[],[f457,f15505]) ).
fof(f15505,plain,
( spl0_891
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11),X5),c_HOL_Oone__class_Oone(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f457,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11),X5),c_HOL_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__less__1__iff_0) ).
fof(f15503,plain,
spl0_890,
inference(avatar_split_clause,[],[f450,f15501]) ).
fof(f15501,plain,
( spl0_890
<=> ! [X6,X9,X7] :
( ~ hBOOL(hAPP(c_lessequals(X9,tc_nat),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,tc_nat),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X6),X9),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f450,axiom,
! [X6,X9,X7] :
( ~ hBOOL(hAPP(c_lessequals(X9,tc_nat),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,tc_nat),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X6),X9),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__less__mono_0) ).
fof(f15499,plain,
spl0_889,
inference(avatar_split_clause,[],[f447,f15497]) ).
fof(f15497,plain,
( spl0_889
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f447,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__neg__neg_0) ).
fof(f15494,plain,
spl0_888,
inference(avatar_split_clause,[],[f443,f15492]) ).
fof(f443,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_one__less__power_0) ).
fof(f15490,plain,
spl0_887,
inference(avatar_split_clause,[],[f427,f15488]) ).
fof(f15488,plain,
( spl0_887
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),X11))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11),X5),c_HOL_Oone__class_Oone(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f427,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),X11))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11),X5),c_HOL_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__le__1__iff_0) ).
fof(f15486,plain,
spl0_886,
inference(avatar_split_clause,[],[f422,f15484]) ).
fof(f15484,plain,
( spl0_886
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X9))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f422,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X9))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__strict__increasing2_0) ).
fof(f15482,plain,
spl0_885,
inference(avatar_split_clause,[],[f345,f15480]) ).
fof(f15480,plain,
( spl0_885
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f345,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__strict__increasing_0) ).
fof(f15478,plain,
spl0_884,
inference(avatar_split_clause,[],[f335,f15476]) ).
fof(f15476,plain,
( spl0_884
<=> ! [X4,X0,X29,X3] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X29))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X29))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f335,axiom,
! [X3,X0,X29,X4] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X29))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X29))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__le__mono_0) ).
fof(f15474,plain,
spl0_883,
inference(avatar_split_clause,[],[f330,f15472]) ).
fof(f15472,plain,
( spl0_883
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f330,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__nonneg__nonneg_0) ).
fof(f15470,plain,
spl0_882,
inference(avatar_split_clause,[],[f322,f15468]) ).
fof(f15468,plain,
( spl0_882
<=> ! [X16,X11,X12,X5,X28] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X16) = X28
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X12),X16)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X12),X28) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f322,axiom,
! [X28,X11,X16,X5,X12] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X16) = X28
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X12),X16)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X12),X28) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__cancel__21_0) ).
fof(f15466,plain,
spl0_881,
inference(avatar_split_clause,[],[f242,f15464]) ).
fof(f15464,plain,
( spl0_881
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X4))
| ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0),tc_nat),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f242,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X4))
| ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0),tc_nat),X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__diff__conv2_0) ).
fof(f15462,plain,
spl0_880,
inference(avatar_split_clause,[],[f241,f15460]) ).
fof(f15460,plain,
( spl0_880
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X9))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f241,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X9))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__increasing_0) ).
fof(f15458,plain,
spl0_879,
inference(avatar_split_clause,[],[f240,f15456]) ).
fof(f15456,plain,
( spl0_879
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f240,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X9))
| hBOOL(hAPP(c_lessequals(X7,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__increasing2_0) ).
fof(f15454,plain,
spl0_878,
inference(avatar_split_clause,[],[f213,f15452]) ).
fof(f15452,plain,
( spl0_878
<=> ! [X10,X11,X20,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ class_RealVector_Ometric__space(X20)
| c_Lim_OisCont(X10,X11,X5,X20)
| ~ c_Lim_OLIM(hAPP(hAPP(c_COMBB(X5,X20,X5),X10),hAPP(c_HOL_Oplus__class_Oplus(X5),X11)),c_HOL_Ozero__class_Ozero(X5),hAPP(X10,X11),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f213,axiom,
! [X10,X11,X5,X20] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ class_RealVector_Ometric__space(X20)
| c_Lim_OisCont(X10,X11,X5,X20)
| ~ c_Lim_OLIM(hAPP(hAPP(c_COMBB(X5,X20,X5),X10),hAPP(c_HOL_Oplus__class_Oplus(X5),X11)),c_HOL_Ozero__class_Ozero(X5),hAPP(X10,X11),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_isCont__iff_1) ).
fof(f15450,plain,
spl0_877,
inference(avatar_split_clause,[],[f212,f15448]) ).
fof(f15448,plain,
( spl0_877
<=> ! [X10,X11,X20,X5] :
( ~ class_RealVector_Ometric__space(X20)
| ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Lim_OisCont(X10,X11,X5,X20)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X5,X20,X5),X10),hAPP(c_HOL_Oplus__class_Oplus(X5),X11)),c_HOL_Ozero__class_Ozero(X5),hAPP(X10,X11),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f212,axiom,
! [X10,X11,X5,X20] :
( ~ class_RealVector_Ometric__space(X20)
| ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Lim_OisCont(X10,X11,X5,X20)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X5,X20,X5),X10),hAPP(c_HOL_Oplus__class_Oplus(X5),X11)),c_HOL_Ozero__class_Ozero(X5),hAPP(X10,X11),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_isCont__iff_0) ).
fof(f15446,plain,
spl0_876,
inference(avatar_split_clause,[],[f192,f15444]) ).
fof(f15444,plain,
( spl0_876
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f192,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__pos__nonneg_0) ).
fof(f15442,plain,
( spl0_875
| ~ spl0_186
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f4174,f4039,f2400,f15440]) ).
fof(f15440,plain,
( spl0_875
<=> ! [X0] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X0),X0) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f4174,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X0),X0) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_186
| ~ spl0_384 ),
inference(superposition,[],[f4040,f2401]) ).
fof(f15438,plain,
spl0_874,
inference(avatar_split_clause,[],[f191,f15436]) ).
fof(f15436,plain,
( spl0_874
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f191,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__nonneg__pos_0) ).
fof(f15434,plain,
spl0_873,
inference(avatar_split_clause,[],[f182,f15432]) ).
fof(f15432,plain,
( spl0_873
<=> ! [X12,X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f182,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__nonpos__neg_0) ).
fof(f15430,plain,
spl0_872,
inference(avatar_split_clause,[],[f181,f15428]) ).
fof(f15428,plain,
( spl0_872
<=> ! [X12,X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f181,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__nonneg__pos_0) ).
fof(f15426,plain,
spl0_871,
inference(avatar_split_clause,[],[f166,f15424]) ).
fof(f15424,plain,
( spl0_871
<=> ! [X12,X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f166,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__pos__pos_0) ).
fof(f15422,plain,
spl0_870,
inference(avatar_split_clause,[],[f165,f15420]) ).
fof(f15420,plain,
( spl0_870
<=> ! [X12,X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f165,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__neg__neg_0) ).
fof(f15418,plain,
spl0_869,
inference(avatar_split_clause,[],[f155,f15416]) ).
fof(f15416,plain,
( spl0_869
<=> ! [X4,X0,X29,X3] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X29))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X29))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f155,axiom,
! [X3,X0,X29,X4] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X29))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X29))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__mono_0) ).
fof(f15414,plain,
spl0_868,
inference(avatar_split_clause,[],[f150,f15412]) ).
fof(f15412,plain,
( spl0_868
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f150,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_one__le__inverse__iff_2) ).
fof(f15410,plain,
spl0_867,
inference(avatar_split_clause,[],[f138,f15408]) ).
fof(f15408,plain,
( spl0_867
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f138,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__mult__distrib_0) ).
fof(f15406,plain,
spl0_866,
inference(avatar_split_clause,[],[f137,f15404]) ).
fof(f15404,plain,
( spl0_866
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f137,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__mult__distrib2_0) ).
fof(f15402,plain,
spl0_865,
inference(avatar_split_clause,[],[f88,f15400]) ).
fof(f15400,plain,
( spl0_865
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f88,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__neg__nonpos_0) ).
fof(f15398,plain,
( spl0_864
| ~ spl0_167
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f4141,f3597,f2314,f15396]) ).
fof(f15396,plain,
( spl0_864
<=> ! [X6] : hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6,hAPP(c_Suc,X6),tc_nat),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f4141,plain,
( ! [X6] : hBOOL(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6,hAPP(c_Suc,X6),tc_nat),X6))
| ~ spl0_167
| ~ spl0_374 ),
inference(superposition,[],[f2315,f3598]) ).
fof(f15394,plain,
spl0_863,
inference(avatar_split_clause,[],[f87,f15392]) ).
fof(f15392,plain,
( spl0_863
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f87,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__nonpos__neg_0) ).
fof(f15390,plain,
spl0_862,
inference(avatar_split_clause,[],[f13,f15388]) ).
fof(f15388,plain,
( spl0_862
<=> ! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f13,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__nonneg__neg_0) ).
fof(f15386,plain,
spl0_861,
inference(avatar_split_clause,[],[f12,f15384]) ).
fof(f15384,plain,
( spl0_861
<=> ! [X12,X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f12,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X12))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__nonpos__pos_0) ).
fof(f15269,plain,
( spl0_860
| ~ spl0_304
| ~ spl0_855 ),
inference(avatar_split_clause,[],[f14807,f14804,f3114,f15267]) ).
fof(f15267,plain,
( spl0_860
<=> ! [X2,X5] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| ~ class_Ring__and__Field_Oordered__idom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f14804,plain,
( spl0_855
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f14807,plain,
( ! [X2,X5] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| ~ class_Ring__and__Field_Oordered__idom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2))) )
| ~ spl0_304
| ~ spl0_855 ),
inference(forward_demodulation,[],[f14805,f3116]) ).
fof(f14805,plain,
( ! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2))) )
| ~ spl0_855 ),
inference(avatar_component_clause,[],[f14804]) ).
fof(f14913,plain,
( ~ spl0_22
| spl0_859
| ~ spl0_166
| ~ spl0_304
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f4132,f3593,f3114,f2310,f14911,f1606]) ).
fof(f2310,plain,
( spl0_166
<=> ! [X2] : hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f4132,plain,
( ! [X1] :
( c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_nat),X1,tc_nat) = X1
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_166
| ~ spl0_304
| ~ spl0_373 ),
inference(forward_demodulation,[],[f4101,f3116]) ).
fof(f4101,plain,
( ! [X1] :
( ~ class_Lattices_Oupper__semilattice(tc_nat)
| c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1 )
| ~ spl0_166
| ~ spl0_373 ),
inference(resolution,[],[f3594,f2311]) ).
fof(f2311,plain,
( ! [X2] : hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f2310]) ).
fof(f14819,plain,
spl0_858,
inference(avatar_split_clause,[],[f1477,f14817]) ).
fof(f14817,plain,
( spl0_858
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X1)),X2)),hAPP(c_Suc,X0)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f1477,plain,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X1)),X2)),hAPP(c_Suc,X0)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0)),
inference(forward_demodulation,[],[f1063,f1069]) ).
fof(f1063,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X1)),X2)),hAPP(c_Suc,X0)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)),X0),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Suc__diff__diff_0) ).
fof(f14815,plain,
spl0_857,
inference(avatar_split_clause,[],[f1246,f14813]) ).
fof(f14813,plain,
( spl0_857
<=> ! [X5,X9,X7,X14,X6] :
( X7 = X14
| X6 = X14
| c_Set_Oinsert(X6,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X9,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f1246,axiom,
! [X6,X9,X7,X14,X5] :
( X7 = X14
| X6 = X14
| c_Set_Oinsert(X6,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X9,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_doubleton__eq__iff_2) ).
fof(f14811,plain,
spl0_856,
inference(avatar_split_clause,[],[f1244,f14809]) ).
fof(f14809,plain,
( spl0_856
<=> ! [X5,X9,X14,X6,X7] :
( X6 = X9
| X6 = X14
| c_Set_Oinsert(X6,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X9,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f1244,axiom,
! [X6,X9,X7,X14,X5] :
( X6 = X9
| X6 = X14
| c_Set_Oinsert(X6,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) != c_Set_Oinsert(X9,c_Set_Oinsert(X14,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_doubleton__eq__iff_0) ).
fof(f14806,plain,
spl0_855,
inference(avatar_split_clause,[],[f1136,f14804]) ).
fof(f1136,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__power__eq_2) ).
fof(f14802,plain,
spl0_854,
inference(avatar_split_clause,[],[f1012,f14800]) ).
fof(f14800,plain,
( spl0_854
<=> ! [X2,X5,X1] :
( ~ class_Ring__and__Field_Oring__1(X5)
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),c_Nat_Osemiring__1__class_Oof__nat(X1,X5)),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f1012,axiom,
! [X2,X1,X5] :
( ~ class_Ring__and__Field_Oring__1(X5)
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),c_Nat_Osemiring__1__class_Oof__nat(X1,X5)),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_of__nat__diff_0) ).
fof(f14798,plain,
spl0_853,
inference(avatar_split_clause,[],[f947,f14796]) ).
fof(f14796,plain,
( spl0_853
<=> ! [X10,X9,X11,X5,X15] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| c_Deriv_Oderiv(hAPP(hAPP(c_COMBB(X5,X5,X5),hAPP(c_HOL_Otimes__class_Otimes(X5),X9)),X10),X11,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X15),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f947,axiom,
! [X10,X11,X9,X15,X5] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| c_Deriv_Oderiv(hAPP(hAPP(c_COMBB(X5,X5,X5),hAPP(c_HOL_Otimes__class_Otimes(X5),X9)),X10),X11,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X15),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__cmult_0) ).
fof(f14774,plain,
spl0_852,
inference(avatar_split_clause,[],[f862,f14772]) ).
fof(f14772,plain,
( spl0_852
<=> ! [X18,X5,X11] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_Series_Osummable(X18,X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),c_Series_Osuminf(X18,X5)) = c_Series_Osuminf(hAPP(hAPP(c_COMBB(X5,X5,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X5),X11)),X18),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f862,axiom,
! [X11,X18,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_Series_Osummable(X18,X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),c_Series_Osuminf(X18,X5)) = c_Series_Osuminf(hAPP(hAPP(c_COMBB(X5,X5,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X5),X11)),X18),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right_Osuminf_0) ).
fof(f14770,plain,
spl0_851,
inference(avatar_split_clause,[],[f854,f14768]) ).
fof(f14768,plain,
( spl0_851
<=> ! [X44,X11,X12,X5,X45] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X44,X5),X45))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X12) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X44),X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f854,axiom,
! [X11,X44,X45,X5,X12] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X44,X5),X45))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X12) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X44),X45) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__eqI_0) ).
fof(f14766,plain,
spl0_850,
inference(avatar_split_clause,[],[f853,f14764]) ).
fof(f14764,plain,
( spl0_850
<=> ! [X44,X11,X12,X5,X45] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X45,X5),X44))
| hBOOL(hAPP(c_lessequals(X12,X5),X11))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X12) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X44),X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f853,axiom,
! [X11,X44,X45,X5,X12] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X45,X5),X44))
| hBOOL(hAPP(c_lessequals(X12,X5),X11))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X12) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X44),X45) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__eqI_1) ).
fof(f14762,plain,
spl0_849,
inference(avatar_split_clause,[],[f830,f14760]) ).
fof(f14760,plain,
( spl0_849
<=> ! [X11,X12,X5,X16] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12)),X16) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16)),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f830,axiom,
! [X11,X16,X5,X12] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X12)),X16) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X16)),X12) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__frac__num_0) ).
fof(f14758,plain,
spl0_848,
inference(avatar_split_clause,[],[f631,f14756]) ).
fof(f14756,plain,
( spl0_848
<=> ! [X5,X10,X20,X6,X21] :
( ~ class_RealVector_Ometric__space(X20)
| ~ class_RealVector_Oreal__normed__vector(X5)
| c_Lim_OLIM(X10,X6,X21,X5,X20)
| ~ c_Lim_OLIM(hAPP(hAPP(c_COMBB(X5,X20,X5),X10),hAPP(c_HOL_Oplus__class_Oplus(X5),X6)),c_HOL_Ozero__class_Ozero(X5),X21,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f631,axiom,
! [X21,X10,X6,X5,X20] :
( ~ class_RealVector_Ometric__space(X20)
| ~ class_RealVector_Oreal__normed__vector(X5)
| c_Lim_OLIM(X10,X6,X21,X5,X20)
| ~ c_Lim_OLIM(hAPP(hAPP(c_COMBB(X5,X20,X5),X10),hAPP(c_HOL_Oplus__class_Oplus(X5),X6)),c_HOL_Ozero__class_Ozero(X5),X21,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__offset__zero__cancel_0) ).
fof(f14754,plain,
spl0_847,
inference(avatar_split_clause,[],[f630,f14752]) ).
fof(f14752,plain,
( spl0_847
<=> ! [X5,X10,X20,X6,X21] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ class_RealVector_Ometric__space(X20)
| ~ c_Lim_OLIM(X10,X6,X21,X5,X20)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X5,X20,X5),X10),hAPP(c_HOL_Oplus__class_Oplus(X5),X6)),c_HOL_Ozero__class_Ozero(X5),X21,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f630,axiom,
! [X21,X10,X6,X5,X20] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ class_RealVector_Ometric__space(X20)
| ~ c_Lim_OLIM(X10,X6,X21,X5,X20)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(X5,X20,X5),X10),hAPP(c_HOL_Oplus__class_Oplus(X5),X6)),c_HOL_Ozero__class_Ozero(X5),X21,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__offset__zero_0) ).
fof(f14750,plain,
spl0_846,
inference(avatar_split_clause,[],[f377,f14748]) ).
fof(f14748,plain,
( spl0_846
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f377,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__imp__inverse__le__neg_0) ).
fof(f14746,plain,
spl0_845,
inference(avatar_split_clause,[],[f376,f14744]) ).
fof(f14744,plain,
( spl0_845
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f376,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__le__imp__le__neg_0) ).
fof(f14742,plain,
spl0_844,
inference(avatar_split_clause,[],[f375,f14740]) ).
fof(f14740,plain,
( spl0_844
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f375,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__imp__inverse__le_0) ).
fof(f14738,plain,
spl0_843,
inference(avatar_split_clause,[],[f374,f14736]) ).
fof(f14736,plain,
( spl0_843
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f374,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__le__imp__le_0) ).
fof(f14734,plain,
( ~ spl0_22
| spl0_842
| ~ spl0_166
| ~ spl0_304
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4079,f3585,f3114,f2310,f14732,f1606]) ).
fof(f14732,plain,
( spl0_842
<=> ! [X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f4079,plain,
( ! [X1] :
( c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = X1
| ~ class_Lattices_Oupper__semilattice(tc_nat) )
| ~ spl0_166
| ~ spl0_304
| ~ spl0_371 ),
inference(forward_demodulation,[],[f4048,f3116]) ).
fof(f4048,plain,
( ! [X1] :
( ~ class_Lattices_Oupper__semilattice(tc_nat)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1 )
| ~ spl0_166
| ~ spl0_371 ),
inference(resolution,[],[f3586,f2311]) ).
fof(f14730,plain,
spl0_841,
inference(avatar_split_clause,[],[f329,f14728]) ).
fof(f14728,plain,
( spl0_841
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f329,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__imp__inverse__less__neg_0) ).
fof(f14726,plain,
spl0_840,
inference(avatar_split_clause,[],[f328,f14724]) ).
fof(f14724,plain,
( spl0_840
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f328,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__less__imp__less__neg_0) ).
fof(f14722,plain,
spl0_839,
inference(avatar_split_clause,[],[f327,f14720]) ).
fof(f14720,plain,
( spl0_839
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f327,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__imp__inverse__less_0) ).
fof(f14718,plain,
spl0_838,
inference(avatar_split_clause,[],[f326,f14716]) ).
fof(f14716,plain,
( spl0_838
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f326,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__less__imp__less_0) ).
fof(f14656,plain,
( ~ spl0_837
| ~ spl0_195
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f3403,f3337,f2437,f14653]) ).
fof(f14653,plain,
( spl0_837
<=> c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f3403,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) != c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_195
| ~ spl0_328 ),
inference(superposition,[],[f2438,f3339]) ).
fof(f14610,plain,
( spl0_836
| ~ spl0_257
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f3400,f3337,f2705,f14607]) ).
fof(f14607,plain,
( spl0_836
<=> c_Orderings_Obot__class_Obot(tc_nat) = c_GCD_Ogcd__class_OLCM(c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f3400,plain,
( c_Orderings_Obot__class_Obot(tc_nat) = c_GCD_Ogcd__class_OLCM(c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),tc_nat)
| ~ spl0_257
| ~ spl0_328 ),
inference(superposition,[],[f2706,f3339]) ).
fof(f14548,plain,
( spl0_835
| ~ spl0_304
| ~ spl0_813 ),
inference(avatar_split_clause,[],[f14411,f14406,f3114,f14546]) ).
fof(f14546,plain,
( spl0_835
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f14406,plain,
( spl0_813
<=> ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f14411,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2)) )
| ~ spl0_304
| ~ spl0_813 ),
inference(forward_demodulation,[],[f14410,f3116]) ).
fof(f14410,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2))) )
| ~ spl0_304
| ~ spl0_813 ),
inference(forward_demodulation,[],[f14409,f3116]) ).
fof(f14409,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2))) )
| ~ spl0_304
| ~ spl0_813 ),
inference(forward_demodulation,[],[f14407,f3116]) ).
fof(f14407,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2))) )
| ~ spl0_813 ),
inference(avatar_component_clause,[],[f14406]) ).
fof(f14542,plain,
( spl0_834
| ~ spl0_304
| ~ spl0_809 ),
inference(avatar_split_clause,[],[f14392,f14387,f3114,f14540]) ).
fof(f14540,plain,
( spl0_834
<=> ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f14387,plain,
( spl0_809
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f14392,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X1)) )
| ~ spl0_304
| ~ spl0_809 ),
inference(forward_demodulation,[],[f14391,f3116]) ).
fof(f14391,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_304
| ~ spl0_809 ),
inference(forward_demodulation,[],[f14390,f3116]) ).
fof(f14390,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_304
| ~ spl0_809 ),
inference(forward_demodulation,[],[f14388,f3116]) ).
fof(f14388,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_809 ),
inference(avatar_component_clause,[],[f14387]) ).
fof(f14492,plain,
spl0_833,
inference(avatar_split_clause,[],[f1174,f14490]) ).
fof(f14490,plain,
( spl0_833
<=> ! [X10,X11,X5,X2] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Odifferentiable(X10,X11,X5)
| c_Deriv_Odifferentiable(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(tc_nat,X5),X5),c_Power_Opower__class_Opower(X5)),X10),X5,tc_nat,X5),X2),X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f1174,axiom,
! [X2,X10,X11,X5] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Odifferentiable(X10,X11,X5)
| c_Deriv_Odifferentiable(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(tc_nat,X5),X5),c_Power_Opower__class_Opower(X5)),X10),X5,tc_nat,X5),X2),X11,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_differentiable__power_0) ).
fof(f14488,plain,
( spl0_832
| ~ spl0_258
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f3399,f3337,f2709,f14485]) ).
fof(f14485,plain,
( spl0_832
<=> c_Orderings_Obot__class_Obot(tc_nat) = c_GCD_Ogcd__class_OGCD(c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f3399,plain,
( c_Orderings_Obot__class_Obot(tc_nat) = c_GCD_Ogcd__class_OGCD(c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),tc_nat)
| ~ spl0_258
| ~ spl0_328 ),
inference(superposition,[],[f2710,f3339]) ).
fof(f14483,plain,
spl0_831,
inference(avatar_split_clause,[],[f1166,f14481]) ).
fof(f14481,plain,
( spl0_831
<=> ! [X18,X5,X19] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X18,X5)
| ~ c_Series_Osummable(X19,X5)
| c_Series_Osummable(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X18),X19,tc_nat,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f1166,axiom,
! [X18,X19,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X18,X5)
| ~ c_Series_Osummable(X19,X5)
| c_Series_Osummable(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X18),X19,tc_nat,X5,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_summable__diff_0) ).
fof(f14479,plain,
spl0_830,
inference(avatar_split_clause,[],[f1165,f14477]) ).
fof(f14477,plain,
( spl0_830
<=> ! [X18,X5,X19] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OZseq(X18,X5)
| ~ c_SEQ_OZseq(X19,X5)
| c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X18),X19,tc_nat,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f1165,axiom,
! [X18,X19,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OZseq(X18,X5)
| ~ c_SEQ_OZseq(X19,X5)
| c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X18),X19,tc_nat,X5,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Zseq__diff_0) ).
fof(f14475,plain,
spl0_829,
inference(avatar_split_clause,[],[f1153,f14473]) ).
fof(f14473,plain,
( spl0_829
<=> ! [X18,X5,X19] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OZseq(X18,X5)
| ~ c_SEQ_OZseq(X19,X5)
| c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X18),X19,tc_nat,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f1153,axiom,
! [X18,X19,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OZseq(X18,X5)
| ~ c_SEQ_OZseq(X19,X5)
| c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X18),X19,tc_nat,X5,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Zseq__mult_0) ).
fof(f14471,plain,
spl0_828,
inference(avatar_split_clause,[],[f1055,f14469]) ).
fof(f14469,plain,
( spl0_828
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5)),X9) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f1055,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5)),X9) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).
fof(f14467,plain,
spl0_827,
inference(avatar_split_clause,[],[f1054,f14465]) ).
fof(f14465,plain,
( spl0_827
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_Lattices_Oupper__semilattice__class_Osup(X7,X9,X5)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f1054,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_Lattices_Oupper__semilattice__class_Osup(X7,X9,X5)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).
fof(f14463,plain,
spl0_826,
inference(avatar_split_clause,[],[f1053,f14461]) ).
fof(f14461,plain,
( spl0_826
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_Lattices_Oupper__semilattice__class_Osup(X7,X9,X5)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f1053,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_Lattices_Oupper__semilattice__class_Osup(X7,X9,X5)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__sup__distrib__left_0) ).
fof(f14459,plain,
spl0_825,
inference(avatar_split_clause,[],[f1052,f14457]) ).
fof(f14457,plain,
( spl0_825
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5)),X9) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f1052,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5)),X9) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__sup__distrib__right_0) ).
fof(f14455,plain,
spl0_824,
inference(avatar_split_clause,[],[f1019,f14453]) ).
fof(f14453,plain,
( spl0_824
<=> ! [X18,X5,X19] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OZseq(X18,X5)
| ~ c_SEQ_OZseq(X19,X5)
| c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oplus__class_Oplus(X5)),X18),X19,tc_nat,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f1019,axiom,
! [X18,X19,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OZseq(X18,X5)
| ~ c_SEQ_OZseq(X19,X5)
| c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oplus__class_Oplus(X5)),X18),X19,tc_nat,X5,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Zseq__add_0) ).
fof(f14451,plain,
spl0_823,
inference(avatar_split_clause,[],[f1017,f14449]) ).
fof(f14449,plain,
( spl0_823
<=> ! [X18,X5,X19] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X18,X5)
| ~ c_Series_Osummable(X19,X5)
| c_Series_Osummable(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oplus__class_Oplus(X5)),X18),X19,tc_nat,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f1017,axiom,
! [X18,X19,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X18,X5)
| ~ c_Series_Osummable(X19,X5)
| c_Series_Osummable(c_COMBS(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oplus__class_Oplus(X5)),X18),X19,tc_nat,X5,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_summable__add_0) ).
fof(f14447,plain,
spl0_822,
inference(avatar_split_clause,[],[f871,f14445]) ).
fof(f14445,plain,
( spl0_822
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f871,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__gt1__lemma_0) ).
fof(f14443,plain,
( spl0_821
| ~ spl0_80
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f2920,f2745,f1896,f14441]) ).
fof(f2745,plain,
( spl0_267
<=> ! [X12,X5,X11] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = c_Lattices_Oupper__semilattice__class_Osup(X12,X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f2920,plain,
( ! [X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_Int_Oint) = c_Lattices_Oupper__semilattice__class_Osup(X9,X8,tc_Int_Oint)
| ~ spl0_80
| ~ spl0_267 ),
inference(resolution,[],[f2746,f1898]) ).
fof(f2746,plain,
( ! [X11,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = c_Lattices_Oupper__semilattice__class_Osup(X12,X11,X5) )
| ~ spl0_267 ),
inference(avatar_component_clause,[],[f2745]) ).
fof(f14439,plain,
spl0_820,
inference(avatar_split_clause,[],[f707,f14437]) ).
fof(f14437,plain,
( spl0_820
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f707,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__mult__distrib_0) ).
fof(f14435,plain,
spl0_819,
inference(avatar_split_clause,[],[f514,f14433]) ).
fof(f14433,plain,
( spl0_819
<=> ! [X6,X5,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Oone__class_Oone(X5))),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f514,axiom,
! [X1,X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Oone__class_Oone(X5))),X1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(f14431,plain,
spl0_818,
inference(avatar_split_clause,[],[f513,f14429]) ).
fof(f14429,plain,
( spl0_818
<=> ! [X6,X5,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X1)),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Oone__class_Oone(X5))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f513,axiom,
! [X1,X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X1)),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Oone__class_Oone(X5))),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(f14427,plain,
spl0_817,
inference(avatar_split_clause,[],[f468,f14425]) ).
fof(f14425,plain,
( spl0_817
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f468,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Suc__mult__le__cancel1_0) ).
fof(f14423,plain,
spl0_816,
inference(avatar_split_clause,[],[f452,f14421]) ).
fof(f14421,plain,
( spl0_816
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f452,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Suc__mult__less__cancel1_1) ).
fof(f14419,plain,
spl0_815,
inference(avatar_split_clause,[],[f312,f14417]) ).
fof(f14417,plain,
( spl0_815
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5)),X9) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f312,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5)),X9) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__inf__distrib__right_0) ).
fof(f14415,plain,
spl0_814,
inference(avatar_split_clause,[],[f311,f14413]) ).
fof(f14413,plain,
( spl0_814
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_Lattices_Olower__semilattice__class_Oinf(X7,X9,X5)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f311,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_Lattices_Olower__semilattice__class_Oinf(X7,X9,X5)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__inf__distrib__left_0) ).
fof(f14408,plain,
spl0_813,
inference(avatar_split_clause,[],[f300,f14406]) ).
fof(f300,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__gr__0_0) ).
fof(f14404,plain,
spl0_812,
inference(avatar_split_clause,[],[f210,f14402]) ).
fof(f14402,plain,
( spl0_812
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_Lattices_Olower__semilattice__class_Oinf(X7,X9,X5)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f210,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_Lattices_Olower__semilattice__class_Oinf(X7,X9,X5)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).
fof(f14400,plain,
spl0_811,
inference(avatar_split_clause,[],[f209,f14398]) ).
fof(f14398,plain,
( spl0_811
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5)),X9) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f209,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5)),X9) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).
fof(f14396,plain,
( spl0_810
| ~ spl0_42
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f2919,f2745,f1706,f14394]) ).
fof(f2919,plain,
( ! [X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X7,X6,tc_bool)
| ~ spl0_42
| ~ spl0_267 ),
inference(resolution,[],[f2746,f1708]) ).
fof(f14389,plain,
spl0_809,
inference(avatar_split_clause,[],[f99,f14387]) ).
fof(f99,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__0__less__mult__iff_2) ).
fof(f14385,plain,
spl0_808,
inference(avatar_split_clause,[],[f26,f14383]) ).
fof(f14383,plain,
( spl0_808
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f26,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X9))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_pos__add__strict_0) ).
fof(f14215,plain,
( spl0_807
| ~ spl0_22
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f2917,f2745,f1606,f14213]) ).
fof(f2917,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_nat)
| ~ spl0_22
| ~ spl0_267 ),
inference(resolution,[],[f2746,f1608]) ).
fof(f14208,plain,
( spl0_806
| ~ spl0_304
| ~ spl0_794 ),
inference(avatar_split_clause,[],[f13955,f13951,f3114,f14206]) ).
fof(f14206,plain,
( spl0_806
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),tc_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f13951,plain,
( spl0_794
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),tc_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f13955,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),tc_nat),X1)) )
| ~ spl0_304
| ~ spl0_794 ),
inference(forward_demodulation,[],[f13954,f3116]) ).
fof(f13954,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),tc_nat),X1)) )
| ~ spl0_304
| ~ spl0_794 ),
inference(forward_demodulation,[],[f13952,f3116]) ).
fof(f13952,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),tc_nat),X1)) )
| ~ spl0_794 ),
inference(avatar_component_clause,[],[f13951]) ).
fof(f14123,plain,
( spl0_805
| ~ spl0_135
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f2916,f2737,f2171,f14121]) ).
fof(f14121,plain,
( spl0_805
<=> ! [X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),X1),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f2737,plain,
( spl0_265
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f2916,plain,
( ! [X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),X1),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X1
| ~ spl0_135
| ~ spl0_265 ),
inference(resolution,[],[f2738,f2173]) ).
fof(f2738,plain,
( ! [X6,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 )
| ~ spl0_265 ),
inference(avatar_component_clause,[],[f2737]) ).
fof(f14087,plain,
( spl0_804
| ~ spl0_304
| ~ spl0_781 ),
inference(avatar_split_clause,[],[f13901,f13898,f3114,f14085]) ).
fof(f14085,plain,
( spl0_804
<=> ! [X29,X5,X10] :
( c_Series_Osums(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X29),hAPP(X10,c_Orderings_Obot__class_Obot(tc_nat))),X5)
| ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc),X29,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f13898,plain,
( spl0_781
<=> ! [X29,X5,X10] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc),X29,X5)
| c_Series_Osums(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X29),hAPP(X10,c_HOL_Ozero__class_Ozero(tc_nat))),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f13901,plain,
( ! [X10,X29,X5] :
( c_Series_Osums(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X29),hAPP(X10,c_Orderings_Obot__class_Obot(tc_nat))),X5)
| ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc),X29,X5) )
| ~ spl0_304
| ~ spl0_781 ),
inference(forward_demodulation,[],[f13899,f3116]) ).
fof(f13899,plain,
( ! [X10,X29,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc),X29,X5)
| c_Series_Osums(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X29),hAPP(X10,c_HOL_Ozero__class_Ozero(tc_nat))),X5) )
| ~ spl0_781 ),
inference(avatar_component_clause,[],[f13898]) ).
fof(f14035,plain,
( spl0_803
| ~ spl0_93
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f2915,f2737,f1961,f14033]) ).
fof(f14033,plain,
( spl0_803
<=> ! [X0] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),X0),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f2915,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),X0),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = X0
| ~ spl0_93
| ~ spl0_265 ),
inference(resolution,[],[f2738,f1963]) ).
fof(f13987,plain,
spl0_802,
inference(avatar_split_clause,[],[f1232,f13985]) ).
fof(f13985,plain,
( spl0_802
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)),X9) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f1232,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7)),X9) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X9)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f13983,plain,
spl0_801,
inference(avatar_split_clause,[],[f1231,f13981]) ).
fof(f13981,plain,
( spl0_801
<=> ! [X51,X53,X50,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X50),X53)),X51) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X50),X51)),X53) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f1231,axiom,
! [X50,X51,X53,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X50),X53)),X51) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X50),X51)),X53) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f13979,plain,
spl0_800,
inference(avatar_split_clause,[],[f1228,f13977]) ).
fof(f13977,plain,
( spl0_800
<=> ! [X51,X50,X5,X52] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X50),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X51),X52)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X51),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X50),X52)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f1228,axiom,
! [X50,X51,X52,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X50),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X51),X52)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X51),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X50),X52)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f13975,plain,
spl0_799,
inference(avatar_split_clause,[],[f1227,f13973]) ).
fof(f13973,plain,
( spl0_799
<=> ! [X11,X12,X5,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X16)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12)),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f1227,axiom,
! [X11,X16,X5,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X16)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12)),X16) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Omul__a_0) ).
fof(f13971,plain,
spl0_798,
inference(avatar_split_clause,[],[f1218,f13969]) ).
fof(f13969,plain,
( spl0_798
<=> ! [X6,X2,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f1218,axiom,
! [X2,X6,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)),X6) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__commutes_0) ).
fof(f13967,plain,
spl0_797,
inference(avatar_split_clause,[],[f1077,f13965]) ).
