TSTP Solution File: SWV594-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV594-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:02:53 EDT 2024
% Result : Unsatisfiable 12.40s 2.18s
% Output : Refutation 12.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2375
% Syntax : Number of formulae : 4319 (1244 unt; 0 def)
% Number of atoms : 11784 (1770 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 13316 (5851 ~;6154 |; 0 &)
% (1311 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 1394 (1392 usr;1312 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 5 con; 0-3 aty)
% Number of variables : 6649 (6649 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26345,plain,
$false,
inference(avatar_sat_refutation,[],[f1337,f1343,f1349,f1355,f1361,f1367,f1373,f1379,f1384,f1389,f1394,f1399,f1404,f1409,f1413,f1418,f1424,f1430,f1436,f1442,f1448,f1453,f1457,f1462,f1467,f1472,f1477,f1482,f1487,f1493,f1499,f1505,f1509,f1514,f1519,f1524,f1529,f1534,f1538,f1542,f1546,f1555,f1560,f1565,f1570,f1575,f1580,f1585,f1590,f1595,f1600,f1605,f1610,f1615,f1620,f1625,f1630,f1635,f1640,f1645,f1650,f1655,f1660,f1665,f1670,f1675,f1680,f1685,f1690,f1695,f1700,f1705,f1710,f1715,f1720,f1725,f1730,f1735,f1740,f1745,f1750,f1755,f1760,f1765,f1770,f1775,f1780,f1785,f1790,f1795,f1800,f1805,f1810,f1815,f1820,f1825,f1830,f1835,f1840,f1845,f1850,f1855,f1860,f1865,f1870,f1875,f1880,f1885,f1890,f1895,f1900,f1905,f1910,f1915,f1920,f1925,f1930,f1935,f1940,f1945,f1950,f1955,f1960,f1965,f1970,f1975,f1980,f1985,f1990,f1995,f2000,f2005,f2010,f2015,f2020,f2025,f2030,f2035,f2040,f2045,f2050,f2055,f2060,f2065,f2070,f2075,f2080,f2085,f2090,f2095,f2100,f2105,f2110,f2115,f2120,f2125,f2129,f2134,f2139,f2144,f2149,f2154,f2160,f2164,f2168,f2172,f2176,f2180,f2189,f2195,f2200,f2205,f2210,f2215,f2220,f2225,f2230,f2235,f2241,f2245,f2252,f2256,f2260,f2264,f2268,f2272,f2276,f2280,f2284,f2289,f2293,f2307,f2312,f2318,f2324,f2330,f2335,f2340,f2346,f2352,f2358,f2364,f2369,f2375,f2379,f2383,f2387,f2391,f2395,f2399,f2405,f2409,f2413,f2417,f2421,f2436,f2455,f2461,f2466,f2472,f2476,f2481,f2485,f2489,f2493,f2504,f2509,f2514,f2519,f2524,f2529,f2534,f2538,f2542,f2546,f2550,f2555,f2559,f2582,f2587,f2592,f2599,f2603,f2609,f2613,f2617,f2621,f2633,f2638,f2643,f2650,f2654,f2658,f2683,f2687,f2697,f2702,f2708,f2713,f2719,f2724,f2730,f2734,f2739,f2743,f2747,f2751,f2755,f2770,f2777,f2782,f2786,f2796,f2801,f2806,f2817,f2822,f2827,f2832,f2837,f2842,f2847,f2851,f2855,f2859,f2864,f2868,f2872,f2876,f2880,f2884,f2920,f2924,f2929,f2940,f2944,f2949,f2954,f2958,f2966,f2971,f2977,f2983,f2989,f2993,f2997,f3001,f3031,f3036,f3041,f3049,f3053,f3057,f3061,f3065,f3069,f3074,f3078,f3082,f3136,f3142,f3146,f3151,f3155,f3177,f3181,f3185,f3189,f3193,f3197,f3201,f3255,f3259,f3263,f3270,f3274,f3278,f3282,f3286,f3290,f3294,f3360,f3366,f3372