fof(f13965,plain,
( spl0_797
<=> ! [X10,X20,X5,X25,X26] : c_Set_Ovimage(X10,c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X20,tc_bool)),X5,X20) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X10,X25,X5,X20),c_Set_Ovimage(X10,X26,X5,X20),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f1077,axiom,
! [X10,X26,X5,X25,X20] : c_Set_Ovimage(X10,c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X20,tc_bool)),X5,X20) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(X10,X25,X5,X20),c_Set_Ovimage(X10,X26,X5,X20),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_vimage__Un_0) ).
fof(f13963,plain,
( spl0_796
| ~ spl0_128
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2912,f2729,f2136,f13961]) ).
fof(f13961,plain,
( spl0_796
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f2136,plain,
( spl0_128
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f2729,plain,
( spl0_263
<=> ! [X5,X11] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2912,plain,
( ! [X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),X1),X1)
| ~ spl0_128
| ~ spl0_263 ),
inference(resolution,[],[f2730,f2138]) ).
fof(f2138,plain,
( class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f2136]) ).
fof(f2730,plain,
( ! [X11,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X11) )
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f2729]) ).
fof(f13959,plain,
spl0_795,
inference(avatar_split_clause,[],[f1011,f13957]) ).
fof(f13957,plain,
( spl0_795
<=> ! [X48,X11,X5,X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X39)),X48) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X39),X48)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f1011,axiom,
! [X39,X48,X11,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X39)),X48) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X39),X48)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Opwr__pwr_0) ).
fof(f13953,plain,
spl0_794,
inference(avatar_split_clause,[],[f998,f13951]) ).
fof(f998,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),tc_nat),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__less_0) ).
fof(f13949,plain,
spl0_793,
inference(avatar_split_clause,[],[f979,f13947]) ).
fof(f13947,plain,
( spl0_793
<=> ! [X5,X9,X10,X6] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_Series_Osums(X10,X6,X5)
| c_Series_Osums(hAPP(hAPP(c_COMBB(X5,X5,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X5),X9)),X10),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f979,axiom,
! [X10,X6,X9,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_Series_Osums(X10,X6,X5)
| c_Series_Osums(hAPP(hAPP(c_COMBB(X5,X5,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X5),X9)),X10),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X6),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sums__mult_0) ).
fof(f13945,plain,
spl0_792,
inference(avatar_split_clause,[],[f973,f13943]) ).
fof(f13943,plain,
( spl0_792
<=> ! [X5,X18,X11,X6] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(X5,X5,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X5),X11)),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X6),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f973,axiom,
! [X11,X18,X6,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(X5,X5,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X5),X11)),X18),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X6),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right_OLIMSEQ_0) ).
fof(f13941,plain,
spl0_791,
inference(avatar_split_clause,[],[f968,f13939]) ).
fof(f13939,plain,
( spl0_791
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f968,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nonzero__power__inverse_0) ).
fof(f13937,plain,
spl0_790,
inference(avatar_split_clause,[],[f961,f13935]) ).
fof(f13935,plain,
( spl0_790
<=> ! [X2,X5,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Ozero__class_Ozero(X5) = X11
| hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X2),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f961,axiom,
! [X2,X11,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_HOL_Ozero__class_Ozero(X5) = X11
| hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X2),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__le__zero__eq_3) ).
fof(f13933,plain,
spl0_789,
inference(avatar_split_clause,[],[f933,f13931]) ).
fof(f13931,plain,
( spl0_789
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f933,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sum__squares__eq__zero__iff_2) ).
fof(f13929,plain,
spl0_788,
inference(avatar_split_clause,[],[f907,f13927]) ).
fof(f13927,plain,
( spl0_788
<=> ! [X5,X6,X2,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f907,axiom,
! [X2,X1,X6,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X1)),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__mult_0) ).
fof(f13925,plain,
spl0_787,
inference(avatar_split_clause,[],[f832,f13923]) ).
fof(f13923,plain,
( spl0_787
<=> ! [X6,X18,X5] :
( ~ class_RealVector_Oreal__normed__div__algebra(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(X5,X5,tc_nat),c_HOL_Oinverse__class_Oinverse(X5)),X18),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f832,axiom,
! [X18,X6,X5] :
( ~ class_RealVector_Oreal__normed__div__algebra(X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(X5,X5,tc_nat),c_HOL_Oinverse__class_Oinverse(X5)),X18),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__inverse_0) ).
fof(f13921,plain,
spl0_786,
inference(avatar_split_clause,[],[f805,f13919]) ).
fof(f13919,plain,
( spl0_786
<=> ! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f805,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Ozero__class_Ozero(X5) = X12
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sum__squares__eq__zero__iff_1) ).
fof(f13917,plain,
( spl0_785
| ~ spl0_85
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2911,f2729,f1921,f13915]) ).
fof(f13915,plain,
( spl0_785
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f1921,plain,
( spl0_85
<=> class_OrderedGroup_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f2911,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),X0),X0)
| ~ spl0_85
| ~ spl0_263 ),
inference(resolution,[],[f2730,f1923]) ).
fof(f1923,plain,
( class_OrderedGroup_Oab__group__add(tc_Int_Oint)
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f1921]) ).
fof(f13913,plain,
spl0_784,
inference(avatar_split_clause,[],[f804,f13911]) ).
fof(f13911,plain,
( spl0_784
<=> ! [X12,X5,X11] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Ozero__class_Ozero(X5) = X11
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f804,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_HOL_Ozero__class_Ozero(X5) = X11
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sum__squares__eq__zero__iff_0) ).
fof(f13909,plain,
spl0_783,
inference(avatar_split_clause,[],[f763,f13907]) ).
fof(f13907,plain,
( spl0_783
<=> ! [X18,X5,X21] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OLIMSEQ(X18,X21,X5)
| c_SEQ_OZseq(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X18),tc_nat,X5,X5),X21),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f763,axiom,
! [X21,X18,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_SEQ_OLIMSEQ(X18,X21,X5)
| c_SEQ_OZseq(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X18),tc_nat,X5,X5),X21),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__Zseq__iff_0) ).
fof(f13905,plain,
spl0_782,
inference(avatar_split_clause,[],[f762,f13903]) ).
fof(f13903,plain,
( spl0_782
<=> ! [X18,X5,X21] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| c_SEQ_OLIMSEQ(X18,X21,X5)
| ~ c_SEQ_OZseq(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X18),tc_nat,X5,X5),X21),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f762,axiom,
! [X21,X18,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| c_SEQ_OLIMSEQ(X18,X21,X5)
| ~ c_SEQ_OZseq(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Ominus__class_Ominus(X5)),X18),tc_nat,X5,X5),X21),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__Zseq__iff_1) ).
fof(f13900,plain,
spl0_781,
inference(avatar_split_clause,[],[f743,f13898]) ).
fof(f743,axiom,
! [X10,X29,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc),X29,X5)
| c_Series_Osums(X10,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X29),hAPP(X10,c_HOL_Ozero__class_Ozero(tc_nat))),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sums__Suc_0) ).
fof(f13896,plain,
spl0_780,
inference(avatar_split_clause,[],[f562,f13894]) ).
fof(f13894,plain,
( spl0_780
<=> ! [X5,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| X1 = X2
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X6))
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f562,axiom,
! [X2,X1,X6,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| X1 = X2
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X6))
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X1) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__inject__exp_0) ).
fof(f13892,plain,
spl0_779,
inference(avatar_split_clause,[],[f366,f13890]) ).
fof(f13890,plain,
( spl0_779
<=> ! [X0,X29,X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X29))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X29) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f366,axiom,
! [X2,X0,X29,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X29))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X29) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__add__eq__less_0) ).
fof(f13888,plain,
spl0_778,
inference(avatar_split_clause,[],[f299,f13886]) ).
fof(f13886,plain,
( spl0_778
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f299,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X9) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(f13884,plain,
spl0_777,
inference(avatar_split_clause,[],[f298,f13882]) ).
fof(f13882,plain,
( spl0_777
<=> ! [X5,X9,X14,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X14)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f298,axiom,
! [X6,X9,X14,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X14)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f13880,plain,
spl0_776,
inference(avatar_split_clause,[],[f297,f13878]) ).
fof(f13878,plain,
( spl0_776
<=> ! [X5,X9,X7,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f297,axiom,
! [X6,X9,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X9) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9)),X7) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f13876,plain,
spl0_775,
inference(avatar_split_clause,[],[f295,f13874]) ).
fof(f13874,plain,
( spl0_775
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Oab__semigroup__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f295,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Oab__semigroup__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X9) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f13872,plain,
( spl0_774
| ~ spl0_100
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2890,f2697,f1996,f13870]) ).
fof(f2697,plain,
( spl0_255
<=> ! [X12,X5,X11] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),X5) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f2890,plain,
( ! [X8,X9] : c_Lattices_Olower__semilattice__class_Oinf(X8,c_Lattices_Oupper__semilattice__class_Osup(X8,X9,tc_Int_Oint),tc_Int_Oint) = X8
| ~ spl0_100
| ~ spl0_255 ),
inference(resolution,[],[f2698,f1998]) ).
fof(f2698,plain,
( ! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),X5) = X11 )
| ~ spl0_255 ),
inference(avatar_component_clause,[],[f2697]) ).
fof(f13868,plain,
spl0_773,
inference(avatar_split_clause,[],[f292,f13866]) ).
fof(f13866,plain,
( spl0_773
<=> ! [X5,X11,X12,X16] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X12),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f292,axiom,
! [X11,X16,X5,X12] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X12),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X16)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__cancel__21_1) ).
fof(f13864,plain,
spl0_772,
inference(avatar_split_clause,[],[f290,f13862]) ).
fof(f13862,plain,
( spl0_772
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f290,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X9) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f13860,plain,
spl0_771,
inference(avatar_split_clause,[],[f289,f13858]) ).
fof(f13858,plain,
( spl0_771
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f289,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f13856,plain,
spl0_770,
inference(avatar_split_clause,[],[f144,f13854]) ).
fof(f13854,plain,
( spl0_770
<=> ! [X10,X20,X5,X25,X26] : c_Set_Ovimage(X10,c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X20,tc_bool)),X5,X20) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X10,X25,X5,X20),c_Set_Ovimage(X10,X26,X5,X20),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f144,axiom,
! [X10,X26,X5,X25,X20] : c_Set_Ovimage(X10,c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X20,tc_bool)),X5,X20) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(X10,X25,X5,X20),c_Set_Ovimage(X10,X26,X5,X20),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_vimage__Int_0) ).
fof(f13796,plain,
( spl0_769
| ~ spl0_47
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2889,f2697,f1731,f13794]) ).
fof(f2889,plain,
( ! [X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,c_Lattices_Oupper__semilattice__class_Osup(X6,X7,tc_bool),tc_bool) = X6
| ~ spl0_47
| ~ spl0_255 ),
inference(resolution,[],[f2698,f1733]) ).
fof(f13789,plain,
( spl0_768
| ~ spl0_304
| ~ spl0_756 ),
inference(avatar_split_clause,[],[f12841,f12838,f3114,f13787]) ).
fof(f13787,plain,
( spl0_768
<=> ! [X5,X37,X10] :
( c_HOL_Ozero__class_Ozero(X5) != hAPP(X10,c_Orderings_Obot__class_Obot(tc_nat))
| ~ class_RealVector_Oreal__normed__vector(X5)
| c_Series_Osums(X10,X37,X5)
| ~ c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc),X37,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f12838,plain,
( spl0_756
<=> ! [X5,X37,X10] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| c_Series_Osums(X10,X37,X5)
| c_HOL_Ozero__class_Ozero(X5) != hAPP(X10,c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc),X37,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f12841,plain,
( ! [X10,X37,X5] :
( c_HOL_Ozero__class_Ozero(X5) != hAPP(X10,c_Orderings_Obot__class_Obot(tc_nat))
| ~ class_RealVector_Oreal__normed__vector(X5)
| c_Series_Osums(X10,X37,X5)
| ~ c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc),X37,X5) )
| ~ spl0_304
| ~ spl0_756 ),
inference(forward_demodulation,[],[f12839,f3116]) ).
fof(f12839,plain,
( ! [X10,X37,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| c_Series_Osums(X10,X37,X5)
| c_HOL_Ozero__class_Ozero(X5) != hAPP(X10,c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc),X37,X5) )
| ~ spl0_756 ),
inference(avatar_component_clause,[],[f12838]) ).
fof(f13468,plain,
( spl0_767
| ~ spl0_36
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2887,f2697,f1676,f13466]) ).
fof(f2887,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_255 ),
inference(resolution,[],[f2698,f1678]) ).
fof(f13265,plain,
( spl0_766
| ~ spl0_100
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2866,f2677,f1996,f13263]) ).
fof(f2677,plain,
( spl0_250
<=> ! [X12,X5,X11] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2866,plain,
( ! [X8,X9] : c_Lattices_Oupper__semilattice__class_Osup(X8,c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_Int_Oint),tc_Int_Oint) = X8
| ~ spl0_100
| ~ spl0_250 ),
inference(resolution,[],[f2678,f1998]) ).
fof(f2678,plain,
( ! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5) = X11 )
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2677]) ).
fof(f12877,plain,
spl0_765,
inference(avatar_split_clause,[],[f1159,f12875]) ).
fof(f12875,plain,
( spl0_765
<=> ! [X18,X5,X12] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_Series_Osummable(X18,X5)
| c_Series_Osummable(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X18),tc_nat,X5,X5),X12),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f1159,axiom,
! [X18,X5,X12] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_Series_Osummable(X18,X5)
| c_Series_Osummable(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X18),tc_nat,X5,X5),X12),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left_Osummable_0) ).
fof(f12873,plain,
spl0_764,
inference(avatar_split_clause,[],[f1158,f12871]) ).
fof(f12871,plain,
( spl0_764
<=> ! [X18,X5,X12] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OCauchy(X18,X5)
| c_SEQ_OCauchy(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X18),tc_nat,X5,X5),X12),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f1158,axiom,
! [X18,X5,X12] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OCauchy(X18,X5)
| c_SEQ_OCauchy(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X18),tc_nat,X5,X5),X12),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left_OCauchy_0) ).
fof(f12869,plain,
spl0_763,
inference(avatar_split_clause,[],[f1156,f12867]) ).
fof(f12867,plain,
( spl0_763
<=> ! [X6,X18,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OZseq(X18,X5)
| c_SEQ_OZseq(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X18),tc_nat,X5,X5),X6),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f1156,axiom,
! [X18,X6,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OZseq(X18,X5)
| c_SEQ_OZseq(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Otimes__class_Otimes(X5)),X18),tc_nat,X5,X5),X6),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Zseq__mult__left_0) ).
fof(f12865,plain,
( spl0_762
| ~ spl0_47
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2865,f2677,f1731,f12863]) ).
fof(f2865,plain,
( ! [X6,X7] : c_Lattices_Oupper__semilattice__class_Osup(X6,c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_bool),tc_bool) = X6
| ~ spl0_47
| ~ spl0_250 ),
inference(resolution,[],[f2678,f1733]) ).
fof(f12861,plain,
spl0_761,
inference(avatar_split_clause,[],[f1087,f12859]) ).
fof(f12859,plain,
( spl0_761
<=> ! [X5,X10,X0,X6] :
( ~ class_RealVector_Ometric__space(X5)
| c_SEQ_OLIMSEQ(X10,X6,X5)
| ~ c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f1087,axiom,
! [X10,X0,X6,X5] :
( ~ class_RealVector_Ometric__space(X5)
| c_SEQ_OLIMSEQ(X10,X6,X5)
| ~ c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X6,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__offset_0) ).
fof(f12857,plain,
spl0_760,
inference(avatar_split_clause,[],[f1086,f12855]) ).
fof(f12855,plain,
( spl0_760
<=> ! [X5,X10,X0,X6] :
( ~ class_RealVector_Ometric__space(X5)
| ~ c_SEQ_OLIMSEQ(X10,X6,X5)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f1086,axiom,
! [X10,X0,X6,X5] :
( ~ class_RealVector_Ometric__space(X5)
| ~ c_SEQ_OLIMSEQ(X10,X6,X5)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X6,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__ignore__initial__segment_0) ).
fof(f12853,plain,
spl0_759,
inference(avatar_split_clause,[],[f1024,f12851]) ).
fof(f12851,plain,
( spl0_759
<=> ! [X18,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_SEQ_OCauchy(X18,X5)
| c_SEQ_OCauchy(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oinverse__class_Odivide(X5)),X18),tc_nat,X5,X5),X12),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f1024,axiom,
! [X18,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_SEQ_OCauchy(X18,X5)
| c_SEQ_OCauchy(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oinverse__class_Odivide(X5)),X18),tc_nat,X5,X5),X12),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_OCauchy_0) ).
fof(f12849,plain,
spl0_758,
inference(avatar_split_clause,[],[f1023,f12847]) ).
fof(f12847,plain,
( spl0_758
<=> ! [X18,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_SEQ_OZseq(X18,X5)
| c_SEQ_OZseq(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oinverse__class_Odivide(X5)),X18),tc_nat,X5,X5),X12),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f1023,axiom,
! [X18,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_SEQ_OZseq(X18,X5)
| c_SEQ_OZseq(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oinverse__class_Odivide(X5)),X18),tc_nat,X5,X5),X12),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_OZseq_0) ).
fof(f12845,plain,
spl0_757,
inference(avatar_split_clause,[],[f1020,f12843]) ).
fof(f12843,plain,
( spl0_757
<=> ! [X18,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Series_Osummable(X18,X5)
| c_Series_Osummable(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oinverse__class_Odivide(X5)),X18),tc_nat,X5,X5),X12),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f1020,axiom,
! [X18,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Series_Osummable(X18,X5)
| c_Series_Osummable(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(X5,tc_fun(X5,X5),tc_nat),c_HOL_Oinverse__class_Odivide(X5)),X18),tc_nat,X5,X5),X12),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_Osummable_0) ).
fof(f12840,plain,
spl0_756,
inference(avatar_split_clause,[],[f756,f12838]) ).
fof(f756,axiom,
! [X10,X37,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| c_Series_Osums(X10,X37,X5)
| c_HOL_Ozero__class_Ozero(X5) != hAPP(X10,c_HOL_Ozero__class_Ozero(tc_nat))
| ~ c_Series_Osums(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc),X37,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sums__Suc__imp_0) ).
fof(f12836,plain,
spl0_755,
inference(avatar_split_clause,[],[f716,f12834]) ).
fof(f12834,plain,
( spl0_755
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f716,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__strict__right__mono_0) ).
fof(f12832,plain,
spl0_754,
inference(avatar_split_clause,[],[f715,f12830]) ).
fof(f12830,plain,
( spl0_754
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f715,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__less__cancel__right_1) ).
fof(f12828,plain,
spl0_753,
inference(avatar_split_clause,[],[f714,f12826]) ).
fof(f12826,plain,
( spl0_753
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f714,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__less__cancel__right_0) ).
fof(f12824,plain,
spl0_752,
inference(avatar_split_clause,[],[f713,f12822]) ).
fof(f12822,plain,
( spl0_752
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f713,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__strict__left__mono_0) ).
fof(f12820,plain,
( spl0_751
| ~ spl0_36
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2863,f2677,f1676,f12818]) ).
fof(f2863,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_250 ),
inference(resolution,[],[f2678,f1678]) ).
fof(f12816,plain,
spl0_750,
inference(avatar_split_clause,[],[f712,f12814]) ).
fof(f12814,plain,
( spl0_750
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f712,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__less__cancel__left_1) ).
fof(f12812,plain,
spl0_749,
inference(avatar_split_clause,[],[f711,f12810]) ).
fof(f12810,plain,
( spl0_749
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f711,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__less__cancel__left_0) ).
fof(f12808,plain,
spl0_748,
inference(avatar_split_clause,[],[f688,f12806]) ).
fof(f12806,plain,
( spl0_748
<=> ! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f688,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sum__squares__ge__zero_0) ).
fof(f12804,plain,
spl0_747,
inference(avatar_split_clause,[],[f682,f12802]) ).
fof(f12802,plain,
( spl0_747
<=> ! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f682,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X12),X12)),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_not__sum__squares__lt__zero_0) ).
fof(f12800,plain,
spl0_746,
inference(avatar_split_clause,[],[f634,f12798]) ).
fof(f12798,plain,
( spl0_746
<=> ! [X5,X11,X10] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Odifferentiable(X10,X11,X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(X10,X11)
| c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBB(X5,X5,X5),c_HOL_Oinverse__class_Oinverse(X5)),X10),X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f634,axiom,
! [X10,X11,X5] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Odifferentiable(X10,X11,X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(X10,X11)
| c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBB(X5,X5,X5),c_HOL_Oinverse__class_Oinverse(X5)),X10),X11,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_differentiable__inverse_0) ).
fof(f12796,plain,
spl0_745,
inference(avatar_split_clause,[],[f579,f12794]) ).
fof(f12794,plain,
( spl0_745
<=> ! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f579,axiom,
! [X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__divide__1__iff_1) ).
fof(f12792,plain,
spl0_744,
inference(avatar_split_clause,[],[f578,f12790]) ).
fof(f12790,plain,
( spl0_744
<=> ! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f578,axiom,
! [X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__divide__1__iff_0) ).
fof(f12788,plain,
spl0_743,
inference(avatar_split_clause,[],[f344,f12786]) ).
fof(f12786,plain,
( spl0_743
<=> ! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f344,axiom,
! [X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__0__1__iff_1) ).
fof(f12784,plain,
spl0_742,
inference(avatar_split_clause,[],[f343,f12782]) ).
fof(f12782,plain,
( spl0_742
<=> ! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f343,axiom,
! [X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__less__0__1__iff_0) ).
fof(f12780,plain,
spl0_741,
inference(avatar_split_clause,[],[f226,f12778]) ).
fof(f12778,plain,
( spl0_741
<=> ! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f226,axiom,
! [X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__divide__1__iff_0) ).
fof(f12776,plain,
( spl0_740
| ~ spl0_41
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f2861,f2673,f1701,f12773]) ).
fof(f12773,plain,
( spl0_740
<=> c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f2673,plain,
( spl0_249
<=> ! [X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| c_Orderings_Obot__class_Obot(X5) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f2861,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),tc_bool)
| ~ spl0_41
| ~ spl0_249 ),
inference(resolution,[],[f2674,f1703]) ).
fof(f2674,plain,
( ! [X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| c_Orderings_Obot__class_Obot(X5) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5) )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2673]) ).
fof(f12771,plain,
spl0_739,
inference(avatar_split_clause,[],[f225,f12769]) ).
fof(f12769,plain,
( spl0_739
<=> ! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f225,axiom,
! [X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X7))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__divide__1__iff_1) ).
fof(f12767,plain,
spl0_738,
inference(avatar_split_clause,[],[f80,f12765]) ).
fof(f12765,plain,
( spl0_738
<=> ! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f80,axiom,
! [X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__0__1__iff_0) ).
fof(f12763,plain,
spl0_737,
inference(avatar_split_clause,[],[f79,f12761]) ).
fof(f12761,plain,
( spl0_737
<=> ! [X5,X7] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f79,axiom,
! [X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__le__0__1__iff_1) ).
fof(f12759,plain,
spl0_736,
inference(avatar_split_clause,[],[f53,f12757]) ).
fof(f12757,plain,
( spl0_736
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f53,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__left__mono_0) ).
fof(f12755,plain,
spl0_735,
inference(avatar_split_clause,[],[f52,f12753]) ).
fof(f12753,plain,
( spl0_735
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f52,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__right__mono_0) ).
fof(f12751,plain,
spl0_734,
inference(avatar_split_clause,[],[f51,f12749]) ).
fof(f12749,plain,
( spl0_734
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f51,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__le__cancel__left_0) ).
fof(f12747,plain,
spl0_733,
inference(avatar_split_clause,[],[f50,f12745]) ).
fof(f12745,plain,
( spl0_733
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f50,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X6),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__le__cancel__left_1) ).
fof(f12743,plain,
spl0_732,
inference(avatar_split_clause,[],[f49,f12741]) ).
fof(f12741,plain,
( spl0_732
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f49,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__le__cancel__right_0) ).
fof(f12739,plain,
spl0_731,
inference(avatar_split_clause,[],[f48,f12737]) ).
fof(f12737,plain,
( spl0_731
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f48,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X9))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__le__cancel__right_1) ).
fof(f12710,plain,
( spl0_730
| ~ spl0_131
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2831,f2649,f2151,f12708]) ).
fof(f12708,plain,
( spl0_730
<=> ! [X2] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),X2) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f2649,plain,
( spl0_243
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Oone__class_Oone(X5)),X6) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2831,plain,
( ! [X2] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),X2) = X2
| ~ spl0_131
| ~ spl0_243 ),
inference(resolution,[],[f2650,f2153]) ).
fof(f2650,plain,
( ! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Oone__class_Oone(X5)),X6) = X6 )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2649]) ).
fof(f12241,plain,
( spl0_729
| ~ spl0_89
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2830,f2649,f1941,f12239]) ).
fof(f12239,plain,
( spl0_729
<=> ! [X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f2830,plain,
( ! [X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),X1) = X1
| ~ spl0_89
| ~ spl0_243 ),
inference(resolution,[],[f2650,f1943]) ).
fof(f11890,plain,
( spl0_728
| ~ spl0_304
| ~ spl0_706 ),
inference(avatar_split_clause,[],[f10694,f10691,f3114,f11888]) ).
fof(f11888,plain,
( spl0_728
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f10691,plain,
( spl0_706
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f10694,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) )
| ~ spl0_304
| ~ spl0_706 ),
inference(forward_demodulation,[],[f10692,f3116]) ).
fof(f10692,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) )
| ~ spl0_706 ),
inference(avatar_component_clause,[],[f10691]) ).
fof(f11886,plain,
( spl0_727
| ~ spl0_304
| ~ spl0_704 ),
inference(avatar_split_clause,[],[f10685,f10682,f3114,f11884]) ).
fof(f11884,plain,
( spl0_727
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f10682,plain,
( spl0_704
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f10685,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) )
| ~ spl0_304
| ~ spl0_704 ),
inference(forward_demodulation,[],[f10683,f3116]) ).
fof(f10683,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) )
| ~ spl0_704 ),
inference(avatar_component_clause,[],[f10682]) ).
fof(f11882,plain,
( spl0_726
| ~ spl0_29
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2829,f2649,f1641,f11880]) ).
fof(f2829,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) = X0
| ~ spl0_29
| ~ spl0_243 ),
inference(resolution,[],[f2650,f1643]) ).
fof(f11878,plain,
( spl0_725
| ~ spl0_304
| ~ spl0_703 ),
inference(avatar_split_clause,[],[f10680,f10677,f3114,f11876]) ).
fof(f11876,plain,
( spl0_725
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| X1 = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f10677,plain,
( spl0_703
<=> ! [X2,X0,X1] :
( X1 = X2
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f10680,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| X1 = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2) )
| ~ spl0_304
| ~ spl0_703 ),
inference(forward_demodulation,[],[f10678,f3116]) ).
fof(f10678,plain,
( ! [X2,X0,X1] :
( X1 = X2
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2) )
| ~ spl0_703 ),
inference(avatar_component_clause,[],[f10677]) ).
fof(f11874,plain,
( spl0_724
| ~ spl0_304
| ~ spl0_702 ),
inference(avatar_split_clause,[],[f10675,f10671,f3114,f11872]) ).
fof(f11872,plain,
( spl0_724
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f10671,plain,
( spl0_702
<=> ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f10675,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X1)) )
| ~ spl0_304
| ~ spl0_702 ),
inference(forward_demodulation,[],[f10674,f3116]) ).
fof(f10674,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_304
| ~ spl0_702 ),
inference(forward_demodulation,[],[f10672,f3116]) ).
fof(f10672,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_702 ),
inference(avatar_component_clause,[],[f10671]) ).
fof(f11870,plain,
( spl0_723
| ~ spl0_304
| ~ spl0_701 ),
inference(avatar_split_clause,[],[f10669,f10665,f3114,f11868]) ).
fof(f11868,plain,
( spl0_723
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f10665,plain,
( spl0_701
<=> ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f10669,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2)) )
| ~ spl0_304
| ~ spl0_701 ),
inference(forward_demodulation,[],[f10668,f3116]) ).
fof(f10668,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_304
| ~ spl0_701 ),
inference(forward_demodulation,[],[f10666,f3116]) ).
fof(f10666,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_701 ),
inference(avatar_component_clause,[],[f10665]) ).
fof(f11514,plain,
( spl0_722
| ~ spl0_304
| ~ spl0_697 ),
inference(avatar_split_clause,[],[f10651,f10648,f3114,f11512]) ).
fof(f11512,plain,
( spl0_722
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f10648,plain,
( spl0_697
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f10651,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) )
| ~ spl0_304
| ~ spl0_697 ),
inference(forward_demodulation,[],[f10649,f3116]) ).
fof(f10649,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) )
| ~ spl0_697 ),
inference(avatar_component_clause,[],[f10648]) ).
fof(f11510,plain,
( spl0_721
| ~ spl0_304
| ~ spl0_696 ),
inference(avatar_split_clause,[],[f10646,f10643,f3114,f11508]) ).
fof(f11508,plain,
( spl0_721
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f10643,plain,
( spl0_696
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f10646,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) )
| ~ spl0_304
| ~ spl0_696 ),
inference(forward_demodulation,[],[f10644,f3116]) ).
fof(f10644,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) )
| ~ spl0_696 ),
inference(avatar_component_clause,[],[f10643]) ).
fof(f11217,plain,
( spl0_720
| ~ spl0_131
| ~ spl0_242 ),
inference(avatar_split_clause,[],[f2828,f2645,f2151,f11215]) ).
fof(f11215,plain,
( spl0_720
<=> ! [X2] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f2645,plain,
( spl0_242
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_HOL_Oone__class_Oone(X5)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f2828,plain,
( ! [X2] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = X2
| ~ spl0_131
| ~ spl0_242 ),
inference(resolution,[],[f2646,f2153]) ).
fof(f2646,plain,
( ! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_HOL_Oone__class_Oone(X5)) = X6 )
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f2645]) ).
fof(f11141,plain,
( spl0_719
| ~ spl0_304
| ~ spl0_691 ),
inference(avatar_split_clause,[],[f10625,f10620,f3114,f11139]) ).
fof(f11139,plain,
( spl0_719
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X2
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f10620,plain,
( spl0_691
<=> ! [X2,X1] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f10625,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X2
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X1 )
| ~ spl0_304
| ~ spl0_691 ),
inference(forward_demodulation,[],[f10624,f3116]) ).
fof(f10624,plain,
( ! [X2,X1] :
( hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X2
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X1
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_304
| ~ spl0_691 ),
inference(forward_demodulation,[],[f10623,f3116]) ).
fof(f10623,plain,
( ! [X2,X1] :
( hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_304
| ~ spl0_691 ),
inference(forward_demodulation,[],[f10621,f3116]) ).
fof(f10621,plain,
( ! [X2,X1] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_691 ),
inference(avatar_component_clause,[],[f10620]) ).
fof(f10742,plain,
spl0_718,
inference(avatar_split_clause,[],[f1476,f10740]) ).
fof(f10740,plain,
( spl0_718
<=> ! [X4,X0,X3] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f1476,plain,
! [X3,X0,X4] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X4)),
inference(forward_demodulation,[],[f1298,f1069]) ).
fof(f1298,axiom,
! [X3,X0,X4] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X0)),X4),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__commute_0) ).
fof(f10738,plain,
spl0_717,
inference(avatar_split_clause,[],[f1287,f10736]) ).
fof(f10736,plain,
( spl0_717
<=> ! [X5,X27,X25,X26] : c_Lattices_Oupper__semilattice__class_Osup(X25,c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X26,c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f1287,axiom,
! [X26,X27,X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X26,c_Lattices_Oupper__semilattice__class_Osup(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Un__left__commute_0) ).
fof(f10734,plain,
( spl0_716
| ~ spl0_89
| ~ spl0_242 ),
inference(avatar_split_clause,[],[f2827,f2645,f1941,f10732]) ).
fof(f10732,plain,
( spl0_716
<=> ! [X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X1),c_HOL_Oone__class_Oone(tc_Int_Oint)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f2827,plain,
( ! [X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),X1),c_HOL_Oone__class_Oone(tc_Int_Oint)) = X1
| ~ spl0_89
| ~ spl0_242 ),
inference(resolution,[],[f2646,f1943]) ).
fof(f10730,plain,
spl0_715,
inference(avatar_split_clause,[],[f1286,f10728]) ).
fof(f10728,plain,
( spl0_715
<=> ! [X5,X27,X25,X26] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),X27,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X25,c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f1286,axiom,
! [X26,X27,X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),X27,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X25,c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Un__assoc_0) ).
fof(f10726,plain,
spl0_714,
inference(avatar_split_clause,[],[f1069,f10724]) ).
fof(f10724,plain,
( spl0_714
<=> ! [X4,X0,X3] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),X4)),X0) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f10722,plain,
spl0_713,
inference(avatar_split_clause,[],[f1062,f10720]) ).
fof(f10720,plain,
( spl0_713
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f1062,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__cancel2_0) ).
fof(f10718,plain,
spl0_712,
inference(avatar_split_clause,[],[f1061,f10716]) ).
fof(f10716,plain,
( spl0_712
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f1061,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__cancel_0) ).
fof(f10714,plain,
spl0_711,
inference(avatar_split_clause,[],[f1032,f10712]) ).
fof(f10712,plain,
( spl0_711
<=> ! [X5,X11,X12,X16] :
( ~ class_Lattices_Oupper__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X16))
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X16))
| hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),X5),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f1032,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X16))
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X16))
| hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),X5),X16)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__sup__iff_2) ).
fof(f10710,plain,
spl0_710,
inference(avatar_split_clause,[],[f909,f10708]) ).
fof(f10708,plain,
( spl0_710
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f909,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__inverse_0) ).
fof(f10706,plain,
spl0_709,
inference(avatar_split_clause,[],[f764,f10704]) ).
fof(f10704,plain,
( spl0_709
<=> ! [X10,X5,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1))
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X2),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f764,axiom,
! [X2,X10,X1,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1))
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,X5),X10),c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X2),tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__op__ivl__Suc_0) ).
fof(f10702,plain,
spl0_708,
inference(avatar_split_clause,[],[f704,f10700]) ).
fof(f10700,plain,
( spl0_708
<=> ! [X10,X11,X5,X32] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Odifferentiable(X32,X11,X5)
| ~ c_Deriv_Odifferentiable(X10,hAPP(X32,X11),X5)
| c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBB(X5,X5,X5),X10),X32),X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f704,axiom,
! [X10,X11,X5,X32] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Odifferentiable(X32,X11,X5)
| ~ c_Deriv_Odifferentiable(X10,hAPP(X32,X11),X5)
| c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBB(X5,X5,X5),X10),X32),X11,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_differentiable__compose_0) ).
fof(f10698,plain,
spl0_707,
inference(avatar_split_clause,[],[f548,f10696]) ).
fof(f10696,plain,
( spl0_707
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Suc,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f548,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Suc,X2)))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__gt1_0) ).
fof(f10693,plain,
spl0_706,
inference(avatar_split_clause,[],[f426,f10691]) ).
fof(f426,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel2_0) ).
fof(f10689,plain,
( spl0_705
| ~ spl0_29
| ~ spl0_242 ),
inference(avatar_split_clause,[],[f2826,f2645,f1641,f10687]) ).
fof(f10687,plain,
( spl0_705
<=> ! [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_705])]) ).
fof(f2826,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),c_HOL_Oone__class_Oone(tc_nat)) = X0
| ~ spl0_29
| ~ spl0_242 ),
inference(resolution,[],[f2646,f1643]) ).
fof(f10684,plain,
spl0_704,
inference(avatar_split_clause,[],[f425,f10682]) ).
fof(f425,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel1_0) ).
fof(f10679,plain,
spl0_703,
inference(avatar_split_clause,[],[f424,f10677]) ).
fof(f424,axiom,
! [X2,X0,X1] :
( X1 = X2
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__mult__eq__cancel1_0) ).
fof(f10673,plain,
spl0_702,
inference(avatar_split_clause,[],[f324,f10671]) ).
fof(f324,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_one__le__mult__iff_0) ).
fof(f10667,plain,
spl0_701,
inference(avatar_split_clause,[],[f323,f10665]) ).
fof(f323,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_one__le__mult__iff_1) ).
fof(f10663,plain,
spl0_700,
inference(avatar_split_clause,[],[f317,f10661]) ).
fof(f10661,plain,
( spl0_700
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f317,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__positive__imp__positive_0) ).
fof(f10659,plain,
spl0_699,
inference(avatar_split_clause,[],[f294,f10657]) ).
fof(f10657,plain,
( spl0_699
<=> ! [X12,X16,X11] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f294,axiom,
! [X11,X16,X12] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X16)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X16)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__add__left__commute_0) ).
fof(f10655,plain,
spl0_698,
inference(avatar_split_clause,[],[f293,f10653]) ).
fof(f10653,plain,
( spl0_698
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f293,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__add__assoc_0) ).
fof(f10650,plain,
spl0_697,
inference(avatar_split_clause,[],[f277,f10648]) ).
fof(f277,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__cancel2_1) ).
fof(f10645,plain,
spl0_696,
inference(avatar_split_clause,[],[f276,f10643]) ).
fof(f276,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X0))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__cancel1_1) ).
fof(f10641,plain,
spl0_695,
inference(avatar_split_clause,[],[f227,f10639]) ).
fof(f227,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Suc__diff__le_0) ).
fof(f10637,plain,
( spl0_694
| ~ spl0_134
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f2808,f2625,f2166,f10635]) ).
fof(f10635,plain,
( spl0_694
<=> ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),X2) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f2166,plain,
( spl0_134
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f2625,plain,
( spl0_237
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X6) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f2808,plain,
( ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),X2) = X2
| ~ spl0_134
| ~ spl0_237 ),
inference(resolution,[],[f2626,f2168]) ).
fof(f2168,plain,
( class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f2166]) ).
fof(f2626,plain,
( ! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X6) = X6 )
| ~ spl0_237 ),
inference(avatar_component_clause,[],[f2625]) ).
fof(f10633,plain,
spl0_693,
inference(avatar_split_clause,[],[f193,f10631]) ).
fof(f10631,plain,
( spl0_693
<=> ! [X11,X12,X5,X16] :
( ~ class_Lattices_Olattice(X5)
| hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),c_Lattices_Olower__semilattice__class_Oinf(X11,X16,X5),X5),X5),c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Oupper__semilattice__class_Osup(X12,X16,X5),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f193,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),c_Lattices_Olower__semilattice__class_Oinf(X11,X16,X5),X5),X5),c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Oupper__semilattice__class_Osup(X12,X16,X5),X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_distrib__inf__le_0) ).
fof(f10629,plain,
spl0_692,
inference(avatar_split_clause,[],[f136,f10627]) ).
fof(f10627,plain,
( spl0_692
<=> ! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f136,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)),X0) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__mult__assoc_0) ).
fof(f10622,plain,
spl0_691,
inference(avatar_split_clause,[],[f119,f10620]) ).
fof(f119,axiom,
! [X2,X1] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__is__1_1) ).
fof(f10618,plain,
spl0_690,
inference(avatar_split_clause,[],[f108,f10616]) ).
fof(f10616,plain,
( spl0_690
<=> ! [X5,X8,X7] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ class_Int_Onumber(X5)
| c_Int_Onumber__class_Onumber__of(X8,X5) = c_HOL_Ozero__class_Ozero(X5)
| c_Int_Onumber__class_Onumber__of(X8,X5) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),c_HOL_Ozero__class_Ozero(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f108,axiom,
! [X8,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ class_Int_Onumber(X5)
| c_Int_Onumber__class_Onumber__of(X8,X5) = c_HOL_Ozero__class_Ozero(X5)
| c_Int_Onumber__class_Onumber__of(X8,X5) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),c_HOL_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_eq__divide__eq__number__of_1) ).
fof(f10614,plain,
spl0_689,
inference(avatar_split_clause,[],[f94,f10612]) ).
fof(f10612,plain,
( spl0_689
<=> ! [X5,X27,X25,X26] : c_Lattices_Olower__semilattice__class_Oinf(X25,c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X26,c_Lattices_Olower__semilattice__class_Oinf(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f94,axiom,
! [X26,X27,X5,X25] : c_Lattices_Olower__semilattice__class_Oinf(X25,c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X26,c_Lattices_Olower__semilattice__class_Oinf(X25,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Int__left__commute_0) ).
fof(f10610,plain,
spl0_688,
inference(avatar_split_clause,[],[f93,f10608]) ).
fof(f10608,plain,
( spl0_688
<=> ! [X5,X27,X25,X26] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),X27,tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X25,c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f93,axiom,
! [X26,X27,X5,X25] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),X27,tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X25,c_Lattices_Olower__semilattice__class_Oinf(X26,X27,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Int__assoc_0) ).
fof(f10606,plain,
spl0_687,
inference(avatar_split_clause,[],[f81,f10604]) ).
fof(f10604,plain,
( spl0_687
<=> ! [X5,X11,X12,X16] :
( ~ class_Lattices_Olattice(X5)
| hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X16,X5),X5),X5),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X5),X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f81,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X16,X5),X5),X5),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X5),X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_distrib__sup__le_0) ).
fof(f10602,plain,
spl0_686,
inference(avatar_split_clause,[],[f29,f10600]) ).
fof(f10600,plain,
( spl0_686
<=> ! [X5,X11,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X6))
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X7))
| hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f29,axiom,
! [X11,X6,X7,X5] :
( ~ class_Lattices_Olower__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X6))
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X7))
| hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__infI_0) ).
fof(f10598,plain,
spl0_685,
inference(avatar_split_clause,[],[f25,f10596]) ).
fof(f10596,plain,
( spl0_685
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f25,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__negative__imp__negative_0) ).
fof(f10590,plain,
( spl0_684
| ~ spl0_92
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f2807,f2625,f1956,f10588]) ).
fof(f10588,plain,
( spl0_684
<=> ! [X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f1956,plain,
( spl0_92
<=> class_OrderedGroup_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f2807,plain,
( ! [X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),X1) = X1
| ~ spl0_92
| ~ spl0_237 ),
inference(resolution,[],[f2626,f1958]) ).
fof(f1958,plain,
( class_OrderedGroup_Omonoid__add(tc_Int_Oint)
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1956]) ).
fof(f10586,plain,
( spl0_683
| ~ spl0_304
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f9815,f9812,f3114,f10584]) ).
fof(f10584,plain,
( spl0_683
<=> ! [X2,X5] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f9812,plain,
( spl0_680
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f9815,plain,
( ! [X2,X5] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2) )
| ~ spl0_304
| ~ spl0_680 ),
inference(forward_demodulation,[],[f9813,f3116]) ).
fof(f9813,plain,
( ! [X2,X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2) )
| ~ spl0_680 ),
inference(avatar_component_clause,[],[f9812]) ).
fof(f10442,plain,
( spl0_682
| ~ spl0_134
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2805,f2621,f2166,f10440]) ).
fof(f10440,plain,
( spl0_682
<=> ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f2621,plain,
( spl0_236
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f2805,plain,
( ! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),X2),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = X2
| ~ spl0_134
| ~ spl0_236 ),
inference(resolution,[],[f2622,f2168]) ).
fof(f2622,plain,
( ! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 )
| ~ spl0_236 ),
inference(avatar_component_clause,[],[f2621]) ).
fof(f10073,plain,
( spl0_681
| ~ spl0_92
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2804,f2621,f1956,f10071]) ).
fof(f10071,plain,
( spl0_681
<=> ! [X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X1),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f2804,plain,
( ! [X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),X1),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = X1
| ~ spl0_92
| ~ spl0_236 ),
inference(resolution,[],[f2622,f1958]) ).
fof(f9814,plain,
spl0_680,
inference(avatar_split_clause,[],[f1240,f9812]) ).
fof(f1240,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__eq__0__iff_2) ).
fof(f9810,plain,
spl0_679,
inference(avatar_split_clause,[],[f1085,f9808]) ).
fof(f9808,plain,
( spl0_679
<=> ! [X5,X0,X10] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5)
| c_Series_Osummable(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f1085,axiom,
! [X10,X0,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5)
| c_Series_Osummable(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),hAPP(c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),tc_nat,tc_nat,tc_nat),X0)),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_summable__ignore__initial__segment_0) ).
fof(f9806,plain,
spl0_678,
inference(avatar_split_clause,[],[f1068,f9804]) ).
fof(f9804,plain,
( spl0_678
<=> ! [X29,X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X29),X2),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X29),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f1068,axiom,
! [X2,X29,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X29),X2),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X29),X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__le__mono2_0) ).
fof(f9802,plain,
( spl0_677
| ~ spl0_81
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2774,f2577,f1901,f9800]) ).
fof(f1901,plain,
( spl0_81
<=> class_Lattices_Olower__semilattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f2774,plain,
( ! [X8,X9] : c_Lattices_Olower__semilattice__class_Oinf(X8,X9,tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(X9,X8,tc_Int_Oint)
| ~ spl0_81
| ~ spl0_225 ),
inference(resolution,[],[f2578,f1903]) ).
fof(f1903,plain,
( class_Lattices_Olower__semilattice(tc_Int_Oint)
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1901]) ).
fof(f9798,plain,
spl0_676,
inference(avatar_split_clause,[],[f1067,f9796]) ).
fof(f9796,plain,
( spl0_676
<=> ! [X29,X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X29),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X29))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f1067,axiom,
! [X2,X29,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X29),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X29))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__le__mono_0) ).
fof(f9794,plain,
spl0_675,
inference(avatar_split_clause,[],[f1015,f9792]) ).
fof(f9792,plain,
( spl0_675
<=> ! [X5,X6,X25,X26] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X6,X25,X5),c_Set_Oinsert(X6,X26,X5),tc_fun(X5,tc_bool)) = c_Set_Oinsert(X6,c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f1015,axiom,
! [X6,X26,X5,X25] : c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(X6,X25,X5),c_Set_Oinsert(X6,X26,X5),tc_fun(X5,tc_bool)) = c_Set_Oinsert(X6,c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),X5),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_insert__inter__insert_0) ).
fof(f9790,plain,
spl0_674,
inference(avatar_split_clause,[],[f987,f9788]) ).
fof(f9788,plain,
( spl0_674
<=> ! [X48,X5,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),hAPP(c_Suc,X48)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X48)),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f987,axiom,
! [X48,X11,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),hAPP(c_Suc,X48)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X48)),X11) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I28_J_0) ).
fof(f9786,plain,
spl0_673,
inference(avatar_split_clause,[],[f986,f9784]) ).
fof(f9784,plain,
( spl0_673
<=> ! [X48,X5,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),hAPP(c_Suc,X48)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X48)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f986,axiom,
! [X48,X11,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),hAPP(c_Suc,X48)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X48)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I27_J_0) ).
fof(f9782,plain,
spl0_672,
inference(avatar_split_clause,[],[f983,f9780]) ).
fof(f9780,plain,
( spl0_672
<=> ! [X6,X2,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f983,axiom,
! [X2,X6,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)),X6) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__Suc2_0) ).
fof(f9778,plain,
spl0_671,
inference(avatar_split_clause,[],[f982,f9776]) ).
fof(f9776,plain,
( spl0_671
<=> ! [X6,X2,X5] :
( ~ class_Power_Opower(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f982,axiom,
! [X2,X6,X5] :
( ~ class_Power_Opower(X5)
| hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__Suc_0) ).
fof(f9774,plain,
spl0_670,
inference(avatar_split_clause,[],[f943,f9772]) ).
fof(f9772,plain,
( spl0_670
<=> ! [X38,X11,X20,X5,X32] :
( ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Limits_OZfun(X32,X38,X5,X20)
| c_Limits_OZfun(hAPP(hAPP(c_COMBB(X20,X20,X5),hAPP(c_HOL_Otimes__class_Otimes(X20),X11)),X32),X38,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f943,axiom,
! [X38,X11,X5,X32,X20] :
( ~ class_RealVector_Oreal__normed__algebra(X20)
| ~ c_Limits_OZfun(X32,X38,X5,X20)
| c_Limits_OZfun(hAPP(hAPP(c_COMBB(X20,X20,X5),hAPP(c_HOL_Otimes__class_Otimes(X20),X11)),X32),X38,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right_OZfun_0) ).
fof(f9770,plain,
spl0_669,
inference(avatar_split_clause,[],[f611,f9768]) ).
fof(f9768,plain,
( spl0_669
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| X6 = X7
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) = X7
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6) != hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f611,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| X6 = X7
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) = X7
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6) != hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nonzero__inverse__eq__imp__eq_0) ).
fof(f9766,plain,
spl0_668,
inference(avatar_split_clause,[],[f610,f9764]) ).
fof(f9764,plain,
( spl0_668
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f610,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__add__left__cancel__less_1) ).
fof(f9762,plain,
spl0_667,
inference(avatar_split_clause,[],[f609,f9760]) ).
fof(f9760,plain,
( spl0_667
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f609,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__add__left__cancel__less_0) ).
fof(f9758,plain,
( spl0_666
| ~ spl0_43
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2773,f2577,f1711,f9756]) ).
fof(f1711,plain,
( spl0_43
<=> class_Lattices_Olower__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f2773,plain,
( ! [X6,X7] : c_Lattices_Olower__semilattice__class_Oinf(X6,X7,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X7,X6,tc_bool)
| ~ spl0_43
| ~ spl0_225 ),
inference(resolution,[],[f2578,f1713]) ).
fof(f1713,plain,
( class_Lattices_Olower__semilattice(tc_bool)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f1711]) ).
fof(f9754,plain,
spl0_665,
inference(avatar_split_clause,[],[f608,f9752]) ).
fof(f9752,plain,
( spl0_665
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),X4))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f608,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),X4))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__less__mono1_0) ).
fof(f9750,plain,
spl0_664,
inference(avatar_split_clause,[],[f593,f9748]) ).
fof(f9748,plain,
( spl0_664
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0),tc_nat),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f593,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0),tc_nat),X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__diff__conv_0) ).
fof(f9746,plain,
spl0_663,
inference(avatar_split_clause,[],[f592,f9744]) ).
fof(f9744,plain,
( spl0_663
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0),tc_nat),X4))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f592,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0),tc_nat),X4))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__diff__conv_1) ).
fof(f9742,plain,
spl0_662,
inference(avatar_split_clause,[],[f458,f9740]) ).
fof(f9740,plain,
( spl0_662
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f458,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_lessequals(X0,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__add__diff_0) ).
fof(f9738,plain,
spl0_661,
inference(avatar_split_clause,[],[f394,f9736]) ).
fof(f9736,plain,
( spl0_661
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0),tc_nat),X3))
| hBOOL(hAPP(c_lessequals(X4,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f394,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0),tc_nat),X3))
| hBOOL(hAPP(c_lessequals(X4,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__diff__conv_0) ).
fof(f9734,plain,
spl0_660,
inference(avatar_split_clause,[],[f393,f9732]) ).
fof(f9732,plain,
( spl0_660
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0),tc_nat),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f393,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X0),tc_nat),X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__diff__conv_1) ).
fof(f9730,plain,
spl0_659,
inference(avatar_split_clause,[],[f380,f9728]) ).
fof(f9728,plain,
( spl0_659
<=> ! [X5,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X1),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Oone__class_Oone(X5)),c_HOL_Oone__class_Oone(X5))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f380,axiom,
! [X1,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X1),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Oone__class_Oone(X5)),c_HOL_Oone__class_Oone(X5))),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(f9726,plain,
spl0_658,
inference(avatar_split_clause,[],[f56,f9724]) ).
fof(f9724,plain,
( spl0_658
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f56,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__add__left__cancel__le_1) ).
fof(f9722,plain,
spl0_657,
inference(avatar_split_clause,[],[f55,f9720]) ).
fof(f9720,plain,
( spl0_657
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f55,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X0),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__add__left__cancel__le_0) ).
fof(f9718,plain,
spl0_656,
inference(avatar_split_clause,[],[f54,f9716]) ).
fof(f9716,plain,
( spl0_656
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f54,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X0),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__le__mono1_0) ).
fof(f9714,plain,
( spl0_655
| ~ spl0_23
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2771,f2577,f1611,f9712]) ).
fof(f9710,plain,
spl0_654,
inference(avatar_split_clause,[],[f47,f9708]) ).
fof(f9708,plain,
( spl0_654
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f47,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel2_1) ).
fof(f9706,plain,
spl0_653,
inference(avatar_split_clause,[],[f46,f9704]) ).
fof(f9704,plain,
( spl0_653
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f46,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__less__cancel1_1) ).
fof(f9702,plain,
spl0_652,
inference(avatar_split_clause,[],[f3,f9700]) ).
fof(f9700,plain,
( spl0_652
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f3,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X3),X0),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X4),X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__mono1_0) ).
fof(f9698,plain,
spl0_651,
inference(avatar_split_clause,[],[f1,f9696]) ).
fof(f9696,plain,
( spl0_651
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__le__cancel1_2) ).
fof(f9623,plain,
( spl0_650
| ~ spl0_304
| ~ spl0_642 ),
inference(avatar_split_clause,[],[f8934,f8930,f3114,f9621]) ).
fof(f9621,plain,
( spl0_650
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1) != c_Orderings_Obot__class_Obot(tc_nat)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f8930,plain,
( spl0_642
<=> ! [X2,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f8934,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1) != c_Orderings_Obot__class_Obot(tc_nat)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| X1 = X2 )
| ~ spl0_304
| ~ spl0_642 ),
inference(forward_demodulation,[],[f8933,f3116]) ).
fof(f8933,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1) )
| ~ spl0_304
| ~ spl0_642 ),
inference(forward_demodulation,[],[f8931,f3116]) ).
fof(f8931,plain,
( ! [X2,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1) )
| ~ spl0_642 ),
inference(avatar_component_clause,[],[f8930]) ).
fof(f9619,plain,
( spl0_649
| ~ spl0_138
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2770,f2573,f2186,f9617]) ).
fof(f9617,plain,
( spl0_649
<=> ! [X0] : hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),X0),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f2573,plain,
( spl0_224
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),c_HOL_Oone__class_Oone(X5)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f2770,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),X0),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = X0
| ~ spl0_138
| ~ spl0_224 ),
inference(resolution,[],[f2574,f2188]) ).
fof(f2574,plain,
( ! [X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),c_HOL_Oone__class_Oone(X5)) = X6 )
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f2573]) ).
fof(f9408,plain,
( spl0_648
| ~ spl0_208
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2769,f2569,f2500,f9406]) ).
fof(f9406,plain,
( spl0_648
<=> ! [X2,X0,X1] :
( c_Deriv_Odifferentiable(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2,X0)
| ~ class_RealVector_Oreal__normed__field(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f2569,plain,
( spl0_223
<=> ! [X10,X11,X5,X15] :
( ~ class_RealVector_Oreal__normed__field(X5)
| c_Deriv_Odifferentiable(X10,X11,X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2769,plain,
( ! [X2,X0,X1] :
( c_Deriv_Odifferentiable(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2,X0)
| ~ class_RealVector_Oreal__normed__field(X0) )
| ~ spl0_208
| ~ spl0_223 ),
inference(duplicate_literal_removal,[],[f2768]) ).
fof(f2768,plain,
( ! [X2,X0,X1] :
( c_Deriv_Odifferentiable(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2,X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| ~ class_RealVector_Oreal__normed__field(X0) )
| ~ spl0_208
| ~ spl0_223 ),
inference(resolution,[],[f2570,f2501]) ).
fof(f2570,plain,
( ! [X10,X11,X15,X5] :
( ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| c_Deriv_Odifferentiable(X10,X11,X5)
| ~ class_RealVector_Oreal__normed__field(X5) )
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f2569]) ).
fof(f9396,plain,
( spl0_647
| ~ spl0_304
| ~ spl0_629 ),
inference(avatar_split_clause,[],[f8867,f8862,f3114,f9394]) ).
fof(f9394,plain,
( spl0_647
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X2
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f8862,plain,
( spl0_629
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f8867,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X2
| c_Orderings_Obot__class_Obot(tc_nat) = X2 )
| ~ spl0_304
| ~ spl0_629 ),
inference(forward_demodulation,[],[f8866,f3116]) ).
fof(f8866,plain,
( ! [X2,X1] :
( hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X2
| c_Orderings_Obot__class_Obot(tc_nat) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_304
| ~ spl0_629 ),
inference(forward_demodulation,[],[f8865,f3116]) ).
fof(f8865,plain,
( ! [X2,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_304
| ~ spl0_629 ),
inference(forward_demodulation,[],[f8863,f3116]) ).
fof(f8863,plain,
( ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_629 ),
inference(avatar_component_clause,[],[f8862]) ).
fof(f9392,plain,
( spl0_646
| ~ spl0_304
| ~ spl0_628 ),
inference(avatar_split_clause,[],[f8860,f8855,f3114,f9390]) ).
fof(f9390,plain,
( spl0_646
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X1
| c_Orderings_Obot__class_Obot(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f8855,plain,
( spl0_628
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f8860,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X1
| c_Orderings_Obot__class_Obot(tc_nat) = X1 )
| ~ spl0_304
| ~ spl0_628 ),
inference(forward_demodulation,[],[f8859,f3116]) ).
fof(f8859,plain,
( ! [X2,X1] :
( hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X1
| c_Orderings_Obot__class_Obot(tc_nat) = X1
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_304
| ~ spl0_628 ),
inference(forward_demodulation,[],[f8858,f3116]) ).
fof(f8858,plain,
( ! [X2,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_304
| ~ spl0_628 ),
inference(forward_demodulation,[],[f8856,f3116]) ).
fof(f8856,plain,
( ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_628 ),
inference(avatar_component_clause,[],[f8855]) ).
fof(f9300,plain,
( spl0_645
| ~ spl0_304
| ~ spl0_623 ),
inference(avatar_split_clause,[],[f8837,f8832,f3114,f9298]) ).
fof(f9298,plain,
( spl0_645
<=> ! [X11] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)))))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X11
| c_Orderings_Obot__class_Obot(tc_nat) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f8832,plain,
( spl0_623
<=> ! [X11] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X11
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X11
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f8837,plain,
( ! [X11] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)))))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X11
| c_Orderings_Obot__class_Obot(tc_nat) = X11 )
| ~ spl0_304
| ~ spl0_623 ),
inference(forward_demodulation,[],[f8836,f3116]) ).
fof(f8836,plain,
( ! [X11] :
( hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X11
| c_Orderings_Obot__class_Obot(tc_nat) = X11
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))))) )
| ~ spl0_304
| ~ spl0_623 ),
inference(forward_demodulation,[],[f8835,f3116]) ).
fof(f8835,plain,
( ! [X11] :
( c_Orderings_Obot__class_Obot(tc_nat) = X11
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X11
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))))) )
| ~ spl0_304
| ~ spl0_623 ),
inference(forward_demodulation,[],[f8833,f3116]) ).
fof(f8833,plain,
( ! [X11] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X11
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X11
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))))) )
| ~ spl0_623 ),
inference(avatar_component_clause,[],[f8832]) ).
fof(f9063,plain,
( ~ spl0_22
| spl0_644
| ~ spl0_22
| ~ spl0_267
| ~ spl0_295
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4083,f3585,f3046,f2745,f1606,f9060,f1606]) ).
fof(f4083,plain,
( v_n = c_Lattices_Oupper__semilattice__class_Osup(v_i,v_n,tc_nat)
| ~ class_Lattices_Oupper__semilattice(tc_nat)
| ~ spl0_22
| ~ spl0_267
| ~ spl0_295
| ~ spl0_371 ),
inference(forward_demodulation,[],[f4070,f2917]) ).
fof(f4070,plain,
( ~ class_Lattices_Oupper__semilattice(tc_nat)
| v_n = c_Lattices_Oupper__semilattice__class_Osup(v_n,v_i,tc_nat)
| ~ spl0_295
| ~ spl0_371 ),
inference(resolution,[],[f3586,f3048]) ).
fof(f8938,plain,
spl0_643,
inference(avatar_split_clause,[],[f1472,f8936]) ).
fof(f8936,plain,
( spl0_643
<=> ! [X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Ozero__class_Ozero(X5)))
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f1472,plain,
! [X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Ozero__class_Ozero(X5)))
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5)) ),
inference(duplicate_literal_removal,[],[f282]) ).
fof(f282,axiom,
! [X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Ozero__class_Ozero(X5)))
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__nonneg__eq__0__iff_2) ).
fof(f8932,plain,
spl0_642,
inference(avatar_split_clause,[],[f1248,f8930]) ).
fof(f1248,axiom,
! [X2,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diffs0__imp__equal_0) ).
fof(f8928,plain,
spl0_641,
inference(avatar_split_clause,[],[f1242,f8926]) ).
fof(f8926,plain,
( spl0_641
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f1242,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__eq__0__iff_0) ).
fof(f8912,plain,
spl0_640,
inference(avatar_split_clause,[],[f967,f8910]) ).
fof(f8910,plain,
( spl0_640
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f967,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__power_0) ).
fof(f8908,plain,
spl0_639,
inference(avatar_split_clause,[],[f966,f8906]) ).
fof(f8906,plain,
( spl0_639
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f966,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__power_0) ).
fof(f8904,plain,
spl0_638,
inference(avatar_split_clause,[],[f965,f8902]) ).
fof(f8902,plain,
( spl0_638
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f965,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__power__iff_1) ).
fof(f8900,plain,
spl0_637,
inference(avatar_split_clause,[],[f962,f8898]) ).
fof(f8898,plain,
( spl0_637
<=> ! [X2,X5,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X2),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f962,axiom,
! [X2,X11,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),X2),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__less__zero__eq_1) ).
fof(f8896,plain,
spl0_636,
inference(avatar_split_clause,[],[f932,f8894]) ).
fof(f8894,plain,
( spl0_636
<=> ! [X9,X5,X7] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = X9
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)),X9) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f932,axiom,
! [X9,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = X9
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X9)),X9) = X7 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_eq__divide__eq_0) ).
fof(f8892,plain,
spl0_635,
inference(avatar_split_clause,[],[f731,f8890]) ).
fof(f8890,plain,
( spl0_635
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11),X5),c_HOL_Oone__class_Oone(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f731,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11),X5),c_HOL_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__less__1__iff_2) ).
fof(f8888,plain,
spl0_634,
inference(avatar_split_clause,[],[f582,f8886]) ).
fof(f8886,plain,
( spl0_634
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f582,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f8884,plain,
spl0_633,
inference(avatar_split_clause,[],[f581,f8882]) ).
fof(f8882,plain,
( spl0_633
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f581,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f8880,plain,
spl0_632,
inference(avatar_split_clause,[],[f532,f8878]) ).
fof(f8878,plain,
( spl0_632
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f532,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__negative__iff__negative_0) ).
fof(f8876,plain,
spl0_631,
inference(avatar_split_clause,[],[f517,f8874]) ).
fof(f8874,plain,
( spl0_631
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f517,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_one__le__inverse__iff_1) ).
fof(f8872,plain,
( ~ spl0_23
| spl0_630
| ~ spl0_23
| ~ spl0_225
| ~ spl0_295
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f3801,f3476,f3046,f2577,f1611,f8869,f1611]) ).
fof(f3801,plain,
( v_i = c_Lattices_Olower__semilattice__class_Oinf(v_i,v_n,tc_nat)
| ~ class_Lattices_Olower__semilattice(tc_nat)
| ~ spl0_23
| ~ spl0_225
| ~ spl0_295
| ~ spl0_346 ),
inference(forward_demodulation,[],[f3789,f2771]) ).
fof(f3789,plain,
( ~ class_Lattices_Olower__semilattice(tc_nat)
| v_i = c_Lattices_Olower__semilattice__class_Oinf(v_n,v_i,tc_nat)
| ~ spl0_295
| ~ spl0_346 ),
inference(resolution,[],[f3477,f3048]) ).
fof(f8864,plain,
spl0_629,
inference(avatar_split_clause,[],[f467,f8862]) ).
fof(f467,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__is__1_3) ).
fof(f8857,plain,
spl0_628,
inference(avatar_split_clause,[],[f466,f8855]) ).
fof(f466,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__is__1_0) ).
fof(f8853,plain,
spl0_627,
inference(avatar_split_clause,[],[f465,f8851]) ).
fof(f8851,plain,
( spl0_627
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f465,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__positive__iff__positive_0) ).
fof(f8849,plain,
spl0_626,
inference(avatar_split_clause,[],[f449,f8847]) ).
fof(f8847,plain,
( spl0_626
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f449,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__nonpositive__iff__nonpositive_0) ).
fof(f8845,plain,
spl0_625,
inference(avatar_split_clause,[],[f448,f8843]) ).
fof(f8843,plain,
( spl0_625
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f448,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__nonpositive__iff__nonpositive_1) ).
fof(f8841,plain,
spl0_624,
inference(avatar_split_clause,[],[f439,f8839]) ).
fof(f8839,plain,
( spl0_624
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f439,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_one__le__inverse__iff_0) ).
fof(f8834,plain,
spl0_623,
inference(avatar_split_clause,[],[f432,f8832]) ).
fof(f432,axiom,
! [X11] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X11
| hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X11
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__lt__two__imp__zero__or__one_0) ).
fof(f8830,plain,
spl0_622,
inference(avatar_split_clause,[],[f400,f8828]) ).
fof(f8828,plain,
( spl0_622
<=> ! [X2,X5,X1] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Nat_Osemiring__1__class_Oof__nat(X1,X5)),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f400,axiom,
! [X2,X1,X5] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2),X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_Nat_Osemiring__1__class_Oof__nat(X1,X5)),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_of__nat__mult_0) ).
fof(f8826,plain,
spl0_621,
inference(avatar_split_clause,[],[f379,f8824]) ).
fof(f8824,plain,
( spl0_621
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),X11))
| hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11),X5),c_HOL_Oone__class_Oone(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f379,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),X11))
| hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11),X5),c_HOL_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__le__1__iff_2) ).
fof(f8822,plain,
spl0_620,
inference(avatar_split_clause,[],[f349,f8820]) ).
fof(f8820,plain,
( spl0_620
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f349,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_one__le__power_0) ).
fof(f8800,plain,
spl0_619,
inference(avatar_split_clause,[],[f342,f8798]) ).
fof(f8798,plain,
( spl0_619
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f342,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f8796,plain,
spl0_618,
inference(avatar_split_clause,[],[f341,f8794]) ).
fof(f8794,plain,
( spl0_618
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f341,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f8792,plain,
spl0_617,
inference(avatar_split_clause,[],[f338,f8790]) ).
fof(f8790,plain,
( spl0_617
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f338,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__nonnegative__iff__nonnegative_1) ).
fof(f8788,plain,
spl0_616,
inference(avatar_split_clause,[],[f337,f8786]) ).
fof(f8786,plain,
( spl0_616
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f337,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__nonnegative__iff__nonnegative_0) ).
fof(f8784,plain,
spl0_615,
inference(avatar_split_clause,[],[f235,f8782]) ).
fof(f8782,plain,
( spl0_615
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5)),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f235,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5)),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__eq__inf__sup_0) ).
fof(f8780,plain,
spl0_614,
inference(avatar_split_clause,[],[f224,f8778]) ).
fof(f8778,plain,
( spl0_614
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11),X5),c_HOL_Oone__class_Oone(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f224,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_lessequals(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11),X5),c_HOL_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__le__1__iff_1) ).
fof(f8776,plain,
spl0_613,
inference(avatar_split_clause,[],[f169,f8774]) ).
fof(f8774,plain,
( spl0_613
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f169,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_HOL_Oone__class_Oone(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_one__less__inverse__iff_1) ).
fof(f8772,plain,
spl0_612,
inference(avatar_split_clause,[],[f143,f8770]) ).
fof(f8770,plain,
( spl0_612
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f143,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(f8768,plain,
spl0_611,
inference(avatar_split_clause,[],[f142,f8766]) ).
fof(f8766,plain,
( spl0_611
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f142,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(f8764,plain,
spl0_610,
inference(avatar_split_clause,[],[f115,f8762]) ).
fof(f8762,plain,
( spl0_610
<=> ! [X2,X5,X1] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Nat_Osemiring__1__class_Oof__nat(X1,X5)),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f115,axiom,
! [X2,X1,X5] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_Nat_Osemiring__1__class_Oof__nat(X1,X5)),c_Nat_Osemiring__1__class_Oof__nat(X2,X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_of__nat__add_0) ).
fof(f8760,plain,
( ~ spl0_81
| spl0_609
| ~ spl0_197
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2755,f2553,f2454,f8758,f1901]) ).
fof(f8758,plain,
( spl0_609
<=> ! [X4] : hBOOL(hAPP(c_lessequals(X4,tc_Int_Oint),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f2454,plain,
( spl0_197
<=> ! [X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X5,tc_Int_Oint) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f2755,plain,
( ! [X4] :
( hBOOL(hAPP(c_lessequals(X4,tc_Int_Oint),X4))
| ~ class_Lattices_Olower__semilattice(tc_Int_Oint) )
| ~ spl0_197
| ~ spl0_219 ),
inference(superposition,[],[f2554,f2455]) ).
fof(f2455,plain,
( ! [X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X5,tc_Int_Oint) = X5
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f2454]) ).
fof(f8756,plain,
spl0_608,
inference(avatar_split_clause,[],[f103,f8754]) ).
fof(f8754,plain,
( spl0_608
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f103,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_even__less__0__iff_1) ).
fof(f8752,plain,
spl0_607,
inference(avatar_split_clause,[],[f102,f8750]) ).
fof(f8750,plain,
( spl0_607
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f102,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_even__less__0__iff_0) ).
fof(f8748,plain,
spl0_606,
inference(avatar_split_clause,[],[f101,f8746]) ).
fof(f8746,plain,
( spl0_606
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f101,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(f8744,plain,
spl0_605,
inference(avatar_split_clause,[],[f100,f8742]) ).
fof(f8742,plain,
( spl0_605
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f100,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(f8740,plain,
spl0_604,
inference(avatar_split_clause,[],[f84,f8738]) ).
fof(f8738,plain,
( spl0_604
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11),X5),c_HOL_Oone__class_Oone(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f84,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11),X5),c_HOL_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__less__1__iff_1) ).
fof(f8736,plain,
spl0_603,
inference(avatar_split_clause,[],[f38,f8734]) ).
fof(f8734,plain,
( spl0_603
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f38,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_one__less__inverse__iff_0) ).
fof(f8410,plain,
( spl0_602
| ~ spl0_304
| ~ spl0_587 ),
inference(avatar_split_clause,[],[f7607,f7603,f3114,f8408]) ).
fof(f8408,plain,
( spl0_602
<=> ! [X2] :
( hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)))) = X2
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f7603,plain,
( spl0_587
<=> ! [X2] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f7607,plain,
( ! [X2] :
( hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)))) = X2
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2)) )
| ~ spl0_304
| ~ spl0_587 ),
inference(forward_demodulation,[],[f7606,f3116]) ).
fof(f7606,plain,
( ! [X2] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))) = X2 )
| ~ spl0_304
| ~ spl0_587 ),
inference(forward_demodulation,[],[f7604,f3116]) ).
fof(f7604,plain,
( ! [X2] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))) = X2 )
| ~ spl0_587 ),
inference(avatar_component_clause,[],[f7603]) ).
fof(f8406,plain,
( spl0_601
| ~ spl0_304
| ~ spl0_586 ),
inference(avatar_split_clause,[],[f7601,f7598,f3114,f8404]) ).
fof(f8404,plain,
( spl0_601
<=> ! [X2,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,X3)),tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f7598,plain,
( spl0_586
<=> ! [X2,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,X3)),tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f7601,plain,
( ! [X2,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,X3)),tc_nat),X2)) )
| ~ spl0_304
| ~ spl0_586 ),
inference(forward_demodulation,[],[f7599,f3116]) ).
fof(f7599,plain,
( ! [X2,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,X3)),tc_nat),X2)) )
| ~ spl0_586 ),
inference(avatar_component_clause,[],[f7598]) ).
fof(f8402,plain,
( ~ spl0_599
| spl0_600
| ~ spl0_165
| ~ spl0_582 ),
inference(avatar_split_clause,[],[f8336,f7581,f2306,f8400,f8396]) ).
fof(f8396,plain,
( spl0_599
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f8400,plain,
( spl0_600
<=> ! [X0,X1] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f2306,plain,
( spl0_165
<=> ! [X1] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f7581,plain,
( spl0_582
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f8336,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),X1))
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_165
| ~ spl0_582 ),
inference(resolution,[],[f7582,f2307]) ).
fof(f2307,plain,
( ! [X1] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f2306]) ).
fof(f7582,plain,
( ! [X6,X7,X5] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ class_OrderedGroup_Opordered__ab__group__add(X5) )
| ~ spl0_582 ),
inference(avatar_component_clause,[],[f7581]) ).
fof(f8394,plain,
( spl0_598
| ~ spl0_304
| ~ spl0_585 ),
inference(avatar_split_clause,[],[f7596,f7593,f3114,f8392]) ).
fof(f8392,plain,
( spl0_598
<=> ! [X6,X24,X7] :
( hBOOL(hAPP(X24,c_Orderings_Obot__class_Obot(tc_nat)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,tc_nat),X7))
| ~ hBOOL(hAPP(X24,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f7593,plain,
( spl0_585
<=> ! [X6,X24,X7] :
( hBOOL(hAPP(X24,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,tc_nat),X7))
| ~ hBOOL(hAPP(X24,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X6),X7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f7596,plain,
( ! [X6,X7,X24] :
( hBOOL(hAPP(X24,c_Orderings_Obot__class_Obot(tc_nat)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,tc_nat),X7))
| ~ hBOOL(hAPP(X24,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X6),X7))) )
| ~ spl0_304
| ~ spl0_585 ),
inference(forward_demodulation,[],[f7594,f3116]) ).
fof(f7594,plain,
( ! [X6,X7,X24] :
( hBOOL(hAPP(X24,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,tc_nat),X7))
| ~ hBOOL(hAPP(X24,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X6),X7))) )
| ~ spl0_585 ),
inference(avatar_component_clause,[],[f7593]) ).
fof(f8271,plain,
( spl0_597
| ~ spl0_304
| ~ spl0_579 ),
inference(avatar_split_clause,[],[f7571,f7568,f3114,f8269]) ).
fof(f8269,plain,
( spl0_597
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X0
| X1 = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f7568,plain,
( spl0_579
<=> ! [X2,X0,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f7571,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X0
| X1 = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0) )
| ~ spl0_304
| ~ spl0_579 ),
inference(forward_demodulation,[],[f7569,f3116]) ).
fof(f7569,plain,
( ! [X2,X0,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0) )
| ~ spl0_579 ),
inference(avatar_component_clause,[],[f7568]) ).
fof(f8267,plain,
( spl0_596
| ~ spl0_304
| ~ spl0_578 ),
inference(avatar_split_clause,[],[f7547,f7544,f3114,f8265]) ).
fof(f8265,plain,
( spl0_596
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X0
| X1 = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f7544,plain,
( spl0_578
<=> ! [X2,X0,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f7547,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X0
| X1 = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2) )
| ~ spl0_304
| ~ spl0_578 ),
inference(forward_demodulation,[],[f7545,f3116]) ).
fof(f7545,plain,
( ! [X2,X0,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2) )
| ~ spl0_578 ),
inference(avatar_component_clause,[],[f7544]) ).
fof(f7783,plain,
( ~ spl0_43
| spl0_595
| ~ spl0_196
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2754,f2553,f2441,f7781,f1711]) ).
fof(f7781,plain,
( spl0_595
<=> ! [X3] : hBOOL(hAPP(c_lessequals(X3,tc_bool),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f2441,plain,
( spl0_196
<=> ! [X4] : c_Lattices_Olower__semilattice__class_Oinf(X4,X4,tc_bool) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f2754,plain,
( ! [X3] :
( hBOOL(hAPP(c_lessequals(X3,tc_bool),X3))
| ~ class_Lattices_Olower__semilattice(tc_bool) )
| ~ spl0_196
| ~ spl0_219 ),
inference(superposition,[],[f2554,f2442]) ).
fof(f2442,plain,
( ! [X4] : c_Lattices_Olower__semilattice__class_Oinf(X4,X4,tc_bool) = X4
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f2441]) ).
fof(f7667,plain,
spl0_594,
inference(avatar_split_clause,[],[f1488,f7665]) ).
fof(f1488,plain,
! [X28,X29,X5] :
( c_SetInterval_Oord__class_OatLeastLessThan(X29,X28,X5) = c_Set_Oinsert(X29,c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X28,X5),X5)
| ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X29,X5),X28)) ),
inference(forward_demodulation,[],[f1194,f1307]) ).
fof(f1307,axiom,
! [X6,X5,X25] : c_Set_Oinsert(X6,X25,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X25,tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_insert__is__Un_0) ).
fof(f1194,axiom,
! [X28,X29,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X29,X5),X28))
| c_SetInterval_Oord__class_OatLeastLessThan(X29,X28,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X29,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X28,X5),tc_fun(X5,tc_bool)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_ivl__disj__un_I3_J_0) ).
fof(f7663,plain,
spl0_593,
inference(avatar_split_clause,[],[f1243,f7661]) ).
fof(f7661,plain,
( spl0_593
<=> ! [X11,X5,X12] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f1243,axiom,
! [X11,X5,X12] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left__idem_0) ).
fof(f7659,plain,
spl0_592,
inference(avatar_split_clause,[],[f1090,f7657]) ).
fof(f1090,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X2),tc_nat) = c_Set_Oinsert(X2,c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_atLeastLessThanSuc_0) ).
fof(f7655,plain,
spl0_591,
inference(avatar_split_clause,[],[f1051,f7653]) ).
fof(f7653,plain,
( spl0_591
<=> ! [X11,X12,X5,X16] :
( ~ class_Lattices_Odistrib__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),c_Lattices_Olower__semilattice__class_Oinf(X11,X16,X5),X5) = c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Oupper__semilattice__class_Osup(X12,X16,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f1051,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Odistrib__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),c_Lattices_Olower__semilattice__class_Oinf(X11,X16,X5),X5) = c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Oupper__semilattice__class_Osup(X12,X16,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__distrib1_0) ).
fof(f7651,plain,
spl0_590,
inference(avatar_split_clause,[],[f1050,f7649]) ).
fof(f7649,plain,
( spl0_590
<=> ! [X5,X11,X12,X16] :
( ~ class_Lattices_Odistrib__lattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X12,X16,X5),X11,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X11,X5),c_Lattices_Olower__semilattice__class_Oinf(X16,X11,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f1050,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Odistrib__lattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X12,X16,X5),X11,X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X11,X5),c_Lattices_Olower__semilattice__class_Oinf(X16,X11,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__distrib2_0) ).
fof(f7647,plain,
spl0_589,
inference(avatar_split_clause,[],[f1048,f7645]) ).
fof(f7645,plain,
( spl0_589
<=> ! [X5,X11,X12,X16] :
( ~ class_Lattices_Odistrib__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X16,X5),X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f1048,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Odistrib__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X16,X5),X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__inf__distrib1_0) ).
fof(f7611,plain,
spl0_588,
inference(avatar_split_clause,[],[f1047,f7609]) ).
fof(f7609,plain,
( spl0_588
<=> ! [X5,X11,X12,X16] :
( ~ class_Lattices_Odistrib__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X16,X5),X11,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X12,X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X16,X11,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f1047,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Odistrib__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X12,X16,X5),X11,X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X12,X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X16,X11,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__inf__distrib2_0) ).
fof(f7605,plain,
spl0_587,
inference(avatar_split_clause,[],[f1014,f7603]) ).
fof(f1014,axiom,
! [X2] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))) = X2 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Suc__pred_0) ).
fof(f7600,plain,
spl0_586,
inference(avatar_split_clause,[],[f1013,f7598]) ).
fof(f1013,axiom,
! [X2,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(c_Suc,X3)),tc_nat),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__Suc__less_0) ).
fof(f7595,plain,
spl0_585,
inference(avatar_split_clause,[],[f997,f7593]) ).
fof(f997,axiom,
! [X6,X7,X24] :
( hBOOL(hAPP(X24,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,tc_nat),X7))
| ~ hBOOL(hAPP(X24,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X6),X7))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__diff__split_0) ).
fof(f7591,plain,
spl0_584,
inference(avatar_split_clause,[],[f971,f7589]) ).
fof(f7589,plain,
( spl0_584
<=> ! [X6,X5,X12] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_Lim_OLIM(hAPP(c_COMBC(c_HOL_Otimes__class_Otimes(X5),X5,X5,X5),X12),X6,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X12),X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f971,axiom,
! [X6,X5,X12] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_Lim_OLIM(hAPP(c_COMBC(c_HOL_Otimes__class_Otimes(X5),X5,X5,X5),X12),X6,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X12),X5,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left_Ocont_0) ).
fof(f7587,plain,
spl0_583,
inference(avatar_split_clause,[],[f951,f7585]) ).
fof(f7585,plain,
( spl0_583
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f951,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__iff__diff__less__0_1) ).
fof(f7583,plain,
spl0_582,
inference(avatar_split_clause,[],[f950,f7581]) ).
fof(f950,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__iff__diff__less__0_0) ).
fof(f7579,plain,
spl0_581,
inference(avatar_split_clause,[],[f949,f7577]) ).
fof(f7577,plain,
( spl0_581
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f949,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__iff__diff__le__0_1) ).
fof(f7575,plain,
spl0_580,
inference(avatar_split_clause,[],[f948,f7573]) ).
fof(f7573,plain,
( spl0_580
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f948,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X7))
| hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__iff__diff__le__0_0) ).
fof(f7570,plain,
spl0_579,
inference(avatar_split_clause,[],[f881,f7568]) ).
fof(f881,axiom,
! [X2,X0,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__cancel2_0) ).
fof(f7546,plain,
spl0_578,
inference(avatar_split_clause,[],[f879,f7544]) ).
fof(f879,axiom,
! [X2,X0,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__mult__eq__cancel__disj_0) ).
fof(f7542,plain,
spl0_577,
inference(avatar_split_clause,[],[f730,f7540]) ).
fof(f7540,plain,
( spl0_577
<=> ! [X5,X11,X12,X16] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X11))
| ~ hBOOL(hAPP(c_lessequals(X16,X5),X12))
| hBOOL(hAPP(c_lessequals(X16,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f730,axiom,
! [X11,X16,X5,X12] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X11))
| ~ hBOOL(hAPP(c_lessequals(X16,X5),X12))
| hBOOL(hAPP(c_lessequals(X16,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_xt1_I6_J_0) ).
fof(f7538,plain,
spl0_576,
inference(avatar_split_clause,[],[f729,f7536]) ).
fof(f7536,plain,
( spl0_576
<=> ! [X11,X12,X5,X16] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X16,X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X16,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f729,axiom,
! [X11,X16,X5,X12] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X16,X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X16,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_xt1_I7_J_0) ).
fof(f7534,plain,
spl0_575,
inference(avatar_split_clause,[],[f728,f7532]) ).
fof(f7532,plain,
( spl0_575
<=> ! [X5,X11,X12,X16] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X16,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X16,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f728,axiom,
! [X11,X16,X5,X12] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X16,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X16,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_xt1_I8_J_0) ).
fof(f7530,plain,
spl0_574,
inference(avatar_split_clause,[],[f726,f7528]) ).
fof(f7528,plain,
( spl0_574
<=> ! [X11,X12,X5,X16] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X16))
| hBOOL(hAPP(c_lessequals(X11,X5),X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f726,axiom,
! [X11,X16,X5,X12] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X16))
| hBOOL(hAPP(c_lessequals(X11,X5),X16)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_order__trans_0) ).
fof(f7526,plain,
spl0_573,
inference(avatar_split_clause,[],[f724,f7524]) ).
fof(f724,axiom,
! [X11,X16,X5,X12] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X16))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X16)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_order__less__le__trans_0) ).
fof(f7522,plain,
spl0_572,
inference(avatar_split_clause,[],[f723,f7520]) ).
fof(f723,axiom,
! [X11,X16,X5,X12] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X16))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X16)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_order__le__less__trans_0) ).
fof(f7518,plain,
spl0_571,
inference(avatar_split_clause,[],[f524,f7516]) ).
fof(f7516,plain,
( spl0_571
<=> ! [X11,X5,X12] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| hBOOL(hAPP(c_lessequals(X12,X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f524,axiom,
! [X11,X5,X12] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| hBOOL(hAPP(c_lessequals(X12,X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__le__not__le_2) ).
fof(f7514,plain,
spl0_570,
inference(avatar_split_clause,[],[f288,f7512]) ).
fof(f288,axiom,
! [X11,X16,X5,X12] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X16))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X16)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_order__less__trans_0) ).
fof(f7510,plain,
spl0_569,
inference(avatar_split_clause,[],[f287,f7508]) ).
fof(f287,axiom,
! [X11,X16,X5,X12] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X16,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X16,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_xt1_I10_J_0) ).
fof(f7506,plain,
spl0_568,
inference(avatar_split_clause,[],[f281,f7504]) ).
fof(f7504,plain,
( spl0_568
<=> ! [X6,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| c_Lim_OLIM(hAPP(c_COMBC(c_HOL_Oinverse__class_Odivide(X5),X5,X5,X5),X12),X6,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X12),X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f281,axiom,
! [X6,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| c_Lim_OLIM(hAPP(c_COMBC(c_HOL_Oinverse__class_Odivide(X5),X5,X5,X5),X12),X6,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X12),X5,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_Ocont_0) ).
fof(f7502,plain,
spl0_567,
inference(avatar_split_clause,[],[f187,f7500]) ).
fof(f7500,plain,
( spl0_567
<=> ! [X11,X12,X5,X16] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| X12 = X16
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f187,axiom,
! [X11,X16,X5,X12] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| X12 = X16
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X16) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__ringb_Oadd__cancel_0) ).
fof(f7498,plain,
spl0_566,
inference(avatar_split_clause,[],[f98,f7496]) ).
fof(f98,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__Suc_0) ).
fof(f7494,plain,
spl0_565,
inference(avatar_split_clause,[],[f97,f7492]) ).
fof(f97,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__Suc__right_0) ).
fof(f7490,plain,
spl0_564,
inference(avatar_split_clause,[],[f59,f7488]) ).
fof(f59,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),X4))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X4,tc_nat),X0))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X3),tc_nat),X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__trans__Suc_0) ).
fof(f7486,plain,
spl0_563,
inference(avatar_split_clause,[],[f24,f7484]) ).
fof(f7484,plain,
( spl0_563
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f24,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X7),X6) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__divide_0) ).
fof(f7482,plain,
spl0_562,
inference(avatar_split_clause,[],[f10,f7480]) ).
fof(f7480,plain,
( spl0_562
<=> ! [X2,X0,X1] :
( X1 = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f10,axiom,
! [X2,X0,X1] :
( X1 = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X1) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,X0)),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Suc__mult__cancel1_0) ).
fof(f7051,plain,
( spl0_561
| ~ spl0_304
| ~ spl0_543 ),
inference(avatar_split_clause,[],[f6933,f6929,f3114,f7049]) ).
fof(f7049,plain,
( spl0_561
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f6929,plain,
( spl0_543
<=> ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f6933,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2)) )
| ~ spl0_304
| ~ spl0_543 ),
inference(forward_demodulation,[],[f6932,f3116]) ).
fof(f6932,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_304
| ~ spl0_543 ),
inference(forward_demodulation,[],[f6930,f3116]) ).
fof(f6930,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_543 ),
inference(avatar_component_clause,[],[f6929]) ).
fof(f7047,plain,
( spl0_560
| ~ spl0_304
| ~ spl0_542 ),
inference(avatar_split_clause,[],[f6927,f6923,f3114,f7045]) ).
fof(f7045,plain,
( spl0_560
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f6923,plain,
( spl0_542
<=> ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f6927,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X1)) )
| ~ spl0_304
| ~ spl0_542 ),
inference(forward_demodulation,[],[f6926,f3116]) ).
fof(f6926,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_304
| ~ spl0_542 ),
inference(forward_demodulation,[],[f6924,f3116]) ).
fof(f6924,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) )
| ~ spl0_542 ),
inference(avatar_component_clause,[],[f6923]) ).
fof(f7043,plain,
( spl0_559
| ~ spl0_304
| ~ spl0_541 ),
inference(avatar_split_clause,[],[f6921,f6916,f3114,f7041]) ).
fof(f7041,plain,
( spl0_559
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| c_Orderings_Obot__class_Obot(tc_nat) = X1
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f6916,plain,
( spl0_541
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X1
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f6921,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| c_Orderings_Obot__class_Obot(tc_nat) = X1
| c_Orderings_Obot__class_Obot(tc_nat) = X2 )
| ~ spl0_304
| ~ spl0_541 ),
inference(forward_demodulation,[],[f6920,f3116]) ).
fof(f6920,plain,
( ! [X2,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X1
| c_Orderings_Obot__class_Obot(tc_nat) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_304
| ~ spl0_541 ),
inference(forward_demodulation,[],[f6919,f3116]) ).
fof(f6919,plain,
( ! [X2,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X1
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_304
| ~ spl0_541 ),
inference(forward_demodulation,[],[f6917,f3116]) ).
fof(f6917,plain,
( ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X1
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_541 ),
inference(avatar_component_clause,[],[f6916]) ).
fof(f7000,plain,
spl0_558,
inference(avatar_split_clause,[],[f1263,f6998]) ).
fof(f6998,plain,
( spl0_558
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| c_HOL_Ozero__class_Ozero(X5) = X7
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f1263,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| c_HOL_Ozero__class_Ozero(X5) = X7
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_no__zero__divirors__neq0_0) ).
fof(f6996,plain,
spl0_557,
inference(avatar_split_clause,[],[f1261,f6994]) ).
fof(f6994,plain,
( spl0_557
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) = X7
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f1261,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) = X7
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__eq__0__iff_0) ).
fof(f6992,plain,
spl0_556,
inference(avatar_split_clause,[],[f1222,f6990]) ).
fof(f6990,plain,
( spl0_556
<=> ! [X5,X6,X25,X26] : c_Lattices_Oupper__semilattice__class_Osup(X25,c_Set_Oinsert(X6,X26,X5),tc_fun(X5,tc_bool)) = c_Set_Oinsert(X6,c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f1222,axiom,
! [X6,X26,X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,c_Set_Oinsert(X6,X26,X5),tc_fun(X5,tc_bool)) = c_Set_Oinsert(X6,c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),X5),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Un__insert__right_0) ).
fof(f6988,plain,
spl0_555,
inference(avatar_split_clause,[],[f1221,f6986]) ).
fof(f6986,plain,
( spl0_555
<=> ! [X5,X6,X27,X26] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X6,X26,X5),X27,tc_fun(X5,tc_bool)) = c_Set_Oinsert(X6,c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f1221,axiom,
! [X6,X26,X27,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X6,X26,X5),X27,tc_fun(X5,tc_bool)) = c_Set_Oinsert(X6,c_Lattices_Oupper__semilattice__class_Osup(X26,X27,tc_fun(X5,tc_bool)),X5),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Un__insert__left_0) ).
fof(f6984,plain,
spl0_554,
inference(avatar_split_clause,[],[f1178,f6982]) ).
fof(f6982,plain,
( spl0_554
<=> ! [X5,X29,X28,X1] :
( ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X1,X5),c_SetInterval_Oord__class_OatLeastLessThan(X1,X28,X5),tc_fun(X5,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f1178,axiom,
! [X28,X29,X1,X5] :
( ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X1,X5),c_SetInterval_Oord__class_OatLeastLessThan(X1,X28,X5),tc_fun(X5,tc_bool)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_ivl__disj__int_I9_J_0) ).
fof(f6980,plain,
spl0_553,
inference(avatar_split_clause,[],[f1169,f6978]) ).
fof(f6978,plain,
( spl0_553
<=> ! [X6,X5,X7] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f1169,axiom,
! [X6,X7,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5) = c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Sup__binary_0) ).
fof(f6976,plain,
spl0_552,
inference(avatar_split_clause,[],[f1064,f6974]) ).
fof(f6974,plain,
( spl0_552
<=> ! [X2,X3] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X2))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f1064,axiom,
! [X2,X3] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X2))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X3)) = X3 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__diff__cancel_0) ).
fof(f6972,plain,
spl0_551,
inference(avatar_split_clause,[],[f1006,f6970]) ).
fof(f6970,plain,
( spl0_551
<=> ! [X5,X29,X28,X1] :
( ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastLessThan(X29,X1,X5),c_SetInterval_Oord__class_OatLeastLessThan(X1,X28,X5),tc_fun(X5,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f1006,axiom,
! [X28,X29,X1,X5] :
( ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatLeastLessThan(X29,X1,X5),c_SetInterval_Oord__class_OatLeastLessThan(X1,X28,X5),tc_fun(X5,tc_bool)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_ivl__disj__int_I11_J_0) ).
fof(f6968,plain,
spl0_550,
inference(avatar_split_clause,[],[f940,f6966]) ).
fof(f6966,plain,
( spl0_550
<=> ! [X9,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),X9)),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f940,axiom,
! [X9,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),X9)),X9) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__eq__eq_4) ).
fof(f6964,plain,
spl0_549,
inference(avatar_split_clause,[],[f790,f6962]) ).
fof(f6962,plain,
( spl0_549
<=> ! [X6,X9,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X9
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)),X9) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f790,axiom,
! [X6,X9,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X9
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X9)),X9) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_eq__divide__imp_0) ).
fof(f6953,plain,
spl0_548,
inference(avatar_split_clause,[],[f744,f6951]) ).
fof(f6951,plain,
( spl0_548
<=> ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f744,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__diff__inverse_0) ).
fof(f6949,plain,
spl0_547,
inference(avatar_split_clause,[],[f554,f6947]) ).
fof(f6947,plain,
( spl0_547
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f554,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2)) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__add__diff__inverse_0) ).
fof(f6945,plain,
spl0_546,
inference(avatar_split_clause,[],[f534,f6943]) ).
fof(f6943,plain,
( spl0_546
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f534,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),c_HOL_Ozero__class_Ozero(X5)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_negative__imp__inverse__negative_0) ).
fof(f6941,plain,
spl0_545,
inference(avatar_split_clause,[],[f463,f6939]) ).
fof(f6939,plain,
( spl0_545
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f463,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_positive__imp__inverse__positive_0) ).
fof(f6937,plain,
spl0_544,
inference(avatar_split_clause,[],[f453,f6935]) ).
fof(f6935,plain,
( spl0_544
<=> ! [X2,X1] :
( hAPP(c_Suc,X1) = X2
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f453,axiom,
! [X2,X1] :
( hAPP(c_Suc,X1) = X2
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),tc_nat),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Suc__lessI_0) ).
fof(f6931,plain,
spl0_543,
inference(avatar_split_clause,[],[f446,f6929]) ).
fof(f446,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__0__less__mult__iff_1) ).
fof(f6925,plain,
spl0_542,
inference(avatar_split_clause,[],[f445,f6923]) ).
fof(f445,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__0__less__mult__iff_0) ).
fof(f6918,plain,
spl0_541,
inference(avatar_split_clause,[],[f391,f6916]) ).
fof(f391,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) = X1
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_one__is__add_2) ).
fof(f6914,plain,
spl0_540,
inference(avatar_split_clause,[],[f164,f6912]) ).
fof(f6912,plain,
( spl0_540
<=> ! [X2,X1] :
( hAPP(c_Suc,X2) = X1
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(c_Suc,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f164,axiom,
! [X2,X1] :
( hAPP(c_Suc,X2) = X1
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(c_Suc,X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__SucE_0) ).
fof(f6910,plain,
spl0_539,
inference(avatar_split_clause,[],[f68,f6908]) ).
fof(f6908,plain,
( spl0_539
<=> ! [X6,X10,X20,X21,X5,X22] :
( ~ class_RealVector_Oreal__normed__algebra__1(X5)
| ~ class_RealVector_Ometric__space(X20)
| X21 = X22
| ~ c_Lim_OLIM(X10,X6,X22,X5,X20)
| ~ c_Lim_OLIM(X10,X6,X21,X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f68,axiom,
! [X21,X10,X6,X5,X22,X20] :
( ~ class_RealVector_Oreal__normed__algebra__1(X5)
| ~ class_RealVector_Ometric__space(X20)
| X21 = X22
| ~ c_Lim_OLIM(X10,X6,X22,X5,X20)
| ~ c_Lim_OLIM(X10,X6,X21,X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__unique_0) ).
fof(f6778,plain,
( spl0_538
| ~ spl0_304
| ~ spl0_527 ),
inference(avatar_split_clause,[],[f6491,f6488,f3114,f6776]) ).
fof(f6776,plain,
( spl0_538
<=> ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_Orderings_Obot__class_Obot(tc_nat))
| ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f6488,plain,
( spl0_527
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f6491,plain,
( ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_Orderings_Obot__class_Obot(tc_nat))
| ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5) )
| ~ spl0_304
| ~ spl0_527 ),
inference(forward_demodulation,[],[f6489,f3116]) ).
fof(f6489,plain,
( ! [X6,X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_527 ),
inference(avatar_component_clause,[],[f6488]) ).
fof(f6774,plain,
( spl0_537
| ~ spl0_304
| ~ spl0_526 ),
inference(avatar_split_clause,[],[f6486,f6483,f3114,f6772]) ).
fof(f6772,plain,
( spl0_537
<=> ! [X2,X5] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| ~ class_Ring__and__Field_Osemiring__0(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f6483,plain,
( spl0_526
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f6486,plain,
( ! [X2,X5] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| ~ class_Ring__and__Field_Osemiring__0(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2) )
| ~ spl0_304
| ~ spl0_526 ),
inference(forward_demodulation,[],[f6484,f3116]) ).
fof(f6484,plain,
( ! [X2,X5] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2) )
| ~ spl0_526 ),
inference(avatar_component_clause,[],[f6483]) ).
fof(f6766,plain,
( spl0_536
| ~ spl0_304
| ~ spl0_524 ),
inference(avatar_split_clause,[],[f6477,f6474,f3114,f6764]) ).
fof(f6764,plain,
( spl0_536
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f6474,plain,
( spl0_524
<=> ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f6477,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2)) )
| ~ spl0_304
| ~ spl0_524 ),
inference(forward_demodulation,[],[f6475,f3116]) ).
fof(f6475,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1))) )
| ~ spl0_524 ),
inference(avatar_component_clause,[],[f6474]) ).
fof(f6762,plain,
( spl0_535
| ~ spl0_304
| ~ spl0_523 ),
inference(avatar_split_clause,[],[f6464,f6461,f3114,f6760]) ).
fof(f6760,plain,
( spl0_535
<=> ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f6461,plain,
( spl0_523
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f6464,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1)))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2)) )
| ~ spl0_304
| ~ spl0_523 ),
inference(forward_demodulation,[],[f6462,f3116]) ).
fof(f6462,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1))) )
| ~ spl0_523 ),
inference(avatar_component_clause,[],[f6461]) ).
fof(f6683,plain,
( spl0_534
| ~ spl0_304
| ~ spl0_512 ),
inference(avatar_split_clause,[],[f6418,f6415,f3114,f6681]) ).
fof(f6681,plain,
( spl0_534
<=> ! [X2,X5] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f6415,plain,
( spl0_512
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f6418,plain,
( ! [X2,X5] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) )
| ~ spl0_304
| ~ spl0_512 ),
inference(forward_demodulation,[],[f6416,f3116]) ).
fof(f6416,plain,
( ! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) )
| ~ spl0_512 ),
inference(avatar_component_clause,[],[f6415]) ).
fof(f6679,plain,
( spl0_533
| ~ spl0_304
| ~ spl0_511 ),
inference(avatar_split_clause,[],[f6413,f6410,f3114,f6677]) ).
fof(f6677,plain,
( spl0_533
<=> ! [X2,X5] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f6410,plain,
( spl0_511
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f6413,plain,
( ! [X2,X5] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X2))
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) )
| ~ spl0_304
| ~ spl0_511 ),
inference(forward_demodulation,[],[f6411,f3116]) ).
fof(f6411,plain,
( ! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) )
| ~ spl0_511 ),
inference(avatar_component_clause,[],[f6410]) ).
fof(f6547,plain,
( ~ spl0_531
| ~ spl0_532
| spl0_397
| ~ spl0_217
| ~ spl0_304
| ~ spl0_430 ),
inference(avatar_split_clause,[],[f4809,f4595,f3114,f2536,f4235,f6544,f6540]) ).
fof(f6540,plain,
( spl0_531
<=> class_Ring__and__Field_Oidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f6544,plain,
( spl0_532
<=> class_Int_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f4235,plain,
( spl0_397
<=> ! [X2] : c_Orderings_Obot__class_Obot(tc_nat) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f2536,plain,
( spl0_217
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f4595,plain,
( spl0_430
<=> ! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| X11 = X12
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f4809,plain,
( ! [X4] :
( c_Orderings_Obot__class_Obot(tc_nat) = X4
| ~ class_Int_Onumber__ring(tc_nat)
| ~ class_Ring__and__Field_Oidom(tc_nat) )
| ~ spl0_217
| ~ spl0_304
| ~ spl0_430 ),
inference(forward_demodulation,[],[f4806,f3116]) ).
fof(f4806,plain,
( ! [X4] :
( ~ class_Int_Onumber__ring(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ class_Ring__and__Field_Oidom(tc_nat) )
| ~ spl0_217
| ~ spl0_430 ),
inference(trivial_inequality_removal,[],[f4802]) ).
fof(f4802,plain,
( ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Int_Onumber__ring(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ class_Ring__and__Field_Oidom(tc_nat) )
| ~ spl0_217
| ~ spl0_430 ),
inference(superposition,[],[f4596,f2537]) ).
fof(f2537,plain,
( ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2)
| ~ spl0_217 ),
inference(avatar_component_clause,[],[f2536]) ).
fof(f4596,plain,
( ! [X11,X5,X12] :
( c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X12)
| ~ class_Int_Onumber__ring(X5)
| X11 = X12
| ~ class_Ring__and__Field_Oidom(X5) )
| ~ spl0_430 ),
inference(avatar_component_clause,[],[f4595]) ).
fof(f6503,plain,
spl0_530,
inference(avatar_split_clause,[],[f1309,f6501]) ).
fof(f6501,plain,
( spl0_530
<=> ! [X25,X5,X26] : c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X25,c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f1309,axiom,
! [X26,X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X25,c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Un__left__absorb_0) ).
fof(f6499,plain,
spl0_529,
inference(avatar_split_clause,[],[f1290,f6497]) ).
fof(f6497,plain,
( spl0_529
<=> ! [X6,X5,X7] :
( X6 = X7
| c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5) != c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f1290,axiom,
! [X6,X7,X5] :
( X6 = X7
| c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5) != c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_singleton__inject_0) ).
fof(f6495,plain,
spl0_528,
inference(avatar_split_clause,[],[f1282,f6493]) ).
fof(f6493,plain,
( spl0_528
<=> ! [X5,X17,X11,X12] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| X12 = X17
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X11) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X17),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f1282,axiom,
! [X11,X17,X5,X12] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| X12 = X17
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X11) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X17),X12) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_eq__eqI_1) ).
fof(f6490,plain,
spl0_527,
inference(avatar_split_clause,[],[f1276,f6488]) ).
fof(f1276,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| ~ class_Ring__and__Field_Ono__zero__divisors(X5)
| ~ class_Ring__and__Field_Omult__zero(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__eq__0__iff_1) ).
fof(f6485,plain,
spl0_526,
inference(avatar_split_clause,[],[f1239,f6483]) ).
fof(f1239,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__0__left_1) ).
fof(f6481,plain,
spl0_525,
inference(avatar_split_clause,[],[f1088,f6479]) ).
fof(f6479,plain,
( spl0_525
<=> ! [X29,X5,X28] :
( ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatMost(X29,X5),c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X28,X5),tc_fun(X5,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f1088,axiom,
! [X28,X29,X5] :
( ~ class_Orderings_Oorder(X5)
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_SetInterval_Oord__class_OatMost(X29,X5),c_SetInterval_Oord__class_OgreaterThanLessThan(X29,X28,X5),tc_fun(X5,tc_bool)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_ivl__disj__int_I1_J_0) ).
fof(f6476,plain,
spl0_524,
inference(avatar_split_clause,[],[f994,f6474]) ).
fof(f994,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__diff_0) ).
fof(f6463,plain,
spl0_523,
inference(avatar_split_clause,[],[f993,f6461]) ).
fof(f993,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__diff_1) ).
fof(f6459,plain,
spl0_522,
inference(avatar_split_clause,[],[f977,f6457]) ).
fof(f6457,plain,
( spl0_522
<=> ! [X18,X5,X11] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_Series_Osummable(X18,X5)
| c_Series_Osummable(hAPP(hAPP(c_COMBB(X5,X5,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X5),X11)),X18),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f977,axiom,
! [X11,X18,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_Series_Osummable(X18,X5)
| c_Series_Osummable(hAPP(hAPP(c_COMBB(X5,X5,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X5),X11)),X18),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right_Osummable_0) ).
fof(f6455,plain,
spl0_521,
inference(avatar_split_clause,[],[f975,f6453]) ).
fof(f6453,plain,
( spl0_521
<=> ! [X6,X18,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OZseq(X18,X5)
| c_SEQ_OZseq(hAPP(hAPP(c_COMBB(X5,X5,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X5),X6)),X18),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f975,axiom,
! [X18,X6,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OZseq(X18,X5)
| c_SEQ_OZseq(hAPP(hAPP(c_COMBB(X5,X5,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X5),X6)),X18),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Zseq__mult__right_0) ).
fof(f6451,plain,
spl0_520,
inference(avatar_split_clause,[],[f972,f6449]) ).
fof(f6449,plain,
( spl0_520
<=> ! [X18,X5,X11] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OCauchy(X18,X5)
| c_SEQ_OCauchy(hAPP(hAPP(c_COMBB(X5,X5,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X5),X11)),X18),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f972,axiom,
! [X11,X18,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| ~ c_SEQ_OCauchy(X18,X5)
| c_SEQ_OCauchy(hAPP(hAPP(c_COMBB(X5,X5,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X5),X11)),X18),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right_OCauchy_0) ).
fof(f6447,plain,
spl0_519,
inference(avatar_split_clause,[],[f721,f6445]) ).
fof(f6445,plain,
( spl0_519
<=> ! [X4,X0,X3] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X0))
| hBOOL(hAPP(c_lessequals(X3,tc_nat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f721,axiom,
! [X3,X0,X4] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| ~ hBOOL(hAPP(c_lessequals(X4,tc_nat),X0))
| hBOOL(hAPP(c_lessequals(X3,tc_nat),X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__trans_0) ).
fof(f6443,plain,
spl0_518,
inference(avatar_split_clause,[],[f669,f6441]) ).
fof(f6441,plain,
( spl0_518
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f669,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),X6) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_field__inverse_0) ).
fof(f6439,plain,
spl0_517,
inference(avatar_split_clause,[],[f668,f6437]) ).
fof(f6437,plain,
( spl0_517
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f668,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)),X6) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_left__inverse_0) ).
fof(f6435,plain,
spl0_516,
inference(avatar_split_clause,[],[f667,f6433]) ).
fof(f6433,plain,
( spl0_516
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f667,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_right__inverse_0) ).
fof(f6431,plain,
spl0_515,
inference(avatar_split_clause,[],[f576,f6429]) ).
fof(f6429,plain,
( spl0_515
<=> ! [X25,X5,X26] : c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X25,c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f576,axiom,
! [X26,X5,X25] : c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X25,c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Int__left__absorb_0) ).
fof(f6427,plain,
spl0_514,
inference(avatar_split_clause,[],[f570,f6425]) ).
fof(f6425,plain,
( spl0_514
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Ofield(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f570,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__inverse_0) ).
fof(f6423,plain,
( ~ spl0_34
| ~ spl0_513
| ~ spl0_153
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f3960,f3547,f2255,f6420,f1666]) ).
fof(f6420,plain,
( spl0_513
<=> hBOOL(hAPP(c_HOL_Oord__class_Oless(v_n,tc_nat),v_i)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f3547,plain,
( spl0_362
<=> ! [X6,X5,X7] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f3960,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_n,tc_nat),v_i))
| ~ class_Orderings_Opreorder(tc_nat)
| ~ spl0_153
| ~ spl0_362 ),
inference(resolution,[],[f3548,f2257]) ).
fof(f3548,plain,
( ! [X6,X7,X5] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ class_Orderings_Opreorder(X5) )
| ~ spl0_362 ),
inference(avatar_component_clause,[],[f3547]) ).
fof(f6417,plain,
spl0_512,
inference(avatar_split_clause,[],[f561,f6415]) ).
fof(f561,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_of__nat__0__less__iff_1) ).
fof(f6412,plain,
spl0_511,
inference(avatar_split_clause,[],[f560,f6410]) ).
fof(f560,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_of__nat__0__less__iff_0) ).
fof(f6408,plain,
spl0_510,
inference(avatar_split_clause,[],[f550,f6406]) ).
fof(f6406,plain,
( spl0_510
<=> ! [X2,X5,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f550,axiom,
! [X2,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_of__nat__less__iff_1) ).
fof(f6404,plain,
spl0_509,
inference(avatar_split_clause,[],[f549,f6402]) ).
fof(f6402,plain,
( spl0_509
<=> ! [X2,X5,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f549,axiom,
! [X2,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_of__nat__less__iff_0) ).
fof(f6400,plain,
spl0_508,
inference(avatar_split_clause,[],[f266,f6398]) ).
fof(f6398,plain,
( spl0_508
<=> ! [X2,X5,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f266,axiom,
! [X2,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_of__nat__le__iff_0) ).
fof(f6396,plain,
spl0_507,
inference(avatar_split_clause,[],[f265,f6394]) ).
fof(f6394,plain,
( spl0_507
<=> ! [X2,X5,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f265,axiom,
! [X2,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X2,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_of__nat__le__iff_1) ).
fof(f6392,plain,
spl0_506,
inference(avatar_split_clause,[],[f190,f6390]) ).
fof(f6390,plain,
( spl0_506
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| X7 = X9
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X6) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f190,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| X7 = X9
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X9),X6) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X6) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__right__cancel_0) ).
fof(f6388,plain,
spl0_505,
inference(avatar_split_clause,[],[f189,f6386]) ).
fof(f6386,plain,
( spl0_505
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| X7 = X9
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f189,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| X7 = X9
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__left__cancel_0) ).
fof(f6384,plain,
spl0_504,
inference(avatar_split_clause,[],[f188,f6382]) ).
fof(f6382,plain,
( spl0_504
<=> ! [X5,X9,X7,X6] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X5)
| X7 = X9
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f188,axiom,
! [X6,X9,X7,X5] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X5)
| X7 = X9
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X9) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__imp__eq_0) ).
fof(f6380,plain,
spl0_503,
inference(avatar_split_clause,[],[f133,f6378]) ).
fof(f6378,plain,
( spl0_503
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Ofield(X5)
| X6 = X7
| c_HOL_Ozero__class_Ozero(X5) = X7
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7) != c_HOL_Oone__class_Oone(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f133,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| X6 = X7
| c_HOL_Ozero__class_Ozero(X5) = X7
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),X7) != c_HOL_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_right__inverse__eq_0) ).
fof(f6376,plain,
( spl0_502
| ~ spl0_172
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f3750,f3464,f2335,f6374]) ).
fof(f6374,plain,
( spl0_502
<=> ! [X12,X11] :
( hBOOL(hAPP(c_lessequals(X11,X12),X11))
| ~ class_Orderings_Olinorder(X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f3750,plain,
( ! [X11,X12] :
( hBOOL(hAPP(c_lessequals(X11,X12),X11))
| ~ class_Orderings_Olinorder(X12) )
| ~ spl0_172
| ~ spl0_343 ),
inference(duplicate_literal_removal,[],[f3737]) ).
fof(f3737,plain,
( ! [X11,X12] :
( hBOOL(hAPP(c_lessequals(X11,X12),X11))
| ~ class_Orderings_Olinorder(X12)
| ~ class_Orderings_Olinorder(X12) )
| ~ spl0_172
| ~ spl0_343 ),
inference(resolution,[],[f3465,f2336]) ).
fof(f6037,plain,
( ~ spl0_34
| ~ spl0_501
| ~ spl0_153
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f3686,f3438,f2255,f6034,f1666]) ).
fof(f3686,plain,
( ~ hBOOL(hAPP(c_lessequals(v_n,tc_nat),v_i))
| ~ class_Orderings_Opreorder(tc_nat)
| ~ spl0_153
| ~ spl0_337 ),
inference(resolution,[],[f3439,f2257]) ).
fof(f5890,plain,
( spl0_500
| ~ spl0_304
| ~ spl0_469 ),
inference(avatar_split_clause,[],[f4989,f4984,f3114,f5888]) ).
fof(f5888,plain,
( spl0_500
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X2
| c_Orderings_Obot__class_Obot(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f4984,plain,
( spl0_469
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f4989,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X2
| c_Orderings_Obot__class_Obot(tc_nat) = X1 )
| ~ spl0_304
| ~ spl0_469 ),
inference(forward_demodulation,[],[f4988,f3116]) ).
fof(f4988,plain,
( ! [X2,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| c_Orderings_Obot__class_Obot(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) )
| ~ spl0_304
| ~ spl0_469 ),
inference(forward_demodulation,[],[f4987,f3116]) ).
fof(f4987,plain,
( ! [X2,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) )
| ~ spl0_304
| ~ spl0_469 ),
inference(forward_demodulation,[],[f4985,f3116]) ).
fof(f4985,plain,
( ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) )
| ~ spl0_469 ),
inference(avatar_component_clause,[],[f4984]) ).
fof(f5793,plain,
( spl0_499
| ~ spl0_304
| ~ spl0_465 ),
inference(avatar_split_clause,[],[f4970,f4966,f3114,f5790]) ).
fof(f5790,plain,
( spl0_499
<=> hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f4966,plain,
( spl0_465
<=> hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f4970,plain,
( hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))),hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)))
| ~ spl0_304
| ~ spl0_465 ),
inference(forward_demodulation,[],[f4968,f3116]) ).
fof(f4968,plain,
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ spl0_465 ),
inference(avatar_component_clause,[],[f4966]) ).
fof(f5788,plain,
( spl0_498
| ~ spl0_149
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f3625,f3406,f2238,f5786]) ).
fof(f5786,plain,
( spl0_498
<=> ! [X1] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),tc_nat),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f3625,plain,
( ! [X1] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),tc_nat),X1))
| ~ spl0_149
| ~ spl0_329 ),
inference(resolution,[],[f3407,f2239]) ).
fof(f5565,plain,
( spl0_497
| ~ spl0_167
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f3404,f3337,f2314,f5562]) ).
fof(f5562,plain,
( spl0_497
<=> hBOOL(hAPP(c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),c_Orderings_Obot__class_Obot(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f3404,plain,
( hBOOL(hAPP(c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),c_Orderings_Obot__class_Obot(tc_nat)))
| ~ spl0_167
| ~ spl0_328 ),
inference(superposition,[],[f2315,f3339]) ).
fof(f5516,plain,
( spl0_496
| ~ spl0_304
| ~ spl0_451 ),
inference(avatar_split_clause,[],[f4907,f4903,f3114,f5514]) ).
fof(f5514,plain,
( spl0_496
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f4903,plain,
( spl0_451
<=> ! [X2,X1] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f4907,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X2 )
| ~ spl0_304
| ~ spl0_451 ),
inference(forward_demodulation,[],[f4906,f3116]) ).
fof(f4906,plain,
( ! [X2,X1] :
( hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_304
| ~ spl0_451 ),
inference(forward_demodulation,[],[f4904,f3116]) ).
fof(f4904,plain,
( ! [X2,X1] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_451 ),
inference(avatar_component_clause,[],[f4903]) ).
fof(f5512,plain,
( spl0_495
| ~ spl0_304
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f4901,f4897,f3114,f5510]) ).
fof(f5510,plain,
( spl0_495
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f4897,plain,
( spl0_450
<=> ! [X2,X1] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f4901,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat))
| hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X1 )
| ~ spl0_304
| ~ spl0_450 ),
inference(forward_demodulation,[],[f4900,f3116]) ).
fof(f4900,plain,
( ! [X2,X1] :
( hAPP(c_Suc,c_Orderings_Obot__class_Obot(tc_nat)) = X1
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_304
| ~ spl0_450 ),
inference(forward_demodulation,[],[f4898,f3116]) ).
fof(f4898,plain,
( ! [X2,X1] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) )
| ~ spl0_450 ),
inference(avatar_component_clause,[],[f4897]) ).
fof(f5357,plain,
( spl0_494
| ~ spl0_170
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3026,f2938,f2327,f5355]) ).
fof(f5355,plain,
( spl0_494
<=> ! [X1] : hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(c_Suc,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f3026,plain,
( ! [X1] : hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(c_Suc,X1)))
| ~ spl0_170
| ~ spl0_276 ),
inference(resolution,[],[f2939,f2328]) ).
fof(f5120,plain,
( spl0_493
| ~ spl0_45
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2549,f2516,f1721,f5118]) ).
fof(f5118,plain,
( spl0_493
<=> ! [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_493])]) ).
fof(f1721,plain,
( spl0_45
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f2516,plain,
( spl0_212
<=> ! [X5,X11] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Orderings_Obot__class_Obot(X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X5),X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f2549,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_45
| ~ spl0_212 ),
inference(resolution,[],[f2517,f1723]) ).
fof(f1723,plain,
( class_Lattices_Obounded__lattice(tc_bool)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f1721]) ).
fof(f2517,plain,
( ! [X11,X5] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Orderings_Obot__class_Obot(X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X5),X11,X5) )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2516]) ).
fof(f5082,plain,
spl0_492,
inference(avatar_split_clause,[],[f1307,f5080]) ).
fof(f5078,plain,
spl0_491,
inference(avatar_split_clause,[],[f1303,f5076]) ).
fof(f5076,plain,
( spl0_491
<=> ! [X25,X5,X26] :
( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = X26
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f1303,axiom,
! [X26,X5,X25] :
( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = X26
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Un__empty_1) ).
fof(f5074,plain,
spl0_490,
inference(avatar_split_clause,[],[f1302,f5072]) ).
fof(f5072,plain,
( spl0_490
<=> ! [X25,X5,X26] :
( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = X25
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f1302,axiom,
! [X26,X5,X25] :
( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = X25
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) != c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Un__empty_0) ).
fof(f5070,plain,
spl0_489,
inference(avatar_split_clause,[],[f1289,f5068]) ).
fof(f5068,plain,
( spl0_489
<=> ! [X11,X12,X5,X16] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X12,X16,X5),X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f1289,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X12,X16,X5),X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),X16,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__aci_I6_J_0) ).
fof(f5066,plain,
spl0_488,
inference(avatar_split_clause,[],[f1288,f5064]) ).
fof(f5064,plain,
( spl0_488
<=> ! [X5,X11,X12,X16] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X12,X16,X5),X5) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f1288,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X12,X16,X5),X5) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__aci_I7_J_0) ).
fof(f5062,plain,
spl0_487,
inference(avatar_split_clause,[],[f1285,f5060]) ).
fof(f5060,plain,
( spl0_487
<=> ! [X11,X12,X5,X16] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X12,X16,X5),X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f1285,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X12,X16,X5),X5) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),X16,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__assoc_0) ).
fof(f5058,plain,
spl0_486,
inference(avatar_split_clause,[],[f1284,f5056]) ).
fof(f5056,plain,
( spl0_486
<=> ! [X5,X11,X12,X16] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X12,X16,X5),X5) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f1284,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X12,X16,X5),X5) = c_Lattices_Oupper__semilattice__class_Osup(X12,c_Lattices_Oupper__semilattice__class_Osup(X11,X16,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__left__commute_0) ).
fof(f5054,plain,
spl0_485,
inference(avatar_split_clause,[],[f1258,f5052]) ).
fof(f5052,plain,
( spl0_485
<=> ! [X11,X5,X25,X26] :
( hBOOL(hAPP(X26,X11))
| hBOOL(hAPP(X25,X11))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f1258,axiom,
! [X11,X26,X5,X25] :
( hBOOL(hAPP(X26,X11))
| hBOOL(hAPP(X25,X11))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup1E_0) ).
fof(f5050,plain,
( spl0_484
| ~ spl0_45
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2547,f2512,f1721,f5048]) ).
fof(f5048,plain,
( spl0_484
<=> ! [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_484])]) ).
fof(f2512,plain,
( spl0_211
<=> ! [X5,X11] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Orderings_Obot__class_Obot(X5) = c_Lattices_Olower__semilattice__class_Oinf(X11,c_Orderings_Obot__class_Obot(X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f2547,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_45
| ~ spl0_211 ),
inference(resolution,[],[f2513,f1723]) ).
fof(f2513,plain,
( ! [X11,X5] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Orderings_Obot__class_Obot(X5) = c_Lattices_Olower__semilattice__class_Oinf(X11,c_Orderings_Obot__class_Obot(X5),X5) )
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f2512]) ).
fof(f5046,plain,
spl0_483,
inference(avatar_split_clause,[],[f1089,f5044]) ).
fof(f5044,plain,
( spl0_483
<=> ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X2),tc_nat) = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f1089,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X2),tc_nat) = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_atLeastLessThanSuc_1) ).
fof(f5042,plain,
spl0_482,
inference(avatar_split_clause,[],[f1057,f5040]) ).
fof(f5040,plain,
( spl0_482
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X1)),hAPP(c_Suc,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f1057,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,X1)),hAPP(c_Suc,X2)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__Suc__Suc_0) ).
fof(f5038,plain,
spl0_481,
inference(avatar_split_clause,[],[f1056,f5036]) ).
fof(f5036,plain,
( spl0_481
<=> ! [X4,X0,X2] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X4,tc_nat),X0))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X2),tc_nat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f1056,axiom,
! [X2,X0,X4] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X4,tc_nat),X0))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X4),X2),tc_nat),X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__imp__diff__less_0) ).
fof(f5034,plain,
spl0_480,
inference(avatar_split_clause,[],[f1046,f5032]) ).
fof(f1046,axiom,
! [X11,X6,X7,X5] :
( ~ class_Lattices_Oupper__semilattice(X5)
| hBOOL(hAPP(c_lessequals(X6,X5),X11))
| ~ hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5),X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__supE_0) ).
fof(f5030,plain,
spl0_479,
inference(avatar_split_clause,[],[f1045,f5028]) ).
fof(f1045,axiom,
! [X11,X6,X7,X5] :
( ~ class_Lattices_Oupper__semilattice(X5)
| hBOOL(hAPP(c_lessequals(X7,X5),X11))
| ~ hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5),X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__supE_1) ).
fof(f5026,plain,
spl0_478,
inference(avatar_split_clause,[],[f1044,f5024]) ).
fof(f5024,plain,
( spl0_478
<=> ! [X5,X11,X6,X7] :
( ~ class_Lattices_Oupper__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X6))
| hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f1044,axiom,
! [X11,X6,X7,X5] :
( ~ class_Lattices_Oupper__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X6))
| hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__supI1_0) ).
fof(f5022,plain,
spl0_477,
inference(avatar_split_clause,[],[f1043,f5020]) ).
fof(f1043,axiom,
! [X11,X6,X7,X5] :
( ~ class_Lattices_Oupper__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X7))
| hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__supI2_0) ).
fof(f5018,plain,
spl0_476,
inference(avatar_split_clause,[],[f1040,f5016]) ).
fof(f1040,axiom,
! [X11,X6,X7,X5] :
( ~ class_Lattices_Oupper__semilattice(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X6))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__supI1_0) ).
fof(f5014,plain,
spl0_475,
inference(avatar_split_clause,[],[f1039,f5012]) ).
fof(f1039,axiom,
! [X11,X6,X7,X5] :
( ~ class_Lattices_Oupper__semilattice(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X7))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X6,X7,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__supI2_0) ).
fof(f5010,plain,
spl0_474,
inference(avatar_split_clause,[],[f1010,f5008]) ).
fof(f1010,axiom,
! [X29,X0,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X29,X5),X0))
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X0,X29,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_greaterThanLessThan__empty_0) ).
fof(f5006,plain,
( spl0_473
| ~ spl0_121
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2541,f2480,f2101,f5003]) ).
fof(f5003,plain,
( spl0_473
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f2480,plain,
( spl0_203
<=> ! [X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Oone__class_Oone(X5) = hAPP(c_HOL_Oinverse__class_Oinverse(X5),c_HOL_Oone__class_Oone(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2541,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ spl0_121
| ~ spl0_203 ),
inference(resolution,[],[f2481,f2103]) ).
fof(f2103,plain,
( class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex)
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f2101]) ).
fof(f2481,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Oone__class_Oone(X5) = hAPP(c_HOL_Oinverse__class_Oinverse(X5),c_HOL_Oone__class_Oone(X5)) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f2480]) ).
fof(f5001,plain,
spl0_472,
inference(avatar_split_clause,[],[f1005,f4999]) ).
fof(f4999,plain,
( spl0_472
<=> ! [X6,X5,X7] :
( ~ class_Orderings_Oorder(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X6,X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f1005,axiom,
! [X6,X7,X5] :
( ~ class_Orderings_Oorder(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X6,X7,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_atLeastLessThan__empty__iff_1) ).
fof(f4997,plain,
spl0_471,
inference(avatar_split_clause,[],[f1004,f4995]) ).
fof(f4995,plain,
( spl0_471
<=> ! [X6,X5,X7] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X6,X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f1004,axiom,
! [X6,X7,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(X6,X7,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_atLeastLessThan__empty__iff_0) ).
fof(f4993,plain,
spl0_470,
inference(avatar_split_clause,[],[f1003,f4991]) ).
fof(f1003,axiom,
! [X6,X7,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X6))
| c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X6,X7,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_atLeastLessThan__empty_0) ).
fof(f4986,plain,
spl0_469,
inference(avatar_split_clause,[],[f887,f4984]) ).
fof(f887,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__is__0_0) ).
fof(f4982,plain,
spl0_468,
inference(avatar_split_clause,[],[f740,f4980]) ).
fof(f4980,plain,
( spl0_468
<=> ! [X2,X1] :
( X1 = X2
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f740,axiom,
! [X2,X1] :
( X1 = X2
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__less__Suc__eq_0) ).
fof(f4978,plain,
spl0_467,
inference(avatar_split_clause,[],[f737,f4976]) ).
fof(f4976,plain,
( spl0_467
<=> ! [X5,X10,X20,X6] :
( ~ class_RealVector_Ometric__space(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OisCont(X10,X6,X5,X20)
| c_Lim_OLIM(X10,X6,hAPP(X10,X6),X5,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f737,axiom,
! [X10,X6,X5,X20] :
( ~ class_RealVector_Ometric__space(X20)
| ~ class_RealVector_Ometric__space(X5)
| ~ c_Lim_OisCont(X10,X6,X5,X20)
| c_Lim_OLIM(X10,X6,hAPP(X10,X6),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_isCont__def_0) ).
fof(f4974,plain,
spl0_466,
inference(avatar_split_clause,[],[f736,f4972]) ).
fof(f736,axiom,
! [X10,X6,X5,X20] :
( ~ class_RealVector_Ometric__space(X5)
| ~ class_RealVector_Ometric__space(X20)
| c_Lim_OisCont(X10,X6,X5,X20)
| ~ c_Lim_OLIM(X10,X6,hAPP(X10,X6),X5,X20) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_isCont__def_1) ).
fof(f4969,plain,
spl0_465,
inference(avatar_split_clause,[],[f511,f4966]) ).
fof(f511,axiom,
hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__eq__1__iff_2) ).
fof(f4964,plain,
spl0_464,
inference(avatar_split_clause,[],[f406,f4962]) ).
fof(f4962,plain,
( spl0_464
<=> ! [X2,X1] :
( X1 = X2
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f406,axiom,
! [X2,X1] :
( X1 = X2
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__antisym_0) ).
fof(f4960,plain,
spl0_463,
inference(avatar_split_clause,[],[f351,f4958]) ).
fof(f4958,plain,
( spl0_463
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f4956,plain,
( spl0_462
| ~ spl0_113
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2540,f2468,f2061,f4953]) ).
fof(f4953,plain,
( spl0_462
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f2468,plain,
( spl0_200
<=> ! [X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(c_HOL_Oinverse__class_Oinverse(X5),c_HOL_Ozero__class_Ozero(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f2540,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_HOL_Oinverse__class_Oinverse(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl0_113
| ~ spl0_200 ),
inference(resolution,[],[f2469,f2063]) ).
fof(f2469,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(c_HOL_Oinverse__class_Oinverse(X5),c_HOL_Ozero__class_Ozero(X5)) )
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f2468]) ).
fof(f4951,plain,
spl0_461,
inference(avatar_split_clause,[],[f350,f4949]) ).
fof(f4949,plain,
( spl0_461
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f4947,plain,
spl0_460,
inference(avatar_split_clause,[],[f306,f4945]) ).
fof(f4945,plain,
( spl0_460
<=> ! [X4,X1,X3] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| hBOOL(hAPP(c_lessequals(X3,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f306,axiom,
! [X3,X1,X4] :
( ~ hBOOL(hAPP(c_lessequals(X3,tc_nat),X4))
| hBOOL(hAPP(c_lessequals(X3,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_trans__le__add2_0) ).
fof(f4943,plain,
spl0_459,
inference(avatar_split_clause,[],[f304,f4941]) ).
fof(f4941,plain,
( spl0_459
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X0,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f304,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X0,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),tc_nat),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__leE_1) ).
fof(f4939,plain,
spl0_458,
inference(avatar_split_clause,[],[f303,f4937]) ).
fof(f4937,plain,
( spl0_458
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f303,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0),tc_nat),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__leE_0) ).
fof(f4935,plain,
spl0_457,
inference(avatar_split_clause,[],[f301,f4933]) ).
fof(f301,axiom,
! [X11,X16,X12] :
( ~ hBOOL(hAPP(c_lessequals(X11,tc_nat),X12))
| hBOOL(hAPP(c_lessequals(X11,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X16))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_termination__basic__simps_I3_J_0) ).
fof(f4931,plain,
spl0_456,
inference(avatar_split_clause,[],[f274,f4929]) ).
fof(f4929,plain,
( spl0_456
<=> ! [X29,X5,X10] :
( ~ class_RealVector_Ometric__space(X5)
| c_SEQ_OLIMSEQ(X10,X29,X5)
| ~ c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc),X29,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f274,axiom,
! [X10,X29,X5] :
( ~ class_RealVector_Ometric__space(X5)
| c_SEQ_OLIMSEQ(X10,X29,X5)
| ~ c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc),X29,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__Suc__iff_0) ).
fof(f4927,plain,
spl0_455,
inference(avatar_split_clause,[],[f273,f4925]) ).
fof(f4925,plain,
( spl0_455
<=> ! [X29,X5,X10] :
( ~ class_RealVector_Ometric__space(X5)
| ~ c_SEQ_OLIMSEQ(X10,X29,X5)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc),X29,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f273,axiom,
! [X10,X29,X5] :
( ~ class_RealVector_Ometric__space(X5)
| ~ c_SEQ_OLIMSEQ(X10,X29,X5)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_nat,X5,tc_nat),X10),c_Suc),X29,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__Suc_0) ).
fof(f4923,plain,
spl0_454,
inference(avatar_split_clause,[],[f234,f4921]) ).
fof(f4921,plain,
( spl0_454
<=> ! [X4,X1,X3] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),X4))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f234,axiom,
! [X3,X1,X4] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),X4))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X4))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_trans__less__add2_0) ).
fof(f4919,plain,
spl0_453,
inference(avatar_split_clause,[],[f232,f4917]) ).
fof(f232,axiom,
! [X3,X0,X4] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),X0))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat),X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__lessD1_0) ).
fof(f4915,plain,
spl0_452,
inference(avatar_split_clause,[],[f230,f4913]) ).
fof(f4913,plain,
( spl0_452
<=> ! [X11,X16,X12] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f230,axiom,
! [X11,X16,X12] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X12),X16))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_termination__basic__simps_I1_J_0) ).
fof(f4905,plain,
spl0_451,
inference(avatar_split_clause,[],[f223,f4903]) ).
fof(f223,axiom,
! [X2,X1] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X2
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__eq__1__iff_1) ).
fof(f4899,plain,
spl0_450,
inference(avatar_split_clause,[],[f222,f4897]) ).
fof(f222,axiom,
! [X2,X1] :
( hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) != hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__eq__1__iff_0) ).
fof(f4895,plain,
spl0_449,
inference(avatar_split_clause,[],[f204,f4893]) ).
fof(f4893,plain,
( spl0_449
<=> ! [X5,X1] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,X1),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Oone__class_Oone(X5)),c_Nat_Osemiring__1__class_Oof__nat(X1,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f204,axiom,
! [X1,X5] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(c_Suc,X1),X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Oone__class_Oone(X5)),c_Nat_Osemiring__1__class_Oof__nat(X1,X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_of__nat__Suc_0) ).
fof(f4891,plain,
spl0_448,
inference(avatar_split_clause,[],[f176,f4889]) ).
fof(f4889,plain,
( spl0_448
<=> ! [X6,X5,X11,X7] :
( ~ class_Lattices_Olower__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X11))
| hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5),X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f176,axiom,
! [X11,X6,X7,X5] :
( ~ class_Lattices_Olower__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X7,X5),X11))
| hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5),X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__infI2_0) ).
fof(f4887,plain,
spl0_447,
inference(avatar_split_clause,[],[f175,f4885]) ).
fof(f4885,plain,
( spl0_447
<=> ! [X5,X11,X6,X7] :
( ~ class_Lattices_Olower__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X11))
| hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5),X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f175,axiom,
! [X11,X6,X7,X5] :
( ~ class_Lattices_Olower__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X6,X5),X11))
| hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5),X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__infI1_0) ).
fof(f4883,plain,
spl0_446,
inference(avatar_split_clause,[],[f174,f4881]) ).
fof(f174,axiom,
! [X11,X6,X7,X5] :
( ~ class_Lattices_Olower__semilattice(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),X7))
| ~ hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__infE_1) ).
fof(f4879,plain,
spl0_445,
inference(avatar_split_clause,[],[f173,f4877]) ).
fof(f173,axiom,
! [X11,X6,X7,X5] :
( ~ class_Lattices_Olower__semilattice(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),X6))
| ~ hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__infE_0) ).
fof(f4875,plain,
spl0_444,
inference(avatar_split_clause,[],[f127,f4873]) ).
fof(f4873,plain,
( spl0_444
<=> ! [X11,X5,X12] :
( ~ class_Orderings_Olinorder(X5)
| X11 = X12
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f127,axiom,
! [X11,X5,X12] :
( ~ class_Orderings_Olinorder(X5)
| X11 = X12
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_linorder__antisym__conv1_0) ).
fof(f4871,plain,
spl0_443,
inference(avatar_split_clause,[],[f121,f4869]) ).
fof(f4869,plain,
( spl0_443
<=> ! [X11,X5,X12] :
( ~ class_Orderings_Oorder(X5)
| X11 = X12
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f121,axiom,
! [X11,X5,X12] :
( ~ class_Orderings_Oorder(X5)
| X11 = X12
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_order__le__less_0) ).
fof(f4867,plain,
spl0_442,
inference(avatar_split_clause,[],[f116,f4865]) ).
fof(f4865,plain,
( spl0_442
<=> ! [X11,X5,X25,X26] :
( ~ hBOOL(hAPP(X25,X11))
| ~ hBOOL(hAPP(X26,X11))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f116,axiom,
! [X11,X26,X5,X25] :
( ~ hBOOL(hAPP(X25,X11))
| ~ hBOOL(hAPP(X26,X11))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf1I_0) ).
fof(f4859,plain,
spl0_441,
inference(avatar_split_clause,[],[f96,f4857]) ).
fof(f4857,plain,
( spl0_441
<=> ! [X11,X12,X5,X16] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X16,X5),X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f96,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X16,X5),X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X16,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__aci_I2_J_0) ).
fof(f4855,plain,
spl0_440,
inference(avatar_split_clause,[],[f95,f4853]) ).
fof(f4853,plain,
( spl0_440
<=> ! [X5,X11,X12,X16] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X16,X5),X5) = c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Olower__semilattice__class_Oinf(X11,X16,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f95,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X16,X5),X5) = c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Olower__semilattice__class_Oinf(X11,X16,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__aci_I3_J_0) ).
fof(f4851,plain,
spl0_439,
inference(avatar_split_clause,[],[f92,f4849]) ).
fof(f4849,plain,
( spl0_439
<=> ! [X11,X12,X5,X16] :
( ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X16,X5),X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X16,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f92,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X16,X5),X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X16,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__assoc_0) ).
fof(f4847,plain,
spl0_438,
inference(avatar_split_clause,[],[f91,f4845]) ).
fof(f4845,plain,
( spl0_438
<=> ! [X5,X11,X12,X16] :
( ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X16,X5),X5) = c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Olower__semilattice__class_Oinf(X11,X16,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f91,axiom,
! [X11,X16,X5,X12] :
( ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X12,X16,X5),X5) = c_Lattices_Olower__semilattice__class_Oinf(X12,c_Lattices_Olower__semilattice__class_Oinf(X11,X16,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__left__commute_0) ).
fof(f4843,plain,
spl0_437,
inference(avatar_split_clause,[],[f77,f4841]) ).
fof(f4841,plain,
( spl0_437
<=> ! [X11,X5,X12] :
( ~ class_Orderings_Oorder(X5)
| X11 = X12
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f77,axiom,
! [X11,X5,X12] :
( ~ class_Orderings_Oorder(X5)
| X11 = X12
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_order__antisym_0) ).
fof(f4839,plain,
spl0_436,
inference(avatar_split_clause,[],[f66,f4837]) ).
fof(f4837,plain,
( spl0_436
<=> ! [X11,X5,X12] :
( ~ class_Orderings_Olinorder(X5)
| X11 = X12
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f66,axiom,
! [X11,X5,X12] :
( ~ class_Orderings_Olinorder(X5)
| X11 = X12
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_linorder__less__linear_0) ).
fof(f4835,plain,
spl0_435,
inference(avatar_split_clause,[],[f63,f4833]) ).
fof(f4833,plain,
( spl0_435
<=> ! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| X11 = X12
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f63,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| X11 = X12
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_linorder__neqE__ordered__idom_0) ).
fof(f4831,plain,
spl0_434,
inference(avatar_split_clause,[],[f62,f4829]) ).
fof(f62,axiom,
! [X11,X6,X7,X5] :
( ~ class_Lattices_Olower__semilattice(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5),X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__infI1_0) ).
fof(f4827,plain,
spl0_433,
inference(avatar_split_clause,[],[f61,f4825]) ).
fof(f61,axiom,
! [X11,X6,X7,X5] :
( ~ class_Lattices_Olower__semilattice(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X11))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X6,X7,X5),X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__infI2_0) ).
fof(f4823,plain,
spl0_432,
inference(avatar_split_clause,[],[f19,f4821]) ).
fof(f4821,plain,
( spl0_432
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6) = X7
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7) != c_HOL_Oone__class_Oone(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f19,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6) = X7
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7) != c_HOL_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__unique_0) ).
fof(f4601,plain,
spl0_431,
inference(avatar_split_clause,[],[f1469,f4599]) ).
fof(f4599,plain,
( spl0_431
<=> ! [X24,X54,X20,X31,X55,X5] : hAPP(hAPP(hAPP(c_COMBB(X20,X5,X31),X24),X54),X55) = hAPP(X24,hAPP(X54,X55)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f1469,axiom,
! [X31,X54,X55,X24,X5,X20] : hAPP(hAPP(hAPP(c_COMBB(X20,X5,X31),X24),X54),X55) = hAPP(X24,hAPP(X54,X55)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_ATP__Linkup_OCOMBB__def_0) ).
fof(f4597,plain,
spl0_430,
inference(avatar_split_clause,[],[f1293,f4595]) ).
fof(f1293,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| X11 = X12
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X12) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__ringb_Osubr0__iff_0) ).
fof(f4593,plain,
spl0_429,
inference(avatar_split_clause,[],[f1280,f4591]) ).
fof(f1280,axiom,
! [X31,X54,X55,X24,X5,X20] : hAPP(c_COMBS(X24,X54,X20,X31,X5),X55) = hAPP(hAPP(X24,X55),hAPP(X54,X55)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_COMBS__def_0) ).
fof(f4589,plain,
spl0_428,
inference(avatar_split_clause,[],[f964,f4587]) ).
fof(f964,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Osemiring__0(X5)
| ~ class_Power_Opower(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Ozero__class_Ozero(X5)),hAPP(c_Suc,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__0__Suc_0) ).
fof(f4581,plain,
spl0_427,
inference(avatar_split_clause,[],[f819,f4579]) ).
fof(f819,axiom,
! [X11,X6,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X6,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X6),X5,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right_Ocont_0) ).
fof(f4577,plain,
spl0_426,
inference(avatar_split_clause,[],[f746,f4575]) ).
fof(f4575,plain,
( spl0_426
<=> ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),hAPP(c_Suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f746,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),hAPP(c_Suc,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Suc__le__mono_0) ).
fof(f4573,plain,
spl0_425,
inference(avatar_split_clause,[],[f745,f4571]) ).
fof(f4571,plain,
( spl0_425
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),hAPP(c_Suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f745,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X1))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),hAPP(c_Suc,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Suc__le__mono_1) ).
fof(f4569,plain,
spl0_424,
inference(avatar_split_clause,[],[f614,f4567]) ).
fof(f4567,plain,
( spl0_424
<=> ! [X6,X5,X11] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X6) != X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f614,axiom,
! [X11,X6,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X6) != X11 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f4565,plain,
spl0_423,
inference(avatar_split_clause,[],[f501,f4563]) ).
fof(f4563,plain,
( spl0_423
<=> ! [X2,X11] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X11),tc_nat),hAPP(c_Suc,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f501,axiom,
! [X2,X11] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X11),tc_nat),hAPP(c_Suc,X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__Suc__eq__0__disj_3) ).
fof(f4561,plain,
spl0_422,
inference(avatar_split_clause,[],[f500,f4559]) ).
fof(f4559,plain,
( spl0_422
<=> ! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),tc_nat),hAPP(c_Suc,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f500,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),tc_nat),hAPP(c_Suc,X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Suc__less__eq_0) ).
fof(f4557,plain,
spl0_421,
inference(avatar_split_clause,[],[f470,f4555]) ).
fof(f470,axiom,
! [X6,X5] :
( ~ class_RealVector_Oreal__normed__div__algebra(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_Lim_OLIM(c_HOL_Oinverse__class_Oinverse(X5),X6,hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6),X5,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIM__inverse__fun_0) ).
fof(f4553,plain,
spl0_420,
inference(avatar_split_clause,[],[f186,f4551]) ).
fof(f186,axiom,
! [X11,X16,X12] :
( X12 = X16
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X12) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X11),X16) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_natgb_Oadd__cancel_0) ).
fof(f4549,plain,
spl0_419,
inference(avatar_split_clause,[],[f184,f4547]) ).
fof(f184,axiom,
! [X2,X0,X1] :
( X1 = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__add__right__cancel_0) ).
fof(f4545,plain,
spl0_418,
inference(avatar_split_clause,[],[f156,f4543]) ).
fof(f4543,plain,
( spl0_418
<=> ! [X1] : hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f156,axiom,
! [X1] : hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X1)))),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__cube_0) ).
fof(f4541,plain,
( spl0_417
| ~ spl0_271
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3321,f3114,f2857,f4538]) ).
fof(f4538,plain,
( spl0_417
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f2857,plain,
( spl0_271
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f3321,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),tc_Complex_Ocomplex)
| ~ spl0_271
| ~ spl0_304 ),
inference(superposition,[],[f2859,f3116]) ).
fof(f2859,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex)
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f2857]) ).
fof(f4536,plain,
spl0_416,
inference(avatar_split_clause,[],[f154,f4534]) ).
fof(f4534,plain,
( spl0_416
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Oone__class_Oone(X5)),c_HOL_Oone__class_Oone(X5)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f154,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Oone__class_Oone(X5)),c_HOL_Oone__class_Oone(X5)))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__two_0) ).
fof(f4532,plain,
spl0_415,
inference(avatar_split_clause,[],[f6,f4530]) ).
fof(f4530,plain,
( spl0_415
<=> ! [X6,X5,X7] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| X6 = X7
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6) != hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f6,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| X6 = X7
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6) != hAPP(c_HOL_Oinverse__class_Oinverse(X5),X7) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__eq__iff__eq_0) ).
fof(f4439,plain,
( spl0_414
| ~ spl0_304
| ~ spl0_404 ),
inference(avatar_split_clause,[],[f4269,f4266,f3114,f4437]) ).
fof(f4437,plain,
( spl0_414
<=> ! [X5,X11] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_Orderings_Obot__class_Obot(tc_nat)),X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ class_Ring__and__Field_Oordered__idom(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f4266,plain,
( spl0_404
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_HOL_Ozero__class_Ozero(tc_nat)),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f4269,plain,
( ! [X11,X5] :
( ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_Orderings_Obot__class_Obot(tc_nat)),X5),c_HOL_Ozero__class_Ozero(X5)))
| ~ class_Ring__and__Field_Oordered__idom(X5) )
| ~ spl0_304
| ~ spl0_404 ),
inference(forward_demodulation,[],[f4267,f3116]) ).
fof(f4267,plain,
( ! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_HOL_Ozero__class_Ozero(tc_nat)),X5),c_HOL_Ozero__class_Ozero(X5))) )
| ~ spl0_404 ),
inference(avatar_component_clause,[],[f4266]) ).
fof(f4435,plain,
( spl0_413
| ~ spl0_304
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f4264,f4261,f3114,f4433]) ).
fof(f4261,plain,
( spl0_403
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_HOL_Ozero__class_Ozero(tc_nat)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f4264,plain,
( ! [X11,X5] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_Orderings_Obot__class_Obot(tc_nat))))
| ~ class_Ring__and__Field_Oordered__idom(X5) )
| ~ spl0_304
| ~ spl0_403 ),
inference(forward_demodulation,[],[f4262,f3116]) ).
fof(f4262,plain,
( ! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_HOL_Ozero__class_Ozero(tc_nat)))) )
| ~ spl0_403 ),
inference(avatar_component_clause,[],[f4261]) ).
fof(f4429,plain,
( spl0_412
| ~ spl0_304
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f4255,f4252,f3114,f4427]) ).
fof(f4252,plain,
( spl0_401
<=> ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f4255,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| hBOOL(hAPP(c_lessequals(X1,tc_nat),X2)) )
| ~ spl0_304
| ~ spl0_401 ),
inference(forward_demodulation,[],[f4253,f3116]) ).
fof(f4253,plain,
( ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) )
| ~ spl0_401 ),
inference(avatar_component_clause,[],[f4252]) ).
fof(f4425,plain,
( spl0_411
| ~ spl0_304
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f4250,f4247,f3114,f4423]) ).
fof(f4247,plain,
( spl0_400
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f4250,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2)) )
| ~ spl0_304
| ~ spl0_400 ),
inference(forward_demodulation,[],[f4248,f3116]) ).
fof(f4248,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) )
| ~ spl0_400 ),
inference(avatar_component_clause,[],[f4247]) ).
fof(f4414,plain,
( ~ spl0_410
| spl0_397
| ~ spl0_217
| ~ spl0_304
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f4163,f3609,f3114,f2536,f4235,f4411]) ).
fof(f4411,plain,
( spl0_410
<=> class_OrderedGroup_Ogroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f3609,plain,
( spl0_377
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| X6 = X7
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f4163,plain,
( ! [X2] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_217
| ~ spl0_304
| ~ spl0_377 ),
inference(forward_demodulation,[],[f4162,f3116]) ).
fof(f4162,plain,
( ! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_217
| ~ spl0_377 ),
inference(trivial_inequality_removal,[],[f4159]) ).
fof(f4159,plain,
( ! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_217
| ~ spl0_377 ),
inference(superposition,[],[f3610,f2537]) ).
fof(f3610,plain,
( ! [X6,X7,X5] :
( c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)
| X6 = X7
| ~ class_OrderedGroup_Ogroup__add(X5) )
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f3609]) ).
fof(f4289,plain,
spl0_409,
inference(avatar_split_clause,[],[f1279,f4287]) ).
fof(f4287,plain,
( spl0_409
<=> ! [X24,X54,X20,X31,X55,X5] : hAPP(hAPP(c_COMBC(X24,X20,X31,X5),X54),X55) = hAPP(hAPP(X24,X55),X54) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f1279,axiom,
! [X31,X54,X55,X24,X5,X20] : hAPP(hAPP(c_COMBC(X24,X20,X31,X5),X54),X55) = hAPP(hAPP(X24,X55),X54),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_COMBC__def_0) ).
fof(f4285,plain,
spl0_408,
inference(avatar_split_clause,[],[f1277,f4283]) ).
fof(f1277,axiom,
! [X11,X5,X12,X25] : c_Set_Oinsert(X11,c_Set_Oinsert(X12,X25,X5),X5) = c_Set_Oinsert(X12,c_Set_Oinsert(X11,X25,X5),X5),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_insert__commute_0) ).
fof(f4281,plain,
spl0_407,
inference(avatar_split_clause,[],[f1273,f4279]) ).
fof(f1273,axiom,
! [X6,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X7) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X7),X6) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f4277,plain,
spl0_406,
inference(avatar_split_clause,[],[f1249,f4275]) ).
fof(f1249,axiom,
! [X10,X5,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Finite__Set_Osetsum(X20,X5),X10),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setsum__empty_0) ).
fof(f4273,plain,
spl0_405,
inference(avatar_split_clause,[],[f1241,f4271]) ).
fof(f4271,plain,
( spl0_405
<=> ! [X6,X2,X5] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f1241,axiom,
! [X2,X6,X5] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_field__power__not__zero_0) ).
fof(f4268,plain,
spl0_404,
inference(avatar_split_clause,[],[f1142,f4266]) ).
fof(f1142,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_HOL_Ozero__class_Ozero(tc_nat)),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__le__zero__eq_0) ).
fof(f4263,plain,
spl0_403,
inference(avatar_split_clause,[],[f1138,f4261]) ).
fof(f1138,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_HOL_Ozero__class_Ozero(tc_nat)))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__power__eq_3) ).
fof(f4259,plain,
spl0_402,
inference(avatar_split_clause,[],[f1000,f4257]) ).
fof(f1000,axiom,
! [X6,X5,X25] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,X25,X5),X5) = c_Lattices_Oupper__semilattice__class_Osup(X6,c_Complete__Lattice_OSup__class_OSup(X25,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Sup__insert_0) ).
fof(f4254,plain,
spl0_401,
inference(avatar_split_clause,[],[f996,f4252]) ).
fof(f996,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__is__0__eq_0) ).
fof(f4249,plain,
spl0_400,
inference(avatar_split_clause,[],[f995,f4247]) ).
fof(f995,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__is__0__eq_1) ).
fof(f4245,plain,
spl0_399,
inference(avatar_split_clause,[],[f860,f4243]) ).
fof(f860,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7)),X7) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__diff__cancel_0) ).
fof(f4241,plain,
spl0_398,
inference(avatar_split_clause,[],[f858,f4239]) ).
fof(f858,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)),X7) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__add__cancel_0) ).
fof(f4237,plain,
( ~ spl0_396
| spl0_397
| ~ spl0_217
| ~ spl0_304
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f4154,f3605,f3114,f2536,f4235,f4231]) ).
fof(f4231,plain,
( spl0_396
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f3605,plain,
( spl0_376
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| X6 = X7
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f4154,plain,
( ! [X2] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_217
| ~ spl0_304
| ~ spl0_376 ),
inference(forward_demodulation,[],[f4153,f3116]) ).
fof(f4153,plain,
( ! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_217
| ~ spl0_376 ),
inference(trivial_inequality_removal,[],[f4150]) ).
fof(f4150,plain,
( ! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_217
| ~ spl0_376 ),
inference(superposition,[],[f3606,f2537]) ).
fof(f3606,plain,
( ! [X6,X7,X5] :
( c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7)
| X6 = X7
| ~ class_OrderedGroup_Oab__group__add(X5) )
| ~ spl0_376 ),
inference(avatar_component_clause,[],[f3605]) ).
fof(f4229,plain,
spl0_395,
inference(avatar_split_clause,[],[f613,f4227]) ).
fof(f4227,plain,
( spl0_395
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f613,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X6) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_double__eq__0__iff_0) ).
fof(f4225,plain,
spl0_394,
inference(avatar_split_clause,[],[f507,f4223]) ).
fof(f4223,plain,
( spl0_394
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f507,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nonzero__inverse__inverse__eq_0) ).
fof(f4221,plain,
spl0_393,
inference(avatar_split_clause,[],[f456,f4219]) ).
fof(f4219,plain,
( spl0_393
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oone__class_Oone(X5) = X11
| c_HOL_Oone__class_Oone(X5) != hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f456,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oone__class_Oone(X5) = X11
| c_HOL_Oone__class_Oone(X5) != hAPP(c_HOL_Oinverse__class_Oinverse(X5),X11) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__eq__1__iff_0) ).
fof(f4217,plain,
spl0_392,
inference(avatar_split_clause,[],[f415,f4215]) ).
fof(f415,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = X11
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X11),X11) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_right__inverse__eq_1) ).
fof(f4213,plain,
spl0_391,
inference(avatar_split_clause,[],[f369,f4211]) ).
fof(f4211,plain,
( spl0_391
<=> ! [X6,X5,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f369,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X7),X6) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_comm__monoid__add_Omult__commute_0) ).
fof(f4209,plain,
spl0_390,
inference(avatar_split_clause,[],[f368,f4207]) ).
fof(f368,axiom,
! [X11,X5,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),X12) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X12),X11) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Oadd__c_0) ).
fof(f4205,plain,
spl0_389,
inference(avatar_split_clause,[],[f124,f4203]) ).
fof(f4203,plain,
( spl0_389
<=> ! [X2,X1] :
( X1 = X2
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f124,axiom,
! [X2,X1] :
( X1 = X2
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__less__le_2) ).
fof(f4201,plain,
spl0_388,
inference(avatar_split_clause,[],[f72,f4199]) ).
fof(f72,axiom,
! [X10,X11,X15,X5,X23] :
( ~ class_RealVector_Oreal__normed__field(X5)
| X15 = X23
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| ~ c_Deriv_Oderiv(X10,X11,X23,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__unique_0) ).
fof(f4197,plain,
spl0_387,
inference(avatar_split_clause,[],[f70,f4195]) ).
fof(f4195,plain,
( spl0_387
<=> ! [X2,X1] :
( X1 = X2
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f70,axiom,
! [X2,X1] :
( X1 = X2
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__neq__iff_0) ).
fof(f4193,plain,
spl0_386,
inference(avatar_split_clause,[],[f69,f4191]) ).
fof(f4191,plain,
( spl0_386
<=> ! [X2,X1] :
( X1 = X2
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f69,axiom,
! [X2,X1] :
( X1 = X2
| ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__antisym_0) ).
fof(f4046,plain,
( ~ spl0_21
| ~ spl0_385
| ~ spl0_164
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3177,f3114,f2302,f4043,f1601]) ).
fof(f1601,plain,
( spl0_21
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f4043,plain,
( spl0_385
<=> c_HOL_Oone__class_Oone(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f2302,plain,
( spl0_164
<=> ! [X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| c_HOL_Ozero__class_Ozero(X5) != c_HOL_Oone__class_Oone(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f3177,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_164
| ~ spl0_304 ),
inference(superposition,[],[f2303,f3116]) ).
fof(f2303,plain,
( ! [X5] :
( c_HOL_Ozero__class_Ozero(X5) != c_HOL_Oone__class_Oone(X5)
| ~ class_Ring__and__Field_Ozero__neq__one(X5) )
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f2302]) ).
fof(f4041,plain,
( spl0_384
| ~ spl0_304
| ~ spl0_370 ),
inference(avatar_split_clause,[],[f3583,f3580,f3114,f4039]) ).
fof(f3580,plain,
( spl0_370
<=> ! [X2,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f3583,plain,
( ! [X2,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ spl0_304
| ~ spl0_370 ),
inference(forward_demodulation,[],[f3581,f3116]) ).
fof(f3581,plain,
( ! [X2,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1))
| ~ spl0_370 ),
inference(avatar_component_clause,[],[f3580]) ).
fof(f3940,plain,
( spl0_383
| ~ spl0_270
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3176,f3114,f2813,f3937]) ).
fof(f3937,plain,
( spl0_383
<=> c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f2813,plain,
( spl0_270
<=> c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f3176,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),tc_Int_Oint)
| ~ spl0_270
| ~ spl0_304 ),
inference(superposition,[],[f2815,f3116]) ).
fof(f2815,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint)
| ~ spl0_270 ),
inference(avatar_component_clause,[],[f2813]) ).
fof(f3850,plain,
( spl0_382
| ~ spl0_269
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3175,f3114,f2783,f3847]) ).
fof(f3847,plain,
( spl0_382
<=> c_Orderings_Obot__class_Obot(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f2783,plain,
( spl0_269
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f3175,plain,
( c_Orderings_Obot__class_Obot(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_Orderings_Obot__class_Obot(tc_nat),tc_nat)
| ~ spl0_269
| ~ spl0_304 ),
inference(superposition,[],[f2785,f3116]) ).
fof(f2785,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f2783]) ).
fof(f3716,plain,
( spl0_381
| ~ spl0_166
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3164,f3114,f2310,f3714]) ).
fof(f3714,plain,
( spl0_381
<=> ! [X1] : hBOOL(hAPP(c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f3164,plain,
( ! [X1] : hBOOL(hAPP(c_lessequals(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),X1))
| ~ spl0_166
| ~ spl0_304 ),
inference(superposition,[],[f2311,f3116]) ).
fof(f3623,plain,
( spl0_380
| ~ spl0_165
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3163,f3114,f2306,f3621]) ).
fof(f3621,plain,
( spl0_380
<=> ! [X0] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),c_Orderings_Obot__class_Obot(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f3163,plain,
( ! [X0] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X0,tc_nat),c_Orderings_Obot__class_Obot(tc_nat)))
| ~ spl0_165
| ~ spl0_304 ),
inference(superposition,[],[f2307,f3116]) ).
fof(f3619,plain,
spl0_379,
inference(avatar_split_clause,[],[f1310,f3617]) ).
fof(f3617,plain,
( spl0_379
<=> ! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f1310,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__aci_I8_J_0) ).
fof(f3615,plain,
spl0_378,
inference(avatar_split_clause,[],[f1308,f3613]) ).
fof(f1308,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__left__idem_0) ).
fof(f3611,plain,
spl0_377,
inference(avatar_split_clause,[],[f1292,f3609]) ).
fof(f1292,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| X6 = X7
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_right__minus__eq_0) ).
fof(f3607,plain,
spl0_376,
inference(avatar_split_clause,[],[f1291,f3605]) ).
fof(f1291,axiom,
! [X6,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| X6 = X7
| c_HOL_Ozero__class_Ozero(X5) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),X7) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_eq__iff__diff__eq__0_1) ).
fof(f3603,plain,
spl0_375,
inference(avatar_split_clause,[],[f1219,f3601]) ).
fof(f3601,plain,
( spl0_375
<=> ! [X11,X12,X5,X25] :
( X11 = X12
| hBOOL(hAPP(X25,X11))
| ~ hBOOL(hAPP(c_Set_Oinsert(X12,X25,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f1219,axiom,
! [X11,X5,X12,X25] :
( X11 = X12
| hBOOL(hAPP(X25,X11))
| ~ hBOOL(hAPP(c_Set_Oinsert(X12,X25,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_insert__code_0) ).
fof(f3599,plain,
spl0_374,
inference(avatar_split_clause,[],[f1182,f3597]) ).
fof(f1182,axiom,
! [X1] : c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Suc,X1),tc_nat) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_atLeastLessThan__singleton_0) ).
fof(f3595,plain,
spl0_373,
inference(avatar_split_clause,[],[f1030,f3593]) ).
fof(f1030,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__iff__sup_0) ).
fof(f3591,plain,
spl0_372,
inference(avatar_split_clause,[],[f1029,f3589]) ).
fof(f3589,plain,
( spl0_372
<=> ! [X11,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) != X12
| hBOOL(hAPP(c_lessequals(X11,X5),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f1029,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) != X12
| hBOOL(hAPP(c_lessequals(X11,X5),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__iff__sup_1) ).
fof(f3587,plain,
spl0_371,
inference(avatar_split_clause,[],[f1028,f3585]) ).
fof(f1028,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X11))
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__absorb1_0) ).
fof(f3582,plain,
spl0_370,
inference(avatar_split_clause,[],[f992,f3580]) ).
fof(f992,axiom,
! [X2,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__add__0_0) ).
fof(f3577,plain,
spl0_369,
inference(avatar_split_clause,[],[f970,f3575]) ).
fof(f3575,plain,
( spl0_369
<=> ! [X6,X5,X12] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_Lim_OisCont(hAPP(c_COMBC(c_HOL_Otimes__class_Otimes(X5),X5,X5,X5),X12),X6,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f970,axiom,
! [X6,X5,X12] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_Lim_OisCont(hAPP(c_COMBC(c_HOL_Otimes__class_Otimes(X5),X5,X5,X5),X12),X6,X5,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__left_OisCont_0) ).
fof(f3573,plain,
spl0_368,
inference(avatar_split_clause,[],[f921,f3571]) ).
fof(f3571,plain,
( spl0_368
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f921,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X6),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_not__square__less__zero_0) ).
fof(f3569,plain,
spl0_367,
inference(avatar_split_clause,[],[f906,f3567]) ).
fof(f906,axiom,
! [X5,X25] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X25,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Int__empty__right_0) ).
fof(f3565,plain,
spl0_366,
inference(avatar_split_clause,[],[f905,f3563]) ).
fof(f905,axiom,
! [X26,X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X26,tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Int__empty__left_0) ).
fof(f3561,plain,
spl0_365,
inference(avatar_split_clause,[],[f809,f3559]) ).
fof(f3559,plain,
( spl0_365
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f809,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),X6))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__square_0) ).
fof(f3557,plain,
spl0_364,
inference(avatar_split_clause,[],[f752,f3555]) ).
fof(f3555,plain,
( spl0_364
<=> ! [X6,X5,X7] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f752,axiom,
! [X6,X7,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_xt1_I9_J_0) ).
fof(f3553,plain,
spl0_363,
inference(avatar_split_clause,[],[f751,f3551]) ).
fof(f751,axiom,
! [X11,X5,X12] :
( ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_not__less__iff__gr__or__eq_1) ).
fof(f3549,plain,
spl0_362,
inference(avatar_split_clause,[],[f750,f3547]) ).
fof(f750,axiom,
! [X6,X7,X5] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),X7))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X7,X5),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_order__less__asym_H_0) ).
fof(f3545,plain,
spl0_361,
inference(avatar_split_clause,[],[f748,f3543]) ).
fof(f3543,plain,
( spl0_361
<=> ! [X11,X5,X12] :
( ~ class_Orderings_Olinorder(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),X12))
| hBOOL(hAPP(c_lessequals(X12,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f748,axiom,
! [X11,X5,X12] :
( ~ class_Orderings_Olinorder(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),X12))
| hBOOL(hAPP(c_lessequals(X12,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_linorder__linear_0) ).
fof(f3541,plain,
spl0_360,
inference(avatar_split_clause,[],[f742,f3539]) ).
fof(f3539,plain,
( spl0_360
<=> ! [X5,X11,X20,X10,X25] :
( hBOOL(hAPP(X25,hAPP(X10,X11)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X10,X25,X5,X20),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f742,axiom,
! [X10,X11,X5,X25,X20] :
( hBOOL(hAPP(X25,hAPP(X10,X11)))
| ~ hBOOL(hAPP(c_Set_Ovimage(X10,X25,X5,X20),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_vimage__code_0) ).
fof(f3537,plain,
( spl0_359
| ~ spl0_304
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f3446,f3442,f3114,f3534]) ).
fof(f3442,plain,
( spl0_338
<=> hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),v_n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f3446,plain,
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),v_n))
| ~ spl0_304
| ~ spl0_338 ),
inference(forward_demodulation,[],[f3444,f3116]) ).
fof(f3444,plain,
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),v_n))
| ~ spl0_338 ),
inference(avatar_component_clause,[],[f3442]) ).
fof(f3532,plain,
spl0_358,
inference(avatar_split_clause,[],[f741,f3530]) ).
fof(f3530,plain,
( spl0_358
<=> ! [X5,X11,X20,X10,X25] :
( ~ hBOOL(hAPP(X25,hAPP(X10,X11)))
| hBOOL(hAPP(c_Set_Ovimage(X10,X25,X5,X20),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f741,axiom,
! [X10,X11,X5,X25,X20] :
( ~ hBOOL(hAPP(X25,hAPP(X10,X11)))
| hBOOL(hAPP(c_Set_Ovimage(X10,X25,X5,X20),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_vimage__code_1) ).
fof(f3528,plain,
spl0_357,
inference(avatar_split_clause,[],[f618,f3526]) ).
fof(f618,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),c_HOL_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__zero_0) ).
fof(f3524,plain,
spl0_356,
inference(avatar_split_clause,[],[f577,f3522]) ).
fof(f3522,plain,
( spl0_356
<=> ! [X11,X5,X12] :
( ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f577,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__left__idem_0) ).
fof(f3520,plain,
spl0_355,
inference(avatar_split_clause,[],[f575,f3518]) ).
fof(f575,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__aci_I4_J_0) ).
fof(f3516,plain,
spl0_354,
inference(avatar_split_clause,[],[f567,f3514]) ).
fof(f567,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X1),tc_nat),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Suc__leD_0) ).
fof(f3512,plain,
spl0_353,
inference(avatar_split_clause,[],[f566,f3510]) ).
fof(f566,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(c_Suc,X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__SucI_0) ).
fof(f3508,plain,
spl0_352,
inference(avatar_split_clause,[],[f539,f3506]) ).
fof(f3506,plain,
( spl0_352
<=> ! [X11,X5,X12] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| hBOOL(hAPP(c_lessequals(X11,X5),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f539,axiom,
! [X11,X5,X12] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| hBOOL(hAPP(c_lessequals(X11,X5),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_order__less__imp__le_0) ).
fof(f3504,plain,
spl0_351,
inference(avatar_split_clause,[],[f537,f3502]) ).
fof(f3502,plain,
( spl0_351
<=> ! [X11,X5,X12] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| hBOOL(hAPP(c_lessequals(X11,X5),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f537,axiom,
! [X11,X5,X12] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12))
| hBOOL(hAPP(c_lessequals(X11,X5),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_order__le__less_1) ).
fof(f3500,plain,
spl0_350,
inference(avatar_split_clause,[],[f455,f3498]) ).
fof(f455,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_not__less__eq__eq_1) ).
fof(f3496,plain,
spl0_349,
inference(avatar_split_clause,[],[f454,f3494]) ).
fof(f3494,plain,
( spl0_349
<=> ! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f454,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_not__less__eq__eq_0) ).
fof(f3486,plain,
spl0_348,
inference(avatar_split_clause,[],[f436,f3484]) ).
fof(f436,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olower__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__iff__inf_0) ).
fof(f3482,plain,
spl0_347,
inference(avatar_split_clause,[],[f435,f3480]) ).
fof(f3480,plain,
( spl0_347
<=> ! [X12,X5,X11] :
( ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) != X11
| hBOOL(hAPP(c_lessequals(X11,X5),X12)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f435,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) != X11
| hBOOL(hAPP(c_lessequals(X11,X5),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__iff__inf_1) ).
fof(f3478,plain,
spl0_346,
inference(avatar_split_clause,[],[f434,f3476]) ).
fof(f434,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olower__semilattice(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X11))
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__absorb2_0) ).
fof(f3474,plain,
spl0_345,
inference(avatar_split_clause,[],[f433,f3472]) ).
fof(f3472,plain,
( spl0_345
<=> ! [X11,X5,X12] :
( ~ class_Int_Oring__char__0(X5)
| ~ class_Int_Onumber__ring(X5)
| X11 = X12
| c_Int_Onumber__class_Onumber__of(X11,X5) != c_Int_Onumber__class_Onumber__of(X12,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f433,axiom,
! [X11,X5,X12] :
( ~ class_Int_Oring__char__0(X5)
| ~ class_Int_Onumber__ring(X5)
| X11 = X12
| c_Int_Onumber__class_Onumber__of(X11,X5) != c_Int_Onumber__class_Onumber__of(X12,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_eq__number__of_0) ).
fof(f3470,plain,
spl0_344,
inference(avatar_split_clause,[],[f414,f3468]) ).
fof(f3468,plain,
( spl0_344
<=> ! [X11,X5,X12] :
( ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f414,axiom,
! [X11,X5,X12] :
( ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X11,X5),X12))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_linorder__not__le_1) ).
fof(f3466,plain,
spl0_343,
inference(avatar_split_clause,[],[f413,f3464]) ).
fof(f413,axiom,
! [X11,X5,X12] :
( ~ class_Orderings_Olinorder(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),X12))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X12,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_linorder__not__le_0) ).
fof(f3462,plain,
spl0_342,
inference(avatar_split_clause,[],[f388,f3460]) ).
fof(f388,axiom,
! [X0] : c_SetInterval_Oord__class_OatMost(hAPP(c_Suc,X0),tc_nat) = c_Set_Oinsert(hAPP(c_Suc,X0),c_SetInterval_Oord__class_OatMost(X0,tc_nat),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_atMost__Suc_0) ).
fof(f3458,plain,
spl0_341,
inference(avatar_split_clause,[],[f378,f3456]) ).
fof(f3456,plain,
( spl0_341
<=> ! [X6,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| c_Lim_OisCont(hAPP(c_COMBC(c_HOL_Oinverse__class_Odivide(X5),X5,X5,X5),X12),X6,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f378,axiom,
! [X6,X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| c_Lim_OisCont(hAPP(c_COMBC(c_HOL_Oinverse__class_Odivide(X5),X5,X5,X5),X12),X6,X5,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_OisCont_0) ).
fof(f3454,plain,
spl0_340,
inference(avatar_split_clause,[],[f333,f3452]) ).
fof(f333,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(c_Suc,X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__Suc__eq__le_0) ).
fof(f3450,plain,
spl0_339,
inference(avatar_split_clause,[],[f332,f3448]) ).
fof(f332,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(c_Suc,X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__Suc__eq__le_1) ).
fof(f3445,plain,
( spl0_338
| ~ spl0_193
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f2901,f2717,f2429,f3442]) ).
fof(f2901,plain,
( hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),v_n))
| ~ spl0_193
| ~ spl0_260 ),
inference(superposition,[],[f2718,f2430]) ).
fof(f3440,plain,
spl0_337,
inference(avatar_split_clause,[],[f307,f3438]) ).
fof(f307,axiom,
! [X11,X5,X12] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_lessequals(X12,X5),X11))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__le__not__le_1) ).
fof(f3436,plain,
spl0_336,
inference(avatar_split_clause,[],[f252,f3434]) ).
fof(f252,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Oone__class_Oone(X5)),X6) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__eq__divide_0) ).
fof(f3432,plain,
spl0_335,
inference(avatar_split_clause,[],[f239,f3430]) ).
fof(f239,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1))
| ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__eq__Suc__le_1) ).
fof(f3428,plain,
spl0_334,
inference(avatar_split_clause,[],[f236,f3426]) ).
fof(f3426,plain,
( spl0_334
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X1),tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f236,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X1),tc_nat),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Suc__leI_0) ).
fof(f3424,plain,
spl0_333,
inference(avatar_split_clause,[],[f163,f3422]) ).
fof(f163,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_not__less__eq_0) ).
fof(f3420,plain,
spl0_332,
inference(avatar_split_clause,[],[f162,f3418]) ).
fof(f162,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_not__less__eq_1) ).
fof(f3416,plain,
spl0_331,
inference(avatar_split_clause,[],[f45,f3414]) ).
fof(f45,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X6,X5),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Oone__class_Oone(X5)))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__add__one_0) ).
fof(f3412,plain,
spl0_330,
inference(avatar_split_clause,[],[f5,f3410]) ).
fof(f5,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(c_Suc,X1),tc_nat),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Suc__lessD_0) ).
fof(f3408,plain,
spl0_329,
inference(avatar_split_clause,[],[f4,f3406]) ).
fof(f4,axiom,
! [X2,X1] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),X2))
| hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),hAPP(c_Suc,X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__SucI_0) ).
fof(f3340,plain,
( spl0_328
| ~ spl0_304
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f3202,f3198,f3114,f3337]) ).
fof(f3198,plain,
( spl0_318
<=> c_SetInterval_Oord__class_OatMost(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Set_Oinsert(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f3202,plain,
( c_SetInterval_Oord__class_OatMost(c_Orderings_Obot__class_Obot(tc_nat),tc_nat) = c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_nat),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)
| ~ spl0_304
| ~ spl0_318 ),
inference(forward_demodulation,[],[f3200,f3116]) ).
fof(f3200,plain,
( c_SetInterval_Oord__class_OatMost(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Set_Oinsert(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat)
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f3198]) ).
fof(f3310,plain,
( spl0_327
| ~ spl0_304
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3157,f3153,f3114,f3308]) ).
fof(f3308,plain,
( spl0_327
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f3153,plain,
( spl0_313
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f3157,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X2 )
| ~ spl0_304
| ~ spl0_313 ),
inference(forward_demodulation,[],[f3156,f3116]) ).
fof(f3156,plain,
( ! [X2,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) )
| ~ spl0_304
| ~ spl0_313 ),
inference(forward_demodulation,[],[f3154,f3116]) ).
fof(f3154,plain,
( ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) )
| ~ spl0_313 ),
inference(avatar_component_clause,[],[f3153]) ).
fof(f3306,plain,
( spl0_326
| ~ spl0_304
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f3151,f3147,f3114,f3304]) ).
fof(f3304,plain,
( spl0_326
<=> ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f3147,plain,
( spl0_312
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f3151,plain,
( ! [X2,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != c_Orderings_Obot__class_Obot(tc_nat)
| c_Orderings_Obot__class_Obot(tc_nat) = X1 )
| ~ spl0_304
| ~ spl0_312 ),
inference(forward_demodulation,[],[f3150,f3116]) ).
fof(f3150,plain,
( ! [X2,X1] :
( c_Orderings_Obot__class_Obot(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) )
| ~ spl0_304
| ~ spl0_312 ),
inference(forward_demodulation,[],[f3148,f3116]) ).
fof(f3148,plain,
( ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) )
| ~ spl0_312 ),
inference(avatar_component_clause,[],[f3147]) ).
fof(f3231,plain,
( spl0_325
| ~ spl0_152
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3162,f3114,f2250,f3228]) ).
fof(f3228,plain,
( spl0_325
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_FFT__Mirabelle_Oroot(c_Orderings_Obot__class_Obot(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f3162,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_FFT__Mirabelle_Oroot(c_Orderings_Obot__class_Obot(tc_nat))
| ~ spl0_152
| ~ spl0_304 ),
inference(superposition,[],[f2252,f3116]) ).
fof(f3226,plain,
spl0_324,
inference(avatar_split_clause,[],[f1305,f3224]) ).
fof(f1305,axiom,
! [X26,X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X26,X25,tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Un__commute_0) ).
fof(f3222,plain,
spl0_323,
inference(avatar_split_clause,[],[f1301,f3220]) ).
fof(f1301,axiom,
! [X26,X5,X25] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Orderings_Obot__class_Obot(X5) = X25
| c_Orderings_Obot__class_Obot(X5) != c_Lattices_Oupper__semilattice__class_Osup(X25,X26,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__eq__bot__eq1_0) ).
fof(f3218,plain,
spl0_322,
inference(avatar_split_clause,[],[f1300,f3216]) ).
fof(f3216,plain,
( spl0_322
<=> ! [X25,X5,X26] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Orderings_Obot__class_Obot(X5) = X26
| c_Orderings_Obot__class_Obot(X5) != c_Lattices_Oupper__semilattice__class_Osup(X25,X26,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f1300,axiom,
! [X26,X5,X25] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Orderings_Obot__class_Obot(X5) = X26
| c_Orderings_Obot__class_Obot(X5) != c_Lattices_Oupper__semilattice__class_Osup(X25,X26,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__eq__bot__eq2_0) ).
fof(f3214,plain,
spl0_321,
inference(avatar_split_clause,[],[f1268,f3212]) ).
fof(f3212,plain,
( spl0_321
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f1268,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X11) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__ringb_Osubr0__iff_1) ).
fof(f3210,plain,
spl0_320,
inference(avatar_split_clause,[],[f1260,f3208]) ).
fof(f3208,plain,
( spl0_320
<=> ! [X11,X5,X25,X26] :
( ~ hBOOL(hAPP(X25,X11))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f1260,axiom,
! [X11,X26,X5,X25] :
( ~ hBOOL(hAPP(X25,X11))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup1CI_1) ).
fof(f3206,plain,
spl0_319,
inference(avatar_split_clause,[],[f1259,f3204]) ).
fof(f3204,plain,
( spl0_319
<=> ! [X25,X5,X11,X26] :
( ~ hBOOL(hAPP(X26,X11))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f1259,axiom,
! [X11,X26,X5,X25] :
( ~ hBOOL(hAPP(X26,X11))
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X25,X26,tc_fun(X5,tc_bool)),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup1CI_0) ).
fof(f3201,plain,
spl0_318,
inference(avatar_split_clause,[],[f1181,f3198]) ).
fof(f1181,axiom,
c_SetInterval_Oord__class_OatMost(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Set_Oinsert(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_atMost__0_0) ).
fof(f3196,plain,
spl0_317,
inference(avatar_split_clause,[],[f1076,f3194]) ).
fof(f3194,plain,
( spl0_317
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X2) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f1076,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X2) = X1,
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__add__inverse2_0) ).
fof(f3192,plain,
spl0_316,
inference(avatar_split_clause,[],[f1075,f3190]) ).
fof(f3190,plain,
( spl0_316
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),X2) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f1075,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1)),X2) = X1,
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__add__inverse_0) ).
fof(f3188,plain,
spl0_315,
inference(avatar_split_clause,[],[f991,f3186]) ).
fof(f991,axiom,
! [X6,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5),X5) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_complete__lattice__class_OSup__singleton_0) ).
fof(f3161,plain,
spl0_314,
inference(avatar_split_clause,[],[f904,f3159]) ).
fof(f3159,plain,
( spl0_314
<=> ! [X20,X5,X10] : c_Set_Ovimage(X10,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X5,X20) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f904,axiom,
! [X10,X5,X20] : c_Set_Ovimage(X10,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X5,X20) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_vimage__empty_0) ).
fof(f3155,plain,
spl0_313,
inference(avatar_split_clause,[],[f889,f3153]) ).
fof(f889,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__is__0_1) ).
fof(f3149,plain,
spl0_312,
inference(avatar_split_clause,[],[f888,f3147]) ).
fof(f888,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__is__0_0) ).
fof(f3145,plain,
spl0_311,
inference(avatar_split_clause,[],[f623,f3143]) ).
fof(f3143,plain,
( spl0_311
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),c_HOL_Ozero__class_Ozero(X5)) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f623,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Oidom(X5)
| ~ class_Int_Onumber__ring(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X11),c_HOL_Ozero__class_Ozero(X5)) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f3141,plain,
spl0_310,
inference(avatar_split_clause,[],[f615,f3139]) ).
fof(f3139,plain,
( spl0_310
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f615,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),c_HOL_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_double__eq__0__iff_1) ).
fof(f3137,plain,
spl0_309,
inference(avatar_split_clause,[],[f504,f3135]) ).
fof(f3135,plain,
( spl0_309
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6) != c_HOL_Ozero__class_Ozero(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f504,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Ozero__class_Ozero(X5) = X6
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6) != c_HOL_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__zero__imp__zero_0) ).
fof(f3133,plain,
spl0_308,
inference(avatar_split_clause,[],[f441,f3131]) ).
fof(f3129,plain,
spl0_307,
inference(avatar_split_clause,[],[f367,f3127]) ).
fof(f367,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__add__commute_0) ).
fof(f3125,plain,
spl0_306,
inference(avatar_split_clause,[],[f331,f3123]) ).
fof(f331,axiom,
! [X2,X1] : hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),tc_nat),hAPP(c_Suc,X1))),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__less__Suc_0) ).
fof(f3121,plain,
spl0_305,
inference(avatar_split_clause,[],[f284,f3119]) ).
fof(f284,axiom,
! [X10,X5,X20] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| c_HOL_Oone__class_Oone(X5) = c_Finite__Set_Osetprod(X10,c_Orderings_Obot__class_Obot(tc_fun(X20,tc_bool)),X20,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_setprod__empty_0) ).
fof(f3117,plain,
( ~ spl0_38
| spl0_304
| ~ spl0_188
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2852,f2669,f2408,f3114,f1686]) ).
fof(f1686,plain,
( spl0_38
<=> class_Orderings_Obot(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f2852,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Obot__class_Obot(tc_nat)
| ~ class_Orderings_Obot(tc_nat)
| ~ spl0_188
| ~ spl0_248 ),
inference(resolution,[],[f2670,f2409]) ).
fof(f3112,plain,
spl0_303,
inference(avatar_split_clause,[],[f283,f3110]) ).
fof(f3110,plain,
( spl0_303
<=> ! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f283,axiom,
! [X2,X1] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X2),X1),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__mult__commute_0) ).
fof(f3108,plain,
spl0_302,
inference(avatar_split_clause,[],[f275,f3106]) ).
fof(f275,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| hAPP(c_HOL_Oinverse__class_Oinverse(X5),hAPP(c_HOL_Oinverse__class_Oinverse(X5),X6)) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__inverse__eq_0) ).
fof(f3104,plain,
spl0_301,
inference(avatar_split_clause,[],[f270,f3102]) ).
fof(f3102,plain,
( spl0_301
<=> ! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f270,axiom,
! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__Suc0_0) ).
fof(f3100,plain,
spl0_300,
inference(avatar_split_clause,[],[f245,f3098]) ).
fof(f245,axiom,
! [X3,X1] : hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)))),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__add__Suc2_0) ).
fof(f3096,plain,
spl0_299,
inference(avatar_split_clause,[],[f244,f3094]) ).
fof(f244,axiom,
! [X3,X1] : hBOOL(hAPP(c_HOL_Oord__class_Oless(X3,tc_nat),hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X1)))),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__add__Suc1_0) ).
fof(f3092,plain,
spl0_298,
inference(avatar_split_clause,[],[f153,f3090]) ).
fof(f3090,plain,
( spl0_298
<=> ! [X11,X5,X25,X26] :
( hBOOL(hAPP(X25,X11))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f153,axiom,
! [X11,X26,X5,X25] :
( hBOOL(hAPP(X25,X11))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf1E_0) ).
fof(f3088,plain,
spl0_297,
inference(avatar_split_clause,[],[f152,f3086]) ).
fof(f3086,plain,
( spl0_297
<=> ! [X25,X5,X11,X26] :
( hBOOL(hAPP(X26,X11))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f152,axiom,
! [X11,X26,X5,X25] :
( hBOOL(hAPP(X26,X11))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X25,X26,tc_fun(X5,tc_bool)),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf1E_1) ).
fof(f3084,plain,
spl0_296,
inference(avatar_split_clause,[],[f71,f3082]) ).
fof(f3082,plain,
( spl0_296
<=> ! [X5,X18,X7,X6] :
( ~ class_RealVector_Ometric__space(X5)
| X6 = X7
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| ~ c_SEQ_OLIMSEQ(X18,X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f71,axiom,
! [X18,X6,X7,X5] :
( ~ class_RealVector_Ometric__space(X5)
| X6 = X7
| ~ c_SEQ_OLIMSEQ(X18,X6,X5)
| ~ c_SEQ_OLIMSEQ(X18,X7,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__unique_0) ).
fof(f3049,plain,
( spl0_295
| ~ spl0_153
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f3024,f2938,f2255,f3046]) ).
fof(f3024,plain,
( hBOOL(hAPP(c_lessequals(v_i,tc_nat),v_n))
| ~ spl0_153
| ~ spl0_276 ),
inference(resolution,[],[f2939,f2257]) ).
fof(f3016,plain,
spl0_294,
inference(avatar_split_clause,[],[f1220,f3014]) ).
fof(f1220,axiom,
! [X11,X5,X25] : c_Set_Oinsert(X11,X25,X5) = c_Set_Oinsert(X11,c_Set_Oinsert(X11,X25,X5),X5),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_insert__absorb2_0) ).
fof(f3010,plain,
spl0_293,
inference(avatar_split_clause,[],[f1216,f3008]) ).
fof(f3008,plain,
( spl0_293
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_HOL_Ozero__class_Ozero(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f1216,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_HOL_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f3006,plain,
spl0_292,
inference(avatar_split_clause,[],[f1214,f3004]) ).
fof(f3004,plain,
( spl0_292
<=> ! [X5,X7] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f1214,axiom,
! [X7,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),X7) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult_Ozero__left_0) ).
fof(f3002,plain,
spl0_291,
inference(avatar_split_clause,[],[f1213,f3000]) ).
fof(f3000,plain,
( spl0_291
<=> ! [X6,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_HOL_Ozero__class_Ozero(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f1213,axiom,
! [X6,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_HOL_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult_Ozero__right_0) ).
fof(f2998,plain,
spl0_290,
inference(avatar_split_clause,[],[f1211,f2996]) ).
fof(f2996,plain,
( spl0_290
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f1211,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),X11) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Omul__0_0) ).
fof(f2994,plain,
spl0_289,
inference(avatar_split_clause,[],[f1206,f2992]) ).
fof(f2992,plain,
( spl0_289
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_HOL_Ozero__class_Ozero(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f1206,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_HOL_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__eq__0__iff_2) ).
fof(f2990,plain,
spl0_288,
inference(avatar_split_clause,[],[f1205,f2988]) ).
fof(f2988,plain,
( spl0_288
<=> ! [X5,X7] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f1205,axiom,
! [X7,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),X7) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__eq__0__iff_1) ).
fof(f2986,plain,
spl0_287,
inference(avatar_split_clause,[],[f1204,f2984]) ).
fof(f1204,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_HOL_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__zero__right_0) ).
fof(f2982,plain,
spl0_286,
inference(avatar_split_clause,[],[f1203,f2980]) ).
fof(f1203,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Omult__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Ozero__class_Ozero(X5)),X6) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__zero__left_0) ).
fof(f2978,plain,
spl0_285,
inference(avatar_split_clause,[],[f989,f2976]) ).
fof(f2976,plain,
( spl0_285
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f989,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X11),c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Opwr__0_0) ).
fof(f2974,plain,
spl0_284,
inference(avatar_split_clause,[],[f988,f2972]) ).
fof(f988,axiom,
! [X6,X5] :
( ~ class_Power_Opower(X5)
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X6),c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__0_0) ).
fof(f2968,plain,
spl0_283,
inference(avatar_split_clause,[],[f908,f2966]) ).
fof(f908,axiom,
! [X2,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_HOL_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_HOL_Oone__class_Oone(X5)),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_power__one_0) ).
fof(f2964,plain,
spl0_282,
inference(avatar_split_clause,[],[f891,f2962]) ).
fof(f891,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != X1 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__eq__self__zero_0) ).
fof(f2960,plain,
spl0_281,
inference(avatar_split_clause,[],[f749,f2958]) ).
fof(f749,axiom,
! [X2,X1] :
( hBOOL(hAPP(c_lessequals(X1,tc_nat),X2))
| hBOOL(hAPP(c_lessequals(X2,tc_nat),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat__le__linear_0) ).
fof(f2956,plain,
spl0_280,
inference(avatar_split_clause,[],[f735,f2954]) ).
fof(f2954,plain,
( spl0_280
<=> ! [X11,X5,X12] :
( ~ class_Orderings_Olinorder(X5)
| X11 = X12
| c_SetInterval_Oord__class_OatMost(X11,X5) != c_SetInterval_Oord__class_OatMost(X12,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f735,axiom,
! [X11,X5,X12] :
( ~ class_Orderings_Olinorder(X5)
| X11 = X12
| c_SetInterval_Oord__class_OatMost(X11,X5) != c_SetInterval_Oord__class_OatMost(X12,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_atMost__eq__iff_0) ).
fof(f2952,plain,
spl0_279,
inference(avatar_split_clause,[],[f619,f2950]) ).
fof(f2950,plain,
( spl0_279
<=> ! [X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Ozero__class_Ozero(X5)),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f619,axiom,
! [X5,X12] :
( ~ class_RealVector_Oreal__normed__field(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Ozero__class_Ozero(X5)),X12) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide_Ozero_0) ).
fof(f2948,plain,
spl0_278,
inference(avatar_split_clause,[],[f616,f2946]) ).
fof(f616,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),c_HOL_Ozero__class_Ozero(X5)),X6) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__zero__left_0) ).
fof(f2944,plain,
spl0_277,
inference(avatar_split_clause,[],[f541,f2942]) ).
fof(f2942,plain,
( spl0_277
<=> ! [X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oone__class_Oone(X5) = hAPP(c_HOL_Oinverse__class_Oinverse(X5),c_HOL_Oone__class_Oone(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f541,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Oone__class_Oone(X5) = hAPP(c_HOL_Oinverse__class_Oinverse(X5),c_HOL_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__eq__1__iff_1) ).
fof(f2940,plain,
spl0_276,
inference(avatar_split_clause,[],[f540,f2938]) ).
fof(f540,axiom,
! [X11,X12] :
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,tc_nat),X12))
| hBOOL(hAPP(c_lessequals(X11,tc_nat),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_termination__basic__simps_I5_J_0) ).
fof(f2936,plain,
spl0_275,
inference(avatar_split_clause,[],[f220,f2934]) ).
fof(f2934,plain,
( spl0_275
<=> ! [X2,X5,X1] :
( ~ class_Nat_Osemiring__char__0(X5)
| X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X5) != c_Nat_Osemiring__1__class_Oof__nat(X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f220,axiom,
! [X2,X1,X5] :
( ~ class_Nat_Osemiring__char__0(X5)
| X1 = X2
| c_Nat_Osemiring__1__class_Oof__nat(X1,X5) != c_Nat_Osemiring__1__class_Oof__nat(X2,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_of__nat__eq__iff_0) ).
fof(f2932,plain,
spl0_274,
inference(avatar_split_clause,[],[f23,f2930]) ).
fof(f23,axiom,
! [X10,X11,X15,X5] :
( ~ class_RealVector_Oreal__normed__field(X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5)
| c_Lim_OisCont(X10,X11,X5,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__isCont_0) ).
fof(f2928,plain,
( spl0_273
| ~ spl0_45
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2457,f2425,f1721,f2926]) ).
fof(f2926,plain,
( spl0_273
<=> ! [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_273])]) ).
fof(f2457,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0
| ~ spl0_45
| ~ spl0_192 ),
inference(resolution,[],[f2426,f1723]) ).
fof(f2898,plain,
( spl0_272
| ~ spl0_45
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2451,f2421,f1721,f2896]) ).
fof(f2451,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
| ~ spl0_45
| ~ spl0_191 ),
inference(resolution,[],[f2422,f1723]) ).
fof(f2860,plain,
( spl0_271
| ~ spl0_126
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f2450,f2412,f2126,f2857]) ).
fof(f2126,plain,
( spl0_126
<=> class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f2412,plain,
( spl0_189
<=> ! [X5] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f2450,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex)
| ~ spl0_126
| ~ spl0_189 ),
inference(resolution,[],[f2413,f2128]) ).
fof(f2128,plain,
( class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex)
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f2126]) ).
fof(f2413,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X5) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f2412]) ).
fof(f2816,plain,
( spl0_270
| ~ spl0_82
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f2449,f2412,f1906,f2813]) ).
fof(f1906,plain,
( spl0_82
<=> class_Ring__and__Field_Osemiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f2449,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint)
| ~ spl0_82
| ~ spl0_189 ),
inference(resolution,[],[f2413,f1908]) ).
fof(f1908,plain,
( class_Ring__and__Field_Osemiring__1(tc_Int_Oint)
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f1906]) ).
fof(f2786,plain,
( spl0_269
| ~ spl0_24
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f2448,f2412,f1616,f2783]) ).
fof(f1616,plain,
( spl0_24
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f2448,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_24
| ~ spl0_189 ),
inference(resolution,[],[f2413,f1618]) ).
fof(f1618,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f1616]) ).
fof(f2751,plain,
spl0_268,
inference(avatar_split_clause,[],[f1306,f2749]) ).
fof(f2749,plain,
( spl0_268
<=> ! [X12,X5,X11] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = c_Lattices_Oupper__semilattice__class_Osup(X12,X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f1306,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = c_Lattices_Oupper__semilattice__class_Osup(X12,X11,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__aci_I5_J_0) ).
fof(f2747,plain,
spl0_267,
inference(avatar_split_clause,[],[f1304,f2745]) ).
fof(f1304,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5) = c_Lattices_Oupper__semilattice__class_Osup(X12,X11,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__commute_0) ).
fof(f2743,plain,
spl0_266,
inference(avatar_split_clause,[],[f1299,f2741]) ).
fof(f1299,axiom,
! [X11,X5,X25,X12] :
( ~ hBOOL(hAPP(X25,X11))
| hBOOL(hAPP(c_Set_Oinsert(X12,X25,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_insert__code_2) ).
fof(f2739,plain,
spl0_265,
inference(avatar_split_clause,[],[f1266,f2737]) ).
fof(f1266,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__0__right_0) ).
fof(f2735,plain,
spl0_264,
inference(avatar_split_clause,[],[f1265,f2733]) ).
fof(f2733,plain,
( spl0_264
<=> ! [X5,X11] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f1265,axiom,
! [X11,X5] :
( ~ class_OrderedGroup_Ogroup__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X11) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_right__minus__eq_1) ).
fof(f2731,plain,
spl0_263,
inference(avatar_split_clause,[],[f1264,f2729]) ).
fof(f1264,axiom,
! [X11,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(X5),X11),X11) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_eq__iff__diff__eq__0_0) ).
fof(f2727,plain,
spl0_262,
inference(avatar_split_clause,[],[f1257,f2725]) ).
fof(f1257,axiom,
! [X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),tc_fun(X5,tc_bool)) = X25,
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Un__empty__right_0) ).
fof(f2723,plain,
spl0_261,
inference(avatar_split_clause,[],[f1256,f2721]) ).
fof(f1256,axiom,
! [X26,X5] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X26,tc_fun(X5,tc_bool)) = X26,
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Un__empty__left_0) ).
fof(f2719,plain,
spl0_260,
inference(avatar_split_clause,[],[f1180,f2717]) ).
fof(f1180,axiom,
! [X0] : hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),v_i),X0),tc_nat),v_n)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_i__diff_0) ).
fof(f2715,plain,
spl0_259,
inference(avatar_split_clause,[],[f1119,f2713]) ).
fof(f2711,plain,
spl0_258,
inference(avatar_split_clause,[],[f1116,f2709]) ).
fof(f1116,axiom,
! [X6] : c_GCD_Ogcd__class_OGCD(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = X6,
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_gcd__lcm__complete__lattice__nat_OInf__singleton_0) ).
fof(f2707,plain,
spl0_257,
inference(avatar_split_clause,[],[f1115,f2705]) ).
fof(f1115,axiom,
! [X6] : c_GCD_Ogcd__class_OLCM(c_Set_Oinsert(X6,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = X6,
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_gcd__lcm__complete__lattice__nat_OSup__singleton_0) ).
fof(f2703,plain,
spl0_256,
inference(avatar_split_clause,[],[f1071,f2701]) ).
fof(f1071,axiom,
! [X2,X1] : hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X2),tc_nat),X1)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__le__self_0) ).
fof(f2699,plain,
spl0_255,
inference(avatar_split_clause,[],[f1049,f2697]) ).
fof(f1049,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5),X5) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__absorb_0) ).
fof(f2695,plain,
spl0_254,
inference(avatar_split_clause,[],[f1038,f2693]) ).
fof(f1038,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__ord_I3_J_0) ).
fof(f2691,plain,
spl0_253,
inference(avatar_split_clause,[],[f1037,f2689]) ).
fof(f1037,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| hBOOL(hAPP(c_lessequals(X12,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__ord_I4_J_0) ).
fof(f2687,plain,
spl0_252,
inference(avatar_split_clause,[],[f1035,f2685]) ).
fof(f1035,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__ge1_0) ).
fof(f2683,plain,
spl0_251,
inference(avatar_split_clause,[],[f1034,f2681]) ).
fof(f1034,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Oupper__semilattice(X5)
| hBOOL(hAPP(c_lessequals(X12,X5),c_Lattices_Oupper__semilattice__class_Osup(X11,X12,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__ge2_0) ).
fof(f2679,plain,
spl0_250,
inference(avatar_split_clause,[],[f1031,f2677]) ).
fof(f1031,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__inf__absorb_0) ).
fof(f2675,plain,
spl0_249,
inference(avatar_split_clause,[],[f990,f2673]) ).
fof(f990,axiom,
! [X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X5)
| c_Orderings_Obot__class_Obot(X5) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Sup__empty_0) ).
fof(f2671,plain,
spl0_248,
inference(avatar_split_clause,[],[f886,f2669]) ).
fof(f886,axiom,
! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| ~ hBOOL(hAPP(c_lessequals(X2,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__0__eq_0) ).
fof(f2667,plain,
spl0_247,
inference(avatar_split_clause,[],[f874,f2665]) ).
fof(f2665,plain,
( spl0_247
<=> ! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f874,axiom,
! [X2] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X2
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_gr0I_0) ).
fof(f2663,plain,
spl0_246,
inference(avatar_split_clause,[],[f825,f2661]) ).
fof(f2661,plain,
( spl0_246
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_HOL_Oone__class_Oone(X5)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f825,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_HOL_Oone__class_Oone(X5)) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(f2659,plain,
spl0_245,
inference(avatar_split_clause,[],[f824,f2657]) ).
fof(f2657,plain,
( spl0_245
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Oone__class_Oone(X5)),X11) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f824,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Oone__class_Oone(X5)),X11) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Omul__1_0) ).
fof(f2655,plain,
spl0_244,
inference(avatar_split_clause,[],[f823,f2653]) ).
fof(f2653,plain,
( spl0_244
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Oone__class_Oone(X5)),X6) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f823,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Oone__class_Oone(X5)),X6) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__1_0) ).
fof(f2651,plain,
spl0_243,
inference(avatar_split_clause,[],[f822,f2649]) ).
fof(f822,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),c_HOL_Oone__class_Oone(X5)),X6) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__1__left_0) ).
fof(f2647,plain,
spl0_242,
inference(avatar_split_clause,[],[f821,f2645]) ).
fof(f821,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X6),c_HOL_Oone__class_Oone(X5)) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__1__right_0) ).
fof(f2643,plain,
spl0_241,
inference(avatar_split_clause,[],[f626,f2641]) ).
fof(f2641,plain,
( spl0_241
<=> ! [X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f626,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f2639,plain,
spl0_240,
inference(avatar_split_clause,[],[f625,f2637]) ).
fof(f2637,plain,
( spl0_240
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X6) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f625,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X6) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_comm__monoid__add_Omult__1_0) ).
fof(f2635,plain,
spl0_239,
inference(avatar_split_clause,[],[f624,f2633]) ).
fof(f2633,plain,
( spl0_239
<=> ! [X5,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X11) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f624,axiom,
! [X11,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X11) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_class__semiring_Oadd__0_0) ).
fof(f2631,plain,
spl0_238,
inference(avatar_split_clause,[],[f622,f2629]) ).
fof(f2629,plain,
( spl0_238
<=> ! [X6,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f622,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f2627,plain,
spl0_237,
inference(avatar_split_clause,[],[f621,f2625]) ).
fof(f621,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),c_HOL_Ozero__class_Ozero(X5)),X6) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_add__0__left_0) ).
fof(f2623,plain,
spl0_236,
inference(avatar_split_clause,[],[f620,f2621]) ).
fof(f620,axiom,
! [X6,X5] :
( ~ class_OrderedGroup_Omonoid__add(X5)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X5),X6),c_HOL_Ozero__class_Ozero(X5)) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f2619,plain,
spl0_235,
inference(avatar_split_clause,[],[f600,f2617]) ).
fof(f2617,plain,
( spl0_235
<=> ! [X5,X10] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5)
| c_Series_Osums(X10,c_Series_Osuminf(X10,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f600,axiom,
! [X10,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5)
| c_Series_Osums(X10,c_Series_Osuminf(X10,X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_summable__sums_0) ).
fof(f2615,plain,
spl0_234,
inference(avatar_split_clause,[],[f591,f2613]) ).
fof(f591,axiom,
! [X3,X4] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat),X3)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_not__add__less1_0) ).
fof(f2611,plain,
spl0_233,
inference(avatar_split_clause,[],[f590,f2609]) ).
fof(f590,axiom,
! [X3,X4] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X3),tc_nat),X3)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_not__add__less2_0) ).
fof(f2607,plain,
spl0_232,
inference(avatar_split_clause,[],[f556,f2605]) ).
fof(f2605,plain,
( spl0_232
<=> ! [X5,X37,X10] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(X10,X37,X5)
| c_Series_Osuminf(X10,X5) = X37 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f556,axiom,
! [X10,X37,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osums(X10,X37,X5)
| c_Series_Osuminf(X10,X5) = X37 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sums__unique_0) ).
fof(f2603,plain,
spl0_231,
inference(avatar_split_clause,[],[f529,f2601]) ).
fof(f2601,plain,
( spl0_231
<=> ! [X2,X1] : hBOOL(hAPP(c_lessequals(X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f529,axiom,
! [X2,X1] : hBOOL(hAPP(c_lessequals(X2,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2))),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__add2_0) ).
fof(f2599,plain,
spl0_230,
inference(avatar_split_clause,[],[f528,f2597]) ).
fof(f528,axiom,
! [X11,X1] : hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X11))),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__iff__add_1) ).
fof(f2595,plain,
spl0_229,
inference(avatar_split_clause,[],[f488,f2593]) ).
fof(f488,axiom,
! [X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),c_Nat_Osemiring__1__class_Oof__nat(X1,X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__imp__of__nat_0) ).
fof(f2591,plain,
spl0_228,
inference(avatar_split_clause,[],[f481,f2589]) ).
fof(f481,axiom,
! [X1] : hBOOL(hAPP(c_lessequals(X1,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),X1))),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le__square_0) ).
fof(f2587,plain,
spl0_227,
inference(avatar_split_clause,[],[f471,f2585]) ).
fof(f2585,plain,
( spl0_227
<=> ! [X5,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f471,axiom,
! [X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X1,X5),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_of__nat__less__0__iff_0) ).
fof(f2583,plain,
spl0_226,
inference(avatar_split_clause,[],[f442,f2581]) ).
fof(f2581,plain,
( spl0_226
<=> ! [X12,X5,X11] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = c_Lattices_Olower__semilattice__class_Oinf(X12,X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f442,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = c_Lattices_Olower__semilattice__class_Oinf(X12,X11,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__aci_I1_J_0) ).
fof(f2579,plain,
spl0_225,
inference(avatar_split_clause,[],[f440,f2577]) ).
fof(f440,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5) = c_Lattices_Olower__semilattice__class_Oinf(X12,X11,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__commute_0) ).
fof(f2575,plain,
spl0_224,
inference(avatar_split_clause,[],[f183,f2573]) ).
fof(f183,axiom,
! [X6,X5] :
( ~ class_Ring__and__Field_Ofield(X5)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(X5),X6),c_HOL_Oone__class_Oone(X5)) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_divide__1_0) ).
fof(f2571,plain,
spl0_223,
inference(avatar_split_clause,[],[f42,f2569]) ).
fof(f42,axiom,
! [X10,X11,X15,X5] :
( ~ class_RealVector_Oreal__normed__field(X5)
| c_Deriv_Odifferentiable(X10,X11,X5)
| ~ c_Deriv_Oderiv(X10,X11,X15,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_differentiableI_0) ).
fof(f2567,plain,
spl0_222,
inference(avatar_split_clause,[],[f33,f2565]) ).
fof(f33,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__ord_I1_J_0) ).
fof(f2563,plain,
spl0_221,
inference(avatar_split_clause,[],[f32,f2561]) ).
fof(f32,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olattice(X5)
| hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__sup__ord_I2_J_0) ).
fof(f2559,plain,
spl0_220,
inference(avatar_split_clause,[],[f31,f2557]) ).
fof(f31,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olower__semilattice(X5)
| hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__le1_0) ).
fof(f2555,plain,
spl0_219,
inference(avatar_split_clause,[],[f30,f2553]) ).
fof(f30,axiom,
! [X11,X5,X12] :
( ~ class_Lattices_Olower__semilattice(X5)
| hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X11,X12,X5),X5),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__le2_0) ).
fof(f2546,plain,
( spl0_218
| ~ spl0_80
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2377,f2363,f1896,f2544]) ).
fof(f2544,plain,
( spl0_218
<=> ! [X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X5,tc_Int_Oint) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2377,plain,
( ! [X5] : c_Lattices_Oupper__semilattice__class_Osup(X5,X5,tc_Int_Oint) = X5
| ~ spl0_80
| ~ spl0_179 ),
inference(resolution,[],[f2364,f1898]) ).
fof(f2538,plain,
spl0_217,
inference(avatar_split_clause,[],[f1283,f2536]) ).
fof(f1283,axiom,
! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__0__eq__0_0) ).
fof(f2534,plain,
spl0_216,
inference(avatar_split_clause,[],[f1238,f2532]) ).
fof(f2532,plain,
( spl0_216
<=> ! [X5,X11] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1238,axiom,
! [X11,X5] :
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X5)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X11) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__idem_0) ).
fof(f2530,plain,
( spl0_215
| ~ spl0_42
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2376,f2363,f1706,f2528]) ).
fof(f2528,plain,
( spl0_215
<=> ! [X4] : c_Lattices_Oupper__semilattice__class_Osup(X4,X4,tc_bool) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f2376,plain,
( ! [X4] : c_Lattices_Oupper__semilattice__class_Osup(X4,X4,tc_bool) = X4
| ~ spl0_42
| ~ spl0_179 ),
inference(resolution,[],[f2364,f1708]) ).
fof(f2526,plain,
spl0_214,
inference(avatar_split_clause,[],[f1208,f2524]) ).
fof(f1208,axiom,
! [X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_atLeastLessThan0_0) ).
fof(f2522,plain,
spl0_213,
inference(avatar_split_clause,[],[f1118,f2520]) ).
fof(f1118,axiom,
! [X2] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(X2)),X2),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_root__unity_0) ).
fof(f2518,plain,
spl0_212,
inference(avatar_split_clause,[],[f900,f2516]) ).
fof(f900,axiom,
! [X11,X5] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Orderings_Obot__class_Obot(X5) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X5),X11,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__bot__left_0) ).
fof(f2514,plain,
spl0_211,
inference(avatar_split_clause,[],[f899,f2512]) ).
fof(f899,axiom,
! [X11,X5] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Orderings_Obot__class_Obot(X5) = c_Lattices_Olower__semilattice__class_Oinf(X11,c_Orderings_Obot__class_Obot(X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__bot__right_0) ).
fof(f2510,plain,
spl0_210,
inference(avatar_split_clause,[],[f878,f2508]) ).
fof(f878,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__is__0_2) ).
fof(f2506,plain,
spl0_209,
inference(avatar_split_clause,[],[f877,f2504]) ).
fof(f877,axiom,
! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__is__0_1) ).
fof(f2502,plain,
spl0_208,
inference(avatar_split_clause,[],[f831,f2500]) ).
fof(f831,axiom,
! [X11,X9,X5] :
( ~ class_RealVector_Oreal__normed__field(X5)
| c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(X5),X9),X11,X9,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_DERIV__cmult__Id_0) ).
fof(f2498,plain,
spl0_207,
inference(avatar_split_clause,[],[f820,f2496]) ).
fof(f2496,plain,
( spl0_207
<=> ! [X6,X5,X11] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_Lim_OisCont(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X6,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f820,axiom,
! [X11,X6,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X5)
| c_Lim_OisCont(hAPP(c_HOL_Otimes__class_Otimes(X5),X11),X6,X5,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_mult__right_OisCont_0) ).
fof(f2494,plain,
spl0_206,
inference(avatar_split_clause,[],[f552,f2492]) ).
fof(f552,axiom,
! [X10,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| ~ c_Series_Osummable(X10,X5)
| c_SEQ_OLIMSEQ(X10,c_HOL_Ozero__class_Ozero(X5),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_summable__LIMSEQ__zero_0) ).
fof(f2490,plain,
spl0_205,
inference(avatar_split_clause,[],[f551,f2488]) ).
fof(f551,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__one_0) ).
fof(f2486,plain,
( spl0_204
| ~ spl0_22
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2374,f2363,f1606,f2484]) ).
fof(f2484,plain,
( spl0_204
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f2374,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0
| ~ spl0_22
| ~ spl0_179 ),
inference(resolution,[],[f2364,f1608]) ).
fof(f2482,plain,
spl0_203,
inference(avatar_split_clause,[],[f543,f2480]) ).
fof(f543,axiom,
! [X5] :
( ~ class_Ring__and__Field_Odivision__ring(X5)
| c_HOL_Oone__class_Oone(X5) = hAPP(c_HOL_Oinverse__class_Oinverse(X5),c_HOL_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__1_0) ).
fof(f2478,plain,
spl0_202,
inference(avatar_split_clause,[],[f531,f2476]) ).
fof(f2476,plain,
( spl0_202
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f531,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(X5),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_not__one__le__zero_0) ).
fof(f2474,plain,
spl0_201,
inference(avatar_split_clause,[],[f512,f2472]) ).
fof(f512,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(X5),X5),c_HOL_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__le__one_0) ).
fof(f2470,plain,
spl0_200,
inference(avatar_split_clause,[],[f509,f2468]) ).
fof(f509,axiom,
! [X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X5)
| c_HOL_Ozero__class_Ozero(X5) = hAPP(c_HOL_Oinverse__class_Oinverse(X5),c_HOL_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inverse__zero_0) ).
fof(f2466,plain,
spl0_199,
inference(avatar_split_clause,[],[f395,f2464]) ).
fof(f2464,plain,
( spl0_199
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),c_HOL_Ozero__class_Ozero(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f395,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X5),X5),c_HOL_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_not__one__less__zero_0) ).
fof(f2462,plain,
spl0_198,
inference(avatar_split_clause,[],[f381,f2460]) ).
fof(f2460,plain,
( spl0_198
<=> ! [X34,X33] :
( X33 = X34
| hAPP(c_Suc,X33) != hAPP(c_Suc,X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f381,axiom,
! [X34,X33] :
( X33 = X34
| hAPP(c_Suc,X33) != hAPP(c_Suc,X34) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat_Oinject_0) ).
fof(f2456,plain,
( spl0_197
| ~ spl0_81
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f2373,f2351,f1901,f2454]) ).
fof(f2373,plain,
( ! [X5] : c_Lattices_Olower__semilattice__class_Oinf(X5,X5,tc_Int_Oint) = X5
| ~ spl0_81
| ~ spl0_176 ),
inference(resolution,[],[f2352,f1903]) ).
fof(f2443,plain,
( spl0_196
| ~ spl0_43
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f2372,f2351,f1711,f2441]) ).
fof(f2372,plain,
( ! [X4] : c_Lattices_Olower__semilattice__class_Oinf(X4,X4,tc_bool) = X4
| ~ spl0_43
| ~ spl0_176 ),
inference(resolution,[],[f2352,f1713]) ).
fof(f2439,plain,
spl0_195,
inference(avatar_split_clause,[],[f1271,f2437]) ).
fof(f1271,axiom,
! [X6,X5,X25] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)) != c_Set_Oinsert(X6,X25,X5),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_insert__not__empty_0) ).
fof(f2435,plain,
spl0_194,
inference(avatar_split_clause,[],[f1270,f2433]) ).
fof(f1270,axiom,
! [X1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_minus__nat_Odiff__0_0) ).
fof(f2431,plain,
spl0_193,
inference(avatar_split_clause,[],[f1269,f2429]) ).
fof(f1269,axiom,
! [X1] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X1),X1),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_diff__self__eq__0_0) ).
fof(f2427,plain,
spl0_192,
inference(avatar_split_clause,[],[f1255,f2425]) ).
fof(f1255,axiom,
! [X11,X5] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X5),X11,X5) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__bot__left_0) ).
fof(f2423,plain,
spl0_191,
inference(avatar_split_clause,[],[f1254,f2421]) ).
fof(f1254,axiom,
! [X11,X5] :
( ~ class_Lattices_Obounded__lattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,c_Orderings_Obot__class_Obot(X5),X5) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__bot__right_0) ).
fof(f2419,plain,
spl0_190,
inference(avatar_split_clause,[],[f1009,f2416]) ).
fof(f2416,plain,
( spl0_190
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_GCD_Ogcd__class_OGCD(c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1009,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) = c_GCD_Ogcd__class_OGCD(c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_GCD__empty__nat_0) ).
fof(f2414,plain,
spl0_189,
inference(avatar_split_clause,[],[f952,f2412]) ).
fof(f952,axiom,
! [X5] :
( ~ class_Ring__and__Field_Osemiring__1(X5)
| c_HOL_Ozero__class_Ozero(X5) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_of__nat__0_0) ).
fof(f2410,plain,
spl0_188,
inference(avatar_split_clause,[],[f901,f2408]) ).
fof(f901,axiom,
! [X11,X5] :
( ~ class_Orderings_Obot(X5)
| hBOOL(hAPP(c_lessequals(c_Orderings_Obot__class_Obot(X5),X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_bot__least_0) ).
fof(f2406,plain,
spl0_187,
inference(avatar_split_clause,[],[f898,f2404]) ).
fof(f898,axiom,
! [X2] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X2) = X2,
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_plus__nat_Oadd__0_0) ).
fof(f2402,plain,
spl0_186,
inference(avatar_split_clause,[],[f897,f2400]) ).
fof(f897,axiom,
! [X1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),c_HOL_Ozero__class_Ozero(tc_nat)) = X1,
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Nat_Oadd__0__right_0) ).
fof(f2398,plain,
( spl0_185
| ~ spl0_23
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f2370,f2351,f1611,f2396]) ).
fof(f2396,plain,
( spl0_185
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f2370,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0
| ~ spl0_23
| ~ spl0_176 ),
inference(resolution,[],[f2352,f1613]) ).
fof(f2394,plain,
spl0_184,
inference(avatar_split_clause,[],[f438,f2392]) ).
fof(f438,axiom,
! [X2] : hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,X2))),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_zero__less__Suc_0) ).
fof(f2390,plain,
spl0_183,
inference(avatar_split_clause,[],[f347,f2388]) ).
fof(f2388,plain,
( spl0_183
<=> ! [X5,X11,X10] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| c_Series_Osummable(X10,X5)
| ~ c_Series_Osums(X10,X11,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f347,axiom,
! [X10,X11,X5] :
( ~ class_RealVector_Oreal__normed__vector(X5)
| c_Series_Osummable(X10,X5)
| ~ c_Series_Osums(X10,X11,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sums__iff_0) ).
fof(f2386,plain,
spl0_182,
inference(avatar_split_clause,[],[f251,f2384]) ).
fof(f251,axiom,
! [X18,X6,X5] :
( ~ class_RealVector_Ometric__space(X5)
| c_SEQ_OCauchy(X18,X5)
| ~ c_SEQ_OLIMSEQ(X18,X6,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_LIMSEQ__imp__Cauchy_0) ).
fof(f2382,plain,
spl0_181,
inference(avatar_split_clause,[],[f78,f2379]) ).
fof(f2379,plain,
( spl0_181
<=> c_HOL_Oord__class_Oless(v_n,tc_nat) = c_lessequals(hAPP(c_Suc,v_n),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f78,axiom,
c_HOL_Oord__class_Oless(v_n,tc_nat) = c_lessequals(hAPP(c_Suc,v_n),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__eq__Suc__le__raw_0) ).
fof(f2369,plain,
spl0_180,
inference(avatar_split_clause,[],[f1275,f2367]) ).
fof(f1275,axiom,
! [X5,X25] : c_Lattices_Oupper__semilattice__class_Osup(X25,X25,tc_fun(X5,tc_bool)) = X25,
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Un__absorb_0) ).
fof(f2365,plain,
spl0_179,
inference(avatar_split_clause,[],[f1274,f2363]) ).
fof(f1274,axiom,
! [X11,X5] :
( ~ class_Lattices_Oupper__semilattice(X5)
| c_Lattices_Oupper__semilattice__class_Osup(X11,X11,X5) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_sup__idem_0) ).
fof(f2361,plain,
spl0_178,
inference(avatar_split_clause,[],[f719,f2359]) ).
fof(f719,axiom,
! [X11,X5] :
( ~ class_Orderings_Oorder(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_order__eq__iff_0) ).
fof(f2357,plain,
spl0_177,
inference(avatar_split_clause,[],[f718,f2355]) ).
fof(f2355,plain,
( spl0_177
<=> ! [X5,X11] :
( ~ class_Orderings_Opreorder(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f718,axiom,
! [X11,X5] :
( ~ class_Orderings_Opreorder(X5)
| hBOOL(hAPP(c_lessequals(X11,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_order__eq__refl_0) ).
fof(f2353,plain,
spl0_176,
inference(avatar_split_clause,[],[f603,f2351]) ).
fof(f603,axiom,
! [X11,X5] :
( ~ class_Lattices_Olower__semilattice(X5)
| c_Lattices_Olower__semilattice__class_Oinf(X11,X11,X5) = X11 ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_inf__idem_0) ).
fof(f2349,plain,
spl0_175,
inference(avatar_split_clause,[],[f602,f2347]) ).
fof(f602,axiom,
! [X5,X25] : c_Lattices_Olower__semilattice__class_Oinf(X25,X25,tc_fun(X5,tc_bool)) = X25,
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Int__absorb_0) ).
fof(f2345,plain,
spl0_174,
inference(avatar_split_clause,[],[f572,f2343]) ).
fof(f572,axiom,
! [X2] : ~ hBOOL(hAPP(c_lessequals(hAPP(c_Suc,X2),tc_nat),X2)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_Suc__n__not__le__n_0) ).
fof(f2341,plain,
spl0_173,
inference(avatar_split_clause,[],[f523,f2339]) ).
fof(f523,axiom,
! [X11,X5] :
( ~ class_Orderings_Opreorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_order__less__irrefl_0) ).
fof(f2337,plain,
spl0_172,
inference(avatar_split_clause,[],[f522,f2335]) ).
fof(f522,axiom,
! [X11,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_linorder__neq__iff_1) ).
fof(f2333,plain,
spl0_171,
inference(avatar_split_clause,[],[f519,f2331]) ).
fof(f519,axiom,
! [X11,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X11,X5),X11)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_order__less__le_1) ).
fof(f2329,plain,
spl0_170,
inference(avatar_split_clause,[],[f57,f2327]) ).
fof(f57,axiom,
! [X2] : hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),hAPP(c_Suc,X2))),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_lessI_0) ).
fof(f2324,plain,
spl0_169,
inference(avatar_split_clause,[],[f1471,f2322]) ).
fof(f2322,plain,
( spl0_169
<=> ! [X18,X5,X19] :
( X18 = X19
| ~ c_fequal(X18,X19,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1471,axiom,
! [X18,X19,X5] :
( X18 = X19
| ~ c_fequal(X18,X19,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f2320,plain,
spl0_168,
inference(avatar_split_clause,[],[f1250,f2318]) ).
fof(f2318,plain,
( spl0_168
<=> ! [X5,X11] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1250,axiom,
! [X11,X5] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),X11)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_bot1E_0) ).
fof(f2316,plain,
spl0_167,
inference(avatar_split_clause,[],[f1209,f2314]) ).
fof(f1209,axiom,
! [X11,X5,X25] : hBOOL(hAPP(c_Set_Oinsert(X11,X25,X5),X11)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_insert__code_1) ).
fof(f2312,plain,
spl0_166,
inference(avatar_split_clause,[],[f895,f2310]) ).
fof(f895,axiom,
! [X2] : hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_le0_0) ).
fof(f2308,plain,
spl0_165,
inference(avatar_split_clause,[],[f883,f2306]) ).
fof(f883,axiom,
! [X1] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_gr__implies__not0_0) ).
fof(f2304,plain,
spl0_164,
inference(avatar_split_clause,[],[f612,f2302]) ).
fof(f612,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ozero__neq__one(X5)
| c_HOL_Ozero__class_Ozero(X5) != c_HOL_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_one__neq__zero_0) ).
fof(f2300,plain,
( ~ spl0_163
| ~ spl0_148
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f2295,f2250,f2234,f2297]) ).
fof(f2297,plain,
( spl0_163
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f2234,plain,
( spl0_148
<=> ! [X2] : c_FFT__Mirabelle_Oroot(X2) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f2295,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ spl0_148
| ~ spl0_152 ),
inference(superposition,[],[f2235,f2252]) ).
fof(f2235,plain,
( ! [X2] : c_FFT__Mirabelle_Oroot(X2) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f2234]) ).
fof(f2294,plain,
spl0_162,
inference(avatar_split_clause,[],[f1321,f2292]) ).
fof(f2292,plain,
( spl0_162
<=> ! [X57,X56] :
( ~ class_Orderings_Obot(X57)
| class_Orderings_Obot(tc_fun(X56,X57)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1321,axiom,
! [X56,X57] :
( ~ class_Orderings_Obot(X57)
| class_Orderings_Obot(tc_fun(X56,X57)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_fun__Orderings_Obot) ).
fof(f2290,plain,
spl0_161,
inference(avatar_split_clause,[],[f1320,f2288]) ).
fof(f2288,plain,
( spl0_161
<=> ! [X57,X56] :
( ~ class_Orderings_Oorder(X57)
| class_Orderings_Oorder(tc_fun(X56,X57)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1320,axiom,
! [X56,X57] :
( ~ class_Orderings_Oorder(X57)
| class_Orderings_Oorder(tc_fun(X56,X57)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_fun__Orderings_Oorder) ).
fof(f2286,plain,
spl0_160,
inference(avatar_split_clause,[],[f1319,f2284]) ).
fof(f2284,plain,
( spl0_160
<=> ! [X57,X56] :
( ~ class_Lattices_Olattice(X57)
| class_Lattices_Olattice(tc_fun(X56,X57)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1319,axiom,
! [X56,X57] :
( ~ class_Lattices_Olattice(X57)
| class_Lattices_Olattice(tc_fun(X56,X57)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_fun__Lattices_Olattice) ).
fof(f2282,plain,
spl0_159,
inference(avatar_split_clause,[],[f1318,f2280]) ).
fof(f2280,plain,
( spl0_159
<=> ! [X57,X56] :
( ~ class_Orderings_Opreorder(X57)
| class_Orderings_Opreorder(tc_fun(X56,X57)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1318,axiom,
! [X56,X57] :
( ~ class_Orderings_Opreorder(X57)
| class_Orderings_Opreorder(tc_fun(X56,X57)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_fun__Orderings_Opreorder) ).
fof(f2278,plain,
spl0_158,
inference(avatar_split_clause,[],[f1317,f2276]) ).
fof(f1317,axiom,
! [X56,X57] :
( ~ class_Lattices_Obounded__lattice(X57)
| class_Lattices_Obounded__lattice(tc_fun(X56,X57)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f2274,plain,
spl0_157,
inference(avatar_split_clause,[],[f1316,f2272]) ).
fof(f2272,plain,
( spl0_157
<=> ! [X57,X56] :
( ~ class_Lattices_Odistrib__lattice(X57)
| class_Lattices_Odistrib__lattice(tc_fun(X56,X57)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1316,axiom,
! [X56,X57] :
( ~ class_Lattices_Odistrib__lattice(X57)
| class_Lattices_Odistrib__lattice(tc_fun(X56,X57)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_fun__Lattices_Odistrib__lattice) ).
fof(f2270,plain,
spl0_156,
inference(avatar_split_clause,[],[f1315,f2268]) ).
fof(f1315,axiom,
! [X56,X57] :
( ~ class_Lattices_Olattice(X57)
| class_Lattices_Olower__semilattice(tc_fun(X56,X57)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f2266,plain,
spl0_155,
inference(avatar_split_clause,[],[f1314,f2264]) ).
fof(f1314,axiom,
! [X56,X57] :
( ~ class_Lattices_Olattice(X57)
| class_Lattices_Oupper__semilattice(tc_fun(X56,X57)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_fun__Lattices_Oupper__semilattice) ).
fof(f2262,plain,
spl0_154,
inference(avatar_split_clause,[],[f1313,f2260]) ).
fof(f2260,plain,
( spl0_154
<=> ! [X57,X56] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X57)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X56,X57)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1313,axiom,
! [X56,X57] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X57)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X56,X57)) ),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f2258,plain,
spl0_153,
inference(avatar_split_clause,[],[f1311,f2255]) ).
fof(f1311,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_i,tc_nat),v_n)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_CHAINED_0) ).
fof(f2253,plain,
spl0_152,
inference(avatar_split_clause,[],[f1112,f2250]) ).
fof(f1112,axiom,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_root0_0) ).
fof(f2248,plain,
spl0_151,
inference(avatar_split_clause,[],[f875,f2246]) ).
fof(f2246,plain,
( spl0_151
<=> ! [X34] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(c_Suc,X34) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f875,axiom,
! [X34] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(c_Suc,X34),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_nat_Osimps_I3_J_0) ).
fof(f2244,plain,
spl0_150,
inference(avatar_split_clause,[],[f720,f2242]) ).
fof(f720,axiom,
! [X11] : hBOOL(hAPP(c_lessequals(X11,tc_nat),X11)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_eq__imp__le_0) ).
fof(f2240,plain,
spl0_149,
inference(avatar_split_clause,[],[f520,f2238]) ).
fof(f520,axiom,
! [X2] : ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X2)),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_less__not__refl_0) ).
fof(f2236,plain,
spl0_148,
inference(avatar_split_clause,[],[f1091,f2234]) ).
fof(f1091,axiom,
! [X2] : c_FFT__Mirabelle_Oroot(X2) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_root__nonzero_0) ).
fof(f2232,plain,
spl0_147,
inference(avatar_split_clause,[],[f21,f2230]) ).
fof(f2230,plain,
( spl0_147
<=> ! [X2] : hAPP(c_Suc,X2) != X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f21,axiom,
! [X2] : hAPP(c_Suc,X2) != X2,
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_n__not__Suc__n_0) ).
fof(f2228,plain,
spl0_146,
inference(avatar_split_clause,[],[f1470,f2226]) ).
fof(f2226,plain,
( spl0_146
<=> ! [X5,X11] : c_fequal(X11,X11,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1470,axiom,
! [X11,X5] : c_fequal(X11,X11,X5),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f2224,plain,
spl0_145,
inference(avatar_split_clause,[],[f1466,f2221]) ).
fof(f2221,plain,
( spl0_145
<=> class_Int_Onumber(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1466,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Int_Onumber) ).
fof(f2219,plain,
spl0_144,
inference(avatar_split_clause,[],[f1465,f2216]) ).
fof(f1465,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Power_Opower) ).
fof(f2214,plain,
spl0_143,
inference(avatar_split_clause,[],[f1464,f2211]) ).
fof(f2211,plain,
( spl0_143
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1464,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f2209,plain,
spl0_142,
inference(avatar_split_clause,[],[f1463,f2206]) ).
fof(f2206,plain,
( spl0_142
<=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1463,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(f2204,plain,
spl0_141,
inference(avatar_split_clause,[],[f1462,f2201]) ).
fof(f2201,plain,
( spl0_141
<=> class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1462,axiom,
class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) ).
fof(f2199,plain,
spl0_140,
inference(avatar_split_clause,[],[f1461,f2196]) ).
fof(f2196,plain,
( spl0_140
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1461,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f2194,plain,
spl0_139,
inference(avatar_split_clause,[],[f1460,f2191]) ).
fof(f2191,plain,
( spl0_139
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1460,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(f2189,plain,
spl0_138,
inference(avatar_split_clause,[],[f1459,f2186]) ).
fof(f1459,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f2184,plain,
spl0_137,
inference(avatar_split_clause,[],[f1458,f2181]) ).
fof(f2181,plain,
( spl0_137
<=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1458,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(f2179,plain,
spl0_136,
inference(avatar_split_clause,[],[f1457,f2176]) ).
fof(f2176,plain,
( spl0_136
<=> class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1457,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
fof(f2174,plain,
spl0_135,
inference(avatar_split_clause,[],[f1456,f2171]) ).
fof(f1456,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(f2169,plain,
spl0_134,
inference(avatar_split_clause,[],[f1455,f2166]) ).
fof(f1455,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(f2164,plain,
spl0_133,
inference(avatar_split_clause,[],[f1454,f2161]) ).
fof(f2161,plain,
( spl0_133
<=> class_RealVector_Ometric__space(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1454,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__RealVector_Ometric__space) ).
fof(f2159,plain,
spl0_132,
inference(avatar_split_clause,[],[f1453,f2156]) ).
fof(f2156,plain,
( spl0_132
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1453,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(f2154,plain,
spl0_131,
inference(avatar_split_clause,[],[f1452,f2151]) ).
fof(f1452,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f2149,plain,
spl0_130,
inference(avatar_split_clause,[],[f1451,f2146]) ).
fof(f2146,plain,
( spl0_130
<=> class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1451,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
fof(f2144,plain,
spl0_129,
inference(avatar_split_clause,[],[f1450,f2141]) ).
fof(f1450,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
fof(f2139,plain,
spl0_128,
inference(avatar_split_clause,[],[f1449,f2136]) ).
fof(f1449,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f2134,plain,
spl0_127,
inference(avatar_split_clause,[],[f1448,f2131]) ).
fof(f1448,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
fof(f2129,plain,
spl0_126,
inference(avatar_split_clause,[],[f1447,f2126]) ).
fof(f1447,axiom,
class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) ).
fof(f2124,plain,
spl0_125,
inference(avatar_split_clause,[],[f1446,f2121]) ).
fof(f2121,plain,
( spl0_125
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1446,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
fof(f2119,plain,
spl0_124,
inference(avatar_split_clause,[],[f1445,f2116]) ).
fof(f1445,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f2114,plain,
spl0_123,
inference(avatar_split_clause,[],[f1444,f2111]) ).
fof(f2111,plain,
( spl0_123
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1444,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f2109,plain,
spl0_122,
inference(avatar_split_clause,[],[f1443,f2106]) ).
fof(f2106,plain,
( spl0_122
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1443,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
fof(f2104,plain,
spl0_121,
inference(avatar_split_clause,[],[f1442,f2101]) ).
fof(f1442,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
fof(f2099,plain,
spl0_120,
inference(avatar_split_clause,[],[f1441,f2096]) ).
fof(f2096,plain,
( spl0_120
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1441,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(f2094,plain,
spl0_119,
inference(avatar_split_clause,[],[f1440,f2091]) ).
fof(f1440,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
fof(f2089,plain,
spl0_118,
inference(avatar_split_clause,[],[f1439,f2086]) ).
fof(f2086,plain,
( spl0_118
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1439,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f2084,plain,
spl0_117,
inference(avatar_split_clause,[],[f1438,f2081]) ).
fof(f2081,plain,
( spl0_117
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1438,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f2079,plain,
spl0_116,
inference(avatar_split_clause,[],[f1437,f2076]) ).
fof(f2076,plain,
( spl0_116
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1437,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f2074,plain,
spl0_115,
inference(avatar_split_clause,[],[f1436,f2071]) ).
fof(f2071,plain,
( spl0_115
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1436,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(f2069,plain,
spl0_114,
inference(avatar_split_clause,[],[f1435,f2066]) ).
fof(f1435,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f2064,plain,
spl0_113,
inference(avatar_split_clause,[],[f1434,f2061]) ).
fof(f1434,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
fof(f2059,plain,
spl0_112,
inference(avatar_split_clause,[],[f1433,f2056]) ).
fof(f2056,plain,
( spl0_112
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1433,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
fof(f2054,plain,
spl0_111,
inference(avatar_split_clause,[],[f1432,f2051]) ).
fof(f2051,plain,
( spl0_111
<=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1432,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(f2049,plain,
spl0_110,
inference(avatar_split_clause,[],[f1431,f2046]) ).
fof(f2046,plain,
( spl0_110
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1431,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(f2044,plain,
spl0_109,
inference(avatar_split_clause,[],[f1430,f2041]) ).
fof(f2041,plain,
( spl0_109
<=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1430,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(f2039,plain,
spl0_108,
inference(avatar_split_clause,[],[f1429,f2036]) ).
fof(f2036,plain,
( spl0_108
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1429,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f2034,plain,
spl0_107,
inference(avatar_split_clause,[],[f1428,f2031]) ).
fof(f2031,plain,
( spl0_107
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1428,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f2029,plain,
spl0_106,
inference(avatar_split_clause,[],[f1427,f2026]) ).
fof(f2026,plain,
( spl0_106
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1427,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f2024,plain,
spl0_105,
inference(avatar_split_clause,[],[f1426,f2021]) ).
fof(f2021,plain,
( spl0_105
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1426,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Int_Onumber) ).
fof(f2019,plain,
spl0_104,
inference(avatar_split_clause,[],[f1425,f2016]) ).
fof(f1425,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Power_Opower) ).
fof(f2014,plain,
spl0_103,
inference(avatar_split_clause,[],[f1424,f2011]) ).
fof(f2011,plain,
( spl0_103
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1424,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Int_Onumber__ring) ).
fof(f2009,plain,
spl0_102,
inference(avatar_split_clause,[],[f1423,f2006]) ).
fof(f2006,plain,
( spl0_102
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1423,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Int_Oring__char__0) ).
fof(f2004,plain,
spl0_101,
inference(avatar_split_clause,[],[f1422,f2001]) ).
fof(f2001,plain,
( spl0_101
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1422,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Orderings_Oorder) ).
fof(f1999,plain,
spl0_100,
inference(avatar_split_clause,[],[f1421,f1996]) ).
fof(f1421,axiom,
class_Lattices_Olattice(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Lattices_Olattice) ).
fof(f1994,plain,
spl0_99,
inference(avatar_split_clause,[],[f1420,f1991]) ).
fof(f1991,plain,
( spl0_99
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1420,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Orderings_Olinorder) ).
fof(f1989,plain,
spl0_98,
inference(avatar_split_clause,[],[f1419,f1986]) ).
fof(f1986,plain,
( spl0_98
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1419,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Orderings_Opreorder) ).
fof(f1984,plain,
spl0_97,
inference(avatar_split_clause,[],[f1418,f1981]) ).
fof(f1981,plain,
( spl0_97
<=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1418,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Nat_Osemiring__char__0) ).
fof(f1979,plain,
spl0_96,
inference(avatar_split_clause,[],[f1417,f1976]) ).
fof(f1976,plain,
( spl0_96
<=> class_Ring__and__Field_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1417,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
fof(f1974,plain,
spl0_95,
inference(avatar_split_clause,[],[f1416,f1971]) ).
fof(f1971,plain,
( spl0_95
<=> class_Ring__and__Field_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1416,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Oring) ).
fof(f1969,plain,
spl0_94,
inference(avatar_split_clause,[],[f1415,f1966]) ).
fof(f1966,plain,
( spl0_94
<=> class_Ring__and__Field_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1415,axiom,
class_Ring__and__Field_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).
fof(f1964,plain,
spl0_93,
inference(avatar_split_clause,[],[f1414,f1961]) ).
fof(f1414,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
fof(f1959,plain,
spl0_92,
inference(avatar_split_clause,[],[f1413,f1956]) ).
fof(f1413,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
fof(f1954,plain,
spl0_91,
inference(avatar_split_clause,[],[f1412,f1951]) ).
fof(f1951,plain,
( spl0_91
<=> class_Ring__and__Field_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1412,axiom,
class_Ring__and__Field_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).
fof(f1949,plain,
spl0_90,
inference(avatar_split_clause,[],[f1411,f1946]) ).
fof(f1946,plain,
( spl0_90
<=> class_Lattices_Odistrib__lattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1411,axiom,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Lattices_Odistrib__lattice) ).
fof(f1944,plain,
spl0_89,
inference(avatar_split_clause,[],[f1410,f1941]) ).
fof(f1410,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
fof(f1939,plain,
spl0_88,
inference(avatar_split_clause,[],[f1409,f1936]) ).
fof(f1936,plain,
( spl0_88
<=> class_Ring__and__Field_Ocomm__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1409,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring) ).
fof(f1934,plain,
spl0_87,
inference(avatar_split_clause,[],[f1408,f1931]) ).
fof(f1931,plain,
( spl0_87
<=> class_Ring__and__Field_Omult__mono(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1408,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).
fof(f1929,plain,
spl0_86,
inference(avatar_split_clause,[],[f1407,f1926]) ).
fof(f1407,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
fof(f1924,plain,
spl0_85,
inference(avatar_split_clause,[],[f1406,f1921]) ).
fof(f1406,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
fof(f1919,plain,
spl0_84,
inference(avatar_split_clause,[],[f1405,f1916]) ).
fof(f1916,plain,
( spl0_84
<=> class_Ring__and__Field_Omult__mono1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1405,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).
fof(f1914,plain,
spl0_83,
inference(avatar_split_clause,[],[f1404,f1911]) ).
fof(f1404,axiom,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
fof(f1909,plain,
spl0_82,
inference(avatar_split_clause,[],[f1403,f1906]) ).
fof(f1403,axiom,
class_Ring__and__Field_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).
fof(f1904,plain,
spl0_81,
inference(avatar_split_clause,[],[f1402,f1901]) ).
fof(f1402,axiom,
class_Lattices_Olower__semilattice(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Lattices_Olower__semilattice) ).
fof(f1899,plain,
spl0_80,
inference(avatar_split_clause,[],[f1401,f1896]) ).
fof(f1401,axiom,
class_Lattices_Oupper__semilattice(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Lattices_Oupper__semilattice) ).
fof(f1894,plain,
spl0_79,
inference(avatar_split_clause,[],[f1400,f1891]) ).
fof(f1891,plain,
( spl0_79
<=> class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1400,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
fof(f1889,plain,
spl0_78,
inference(avatar_split_clause,[],[f1399,f1886]) ).
fof(f1886,plain,
( spl0_78
<=> class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1399,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
fof(f1884,plain,
spl0_77,
inference(avatar_split_clause,[],[f1398,f1881]) ).
fof(f1398,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
fof(f1879,plain,
spl0_76,
inference(avatar_split_clause,[],[f1397,f1876]) ).
fof(f1876,plain,
( spl0_76
<=> class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1397,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) ).
fof(f1874,plain,
spl0_75,
inference(avatar_split_clause,[],[f1396,f1871]) ).
fof(f1871,plain,
( spl0_75
<=> class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1396,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).
fof(f1869,plain,
spl0_74,
inference(avatar_split_clause,[],[f1395,f1866]) ).
fof(f1866,plain,
( spl0_74
<=> class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1395,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
fof(f1864,plain,
spl0_73,
inference(avatar_split_clause,[],[f1394,f1861]) ).
fof(f1394,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1859,plain,
spl0_72,
inference(avatar_split_clause,[],[f1393,f1856]) ).
fof(f1856,plain,
( spl0_72
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1393,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).
fof(f1854,plain,
spl0_71,
inference(avatar_split_clause,[],[f1392,f1851]) ).
fof(f1851,plain,
( spl0_71
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1392,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1849,plain,
spl0_70,
inference(avatar_split_clause,[],[f1391,f1846]) ).
fof(f1391,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1844,plain,
spl0_69,
inference(avatar_split_clause,[],[f1390,f1841]) ).
fof(f1841,plain,
( spl0_69
<=> class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1390,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
fof(f1839,plain,
spl0_68,
inference(avatar_split_clause,[],[f1389,f1836]) ).
fof(f1836,plain,
( spl0_68
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1389,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
fof(f1834,plain,
spl0_67,
inference(avatar_split_clause,[],[f1388,f1831]) ).
fof(f1831,plain,
( spl0_67
<=> class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1388,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).
fof(f1829,plain,
spl0_66,
inference(avatar_split_clause,[],[f1387,f1826]) ).
fof(f1826,plain,
( spl0_66
<=> class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1387,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).
fof(f1824,plain,
spl0_65,
inference(avatar_split_clause,[],[f1386,f1821]) ).
fof(f1821,plain,
( spl0_65
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1386,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1819,plain,
spl0_64,
inference(avatar_split_clause,[],[f1385,f1816]) ).
fof(f1816,plain,
( spl0_64
<=> class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1385,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
fof(f1814,plain,
spl0_63,
inference(avatar_split_clause,[],[f1384,f1811]) ).
fof(f1811,plain,
( spl0_63
<=> class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1384,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
fof(f1809,plain,
spl0_62,
inference(avatar_split_clause,[],[f1383,f1806]) ).
fof(f1806,plain,
( spl0_62
<=> class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1383,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).
fof(f1804,plain,
spl0_61,
inference(avatar_split_clause,[],[f1382,f1801]) ).
fof(f1801,plain,
( spl0_61
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1382,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1799,plain,
spl0_60,
inference(avatar_split_clause,[],[f1381,f1796]) ).
fof(f1796,plain,
( spl0_60
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1381,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1794,plain,
spl0_59,
inference(avatar_split_clause,[],[f1380,f1791]) ).
fof(f1791,plain,
( spl0_59
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1380,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1789,plain,
spl0_58,
inference(avatar_split_clause,[],[f1379,f1786]) ).
fof(f1786,plain,
( spl0_58
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1379,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1784,plain,
spl0_57,
inference(avatar_split_clause,[],[f1378,f1781]) ).
fof(f1781,plain,
( spl0_57
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1378,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1779,plain,
spl0_56,
inference(avatar_split_clause,[],[f1377,f1776]) ).
fof(f1776,plain,
( spl0_56
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f1377,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f1774,plain,
spl0_55,
inference(avatar_split_clause,[],[f1376,f1771]) ).
fof(f1771,plain,
( spl0_55
<=> class_OrderedGroup_Olordered__ab__group__add__join(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1376,axiom,
class_OrderedGroup_Olordered__ab__group__add__join(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__join) ).
fof(f1769,plain,
spl0_54,
inference(avatar_split_clause,[],[f1375,f1766]) ).
fof(f1766,plain,
( spl0_54
<=> class_OrderedGroup_Olordered__ab__group__add__meet(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1375,axiom,
class_OrderedGroup_Olordered__ab__group__add__meet(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__meet) ).
fof(f1764,plain,
spl0_53,
inference(avatar_split_clause,[],[f1374,f1761]) ).
fof(f1761,plain,
( spl0_53
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1374,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1759,plain,
spl0_52,
inference(avatar_split_clause,[],[f1373,f1756]) ).
fof(f1756,plain,
( spl0_52
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1373,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1754,plain,
spl0_51,
inference(avatar_split_clause,[],[f1372,f1751]) ).
fof(f1751,plain,
( spl0_51
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1372,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1749,plain,
spl0_50,
inference(avatar_split_clause,[],[f1371,f1746]) ).
fof(f1746,plain,
( spl0_50
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1371,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1744,plain,
spl0_49,
inference(avatar_split_clause,[],[f1370,f1741]) ).
fof(f1741,plain,
( spl0_49
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f1370,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_bool__Orderings_Obot) ).
fof(f1739,plain,
spl0_48,
inference(avatar_split_clause,[],[f1369,f1736]) ).
fof(f1369,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_bool__Orderings_Oorder) ).
fof(f1734,plain,
spl0_47,
inference(avatar_split_clause,[],[f1368,f1731]) ).
fof(f1368,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_bool__Lattices_Olattice) ).
fof(f1729,plain,
spl0_46,
inference(avatar_split_clause,[],[f1367,f1726]) ).
fof(f1726,plain,
( spl0_46
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f1367,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_bool__Orderings_Opreorder) ).
fof(f1724,plain,
spl0_45,
inference(avatar_split_clause,[],[f1366,f1721]) ).
fof(f1366,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f1719,plain,
spl0_44,
inference(avatar_split_clause,[],[f1365,f1716]) ).
fof(f1716,plain,
( spl0_44
<=> class_Lattices_Odistrib__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1365,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_bool__Lattices_Odistrib__lattice) ).
fof(f1714,plain,
spl0_43,
inference(avatar_split_clause,[],[f1364,f1711]) ).
fof(f1364,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f1709,plain,
spl0_42,
inference(avatar_split_clause,[],[f1363,f1706]) ).
fof(f1363,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_bool__Lattices_Oupper__semilattice) ).
fof(f1704,plain,
spl0_41,
inference(avatar_split_clause,[],[f1362,f1701]) ).
fof(f1362,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
fof(f1699,plain,
spl0_40,
inference(avatar_split_clause,[],[f1361,f1696]) ).
fof(f1696,plain,
( spl0_40
<=> class_Int_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1361,axiom,
class_Int_Onumber(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Int_Onumber) ).
fof(f1694,plain,
spl0_39,
inference(avatar_split_clause,[],[f1360,f1691]) ).
fof(f1360,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Power_Opower) ).
fof(f1689,plain,
spl0_38,
inference(avatar_split_clause,[],[f1359,f1686]) ).
fof(f1359,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Orderings_Obot) ).
fof(f1684,plain,
spl0_37,
inference(avatar_split_clause,[],[f1358,f1681]) ).
fof(f1358,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Orderings_Oorder) ).
fof(f1679,plain,
spl0_36,
inference(avatar_split_clause,[],[f1357,f1676]) ).
fof(f1357,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Lattices_Olattice) ).
fof(f1674,plain,
spl0_35,
inference(avatar_split_clause,[],[f1356,f1671]) ).
fof(f1356,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Orderings_Olinorder) ).
fof(f1669,plain,
spl0_34,
inference(avatar_split_clause,[],[f1355,f1666]) ).
fof(f1355,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Orderings_Opreorder) ).
fof(f1664,plain,
spl0_33,
inference(avatar_split_clause,[],[f1354,f1661]) ).
fof(f1661,plain,
( spl0_33
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1354,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f1659,plain,
spl0_32,
inference(avatar_split_clause,[],[f1353,f1656]) ).
fof(f1656,plain,
( spl0_32
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1353,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f1654,plain,
spl0_31,
inference(avatar_split_clause,[],[f1352,f1651]) ).
fof(f1651,plain,
( spl0_31
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1352,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f1649,plain,
spl0_30,
inference(avatar_split_clause,[],[f1351,f1646]) ).
fof(f1646,plain,
( spl0_30
<=> class_Lattices_Odistrib__lattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1351,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Lattices_Odistrib__lattice) ).
fof(f1644,plain,
spl0_29,
inference(avatar_split_clause,[],[f1350,f1641]) ).
fof(f1350,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f1639,plain,
spl0_28,
inference(avatar_split_clause,[],[f1349,f1636]) ).
fof(f1636,plain,
( spl0_28
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1349,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f1634,plain,
spl0_27,
inference(avatar_split_clause,[],[f1348,f1631]) ).
fof(f1631,plain,
( spl0_27
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1348,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f1629,plain,
spl0_26,
inference(avatar_split_clause,[],[f1347,f1626]) ).
fof(f1626,plain,
( spl0_26
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1347,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f1624,plain,
spl0_25,
inference(avatar_split_clause,[],[f1346,f1621]) ).
fof(f1346,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f1619,plain,
spl0_24,
inference(avatar_split_clause,[],[f1345,f1616]) ).
fof(f1345,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f1614,plain,
spl0_23,
inference(avatar_split_clause,[],[f1344,f1611]) ).
fof(f1344,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Lattices_Olower__semilattice) ).
fof(f1609,plain,
spl0_22,
inference(avatar_split_clause,[],[f1343,f1606]) ).
fof(f1343,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Lattices_Oupper__semilattice) ).
fof(f1604,plain,
spl0_21,
inference(avatar_split_clause,[],[f1342,f1601]) ).
fof(f1342,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f1599,plain,
spl0_20,
inference(avatar_split_clause,[],[f1341,f1596]) ).
fof(f1341,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1594,plain,
spl0_19,
inference(avatar_split_clause,[],[f1340,f1591]) ).
fof(f1591,plain,
( spl0_19
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1340,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f1589,plain,
spl0_18,
inference(avatar_split_clause,[],[f1339,f1586]) ).
fof(f1586,plain,
( spl0_18
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1339,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1584,plain,
spl0_17,
inference(avatar_split_clause,[],[f1338,f1581]) ).
fof(f1338,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1579,plain,
spl0_16,
inference(avatar_split_clause,[],[f1337,f1576]) ).
fof(f1576,plain,
( spl0_16
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1337,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f1574,plain,
spl0_15,
inference(avatar_split_clause,[],[f1336,f1571]) ).
fof(f1571,plain,
( spl0_15
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1336,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1569,plain,
spl0_14,
inference(avatar_split_clause,[],[f1335,f1566]) ).
fof(f1566,plain,
( spl0_14
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1335,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1564,plain,
spl0_13,
inference(avatar_split_clause,[],[f1334,f1561]) ).
fof(f1334,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f1559,plain,
spl0_12,
inference(avatar_split_clause,[],[f1333,f1556]) ).
fof(f1556,plain,
( spl0_12
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1333,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f1554,plain,
spl0_11,
inference(avatar_split_clause,[],[f1332,f1551]) ).
fof(f1551,plain,
( spl0_11
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1332,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f1549,plain,
spl0_10,
inference(avatar_split_clause,[],[f1331,f1546]) ).
fof(f1546,plain,
( spl0_10
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1331,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f1544,plain,
spl0_9,
inference(avatar_split_clause,[],[f1330,f1541]) ).
fof(f1541,plain,
( spl0_9
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1330,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1539,plain,
spl0_8,
inference(avatar_split_clause,[],[f1329,f1536]) ).
fof(f1536,plain,
( spl0_8
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1329,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1534,plain,
spl0_7,
inference(avatar_split_clause,[],[f1328,f1531]) ).
fof(f1531,plain,
( spl0_7
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1328,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1529,plain,
spl0_6,
inference(avatar_split_clause,[],[f1327,f1526]) ).
fof(f1526,plain,
( spl0_6
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1327,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1524,plain,
spl0_5,
inference(avatar_split_clause,[],[f1326,f1521]) ).
fof(f1521,plain,
( spl0_5
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1326,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1519,plain,
spl0_4,
inference(avatar_split_clause,[],[f1325,f1516]) ).
fof(f1516,plain,
( spl0_4
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1325,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1514,plain,
spl0_3,
inference(avatar_split_clause,[],[f1324,f1511]) ).
fof(f1511,plain,
( spl0_3
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1324,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1509,plain,
spl0_2,
inference(avatar_split_clause,[],[f1323,f1506]) ).
fof(f1506,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1323,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1504,plain,
spl0_1,
inference(avatar_split_clause,[],[f1322,f1501]) ).
fof(f1501,plain,
( spl0_1
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1322,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.buCajYBDeu/Vampire---4.8_22737',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.27 % Problem : SWV693-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.28 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.27/0.47 % Computer : n022.cluster.edu
% 0.27/0.47 % Model : x86_64 x86_64
% 0.27/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.47 % Memory : 8042.1875MB
% 0.27/0.47 % OS : Linux 3.10.0-693.el7.x86_64
% 0.27/0.47 % CPULimit : 300
% 0.27/0.47 % WCLimit : 300
% 0.27/0.47 % DateTime : Wed Aug 30 17:42:53 EDT 2023
% 0.31/0.48 % CPUTime :
% 0.31/0.51 % (22844)Running in auto input_syntax mode. Trying TPTP
% 0.38/0.56 % (22845)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.38/0.56 % (22847)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)
% 0.38/0.56 % (22849)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)
% 0.38/0.56 % (22848)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.38/0.56 % (22851)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)
% 0.38/0.56 % (22850)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)
% 0.38/0.56 % (22846)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.39/1.05 TRYING [1]
% 4.27/1.14 TRYING [2]
% 11.24/2.13 TRYING [1]
% 11.56/2.22 TRYING [2]
% 14.94/2.67 TRYING [1]
% 16.38/2.87 TRYING [3]
% 16.60/2.89 TRYING [2]
% 20.96/3.52 TRYING [3]
% 29.78/4.82 % (22849)First to succeed.
% 30.47/4.91 % (22849)Refutation found. Thanks to Tanya!
% 30.47/4.91 % SZS status Unsatisfiable for Vampire---4
% 30.47/4.91 % SZS output start Proof for Vampire---4
% See solution above
% 30.90/4.95 % (22849)------------------------------
% 30.90/4.95 % (22849)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 30.90/4.95 % (22849)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 30.90/4.95 % (22849)Termination reason: Refutation
% 30.90/4.95
% 30.90/4.95 % (22849)Memory used [KB]: 66523
% 30.90/4.95 % (22849)Time elapsed: 4.338 s
% 30.90/4.95 % (22849)------------------------------
% 30.90/4.95 % (22849)------------------------------
% 30.90/4.95 % (22844)Success in time 4.454 s
% 30.90/4.95 % Vampire---4.8 exiting
%------------------------------------------------------------------------------