,f3376,f3380,f3415,f3419,f3423,f3427,f3431,f3435,f3439,f3461,f3465,f3469,f3473,f3477,f3481,f3485,f3489,f3493,f3497,f3501,f3505,f3509,f3513,f3517,f3521,f3525,f3529,f3533,f3537,f3541,f3545,f3549,f3553,f3557,f3561,f3565,f3569,f3573,f3577,f3581,f3585,f3589,f3593,f3597,f3601,f3605,f3609,f3613,f3617,f3621,f3625,f3629,f3636,f3640,f3644,f3648,f3652,f3656,f3660,f3664,f3668,f3688,f3793,f3824,f3873,f3877,f3881,f3885,f3889,f3894,f3898,f3902,f3906,f3910,f3914,f3918,f3922,f3926,f3930,f3934,f3938,f3942,f3946,f3950,f3954,f3958,f3962,f3966,f3970,f3974,f3979,f3983,f3987,f3991,f3995,f3999,f4003,f4007,f4011,f4015,f4019,f4024,f4028,f4032,f4036,f4040,f4044,f4212,f4403,f4416,f4420,f4424,f4428,f4432,f4440,f4444,f4448,f4452,f4456,f4460,f4464,f4468,f4472,f4476,f4481,f4485,f4489,f4493,f4497,f4501,f4505,f4509,f4513,f4517,f4521,f4527,f4531,f4535,f4539,f4543,f4547,f4551,f4555,f4559,f4563,f4568,f4572,f4576,f4580,f4584,f4588,f4592,f4596,f4600,f4609,f4614,f4840,f4934,f4938,f4942,f4946,f4950,f4954,f4964,f4968,f4972,f4976,f4980,f4984,f4988,f4992,f4996,f5000,f5004,f5008,f5012,f5016,f5020,f5024,f5028,f5032,f5036,f5040,f5044,f5059,f5063,f5067,f5071,f5075,f5079,f5083,f5087,f5091,f5095,f5099,f5103,f5107,f5111,f5115,f5119,f5123,f5127,f5131,f5135,f5139,f5227,f5668,f5836,f5840,f5844,f5848,f5852,f5856,f5860,f5864,f5868,f5872,f5876,f5880,f5884,f5888,f5892,f5911,f5915,f5919,f5923,f5927,f5931,f5935,f5939,f5943,f5947,f5952,f5956,f5960,f5964,f5968,f5972,f5976,f5980,f5984,f5988,f5992,f5996,f6000,f6004,f6008,f6012,f6016,f6020,f6024,f6028,f6032,f6036,f6040,f6044,f6048,f6052,f6056,f6060,f6064,f6068,f6072,f6076,f6080,f6084,f6088,f6092,f6097,f6101,f6105,f6109,f6113,f6117,f6121,f6125,f6145,f6149,f6878,f7165,f7255,f7259,f7264,f7268,f7272,f7276,f7280,f7284,f7288,f7292,f7296,f7300,f7304,f7316,f7320,f7324,f7328,f7332,f7336,f7340,f7344,f7348,f7352,f7380,f7384,f7388,f7392,f7396,f7400,f7404,f7408,f7412,f7416,f7420,f7424,f7428,f7432,f7436,f7440,f7444,f7448,f7452,f7456,f7460,f7464,f7468,f7472,f7476,f7480,f7484,f7488,f7492,f7496,f7500,f7504,f7508,f7512,f7516,f7520,f7524,f7528,f7532,f7536,f7540,f7544,f7548,f7577,f7581,f7585,f8314,f8492,f9094,f9098,f9103,f9107,f9111,f9115,f9119,f9123,f9127,f9131,f9135,f9139,f9143,f9148,f9152,f9156,f9160,f9164,f9168,f9172,f9176,f9180,f9184,f9188,f9192,f9196,f9200,f9204,f9208,f9212,f9216,f9220,f9224,f9228,f9232,f9236,f9240,f9244,f9248,f9252,f9256,f9260,f9264,f9268,f9272,f9276,f9280,f9284,f9288,f9292,f9296,f9300,f9304,f9308,f9312,f9316,f9320,f9324,f9444,f9566,f9853,f9857,f9861,f9865,f9869,f9873,f9877,f9881,f9886,f9890,f9894,f9898,f9902,f9906,f9910,f9914,f9918,f9922,f9926,f9930,f9934,f9938,f9942,f9946,f9950,f9954,f9958,f9962,f9966,f9971,f9975,f9979,f9983,f9987,f9991,f9995,f9999,f10003,f10007,f10011,f10016,f10148,f10364,f10512,f10628,f10632,f10651,f10655,f10659,f10663,f10667,f10671,f10675,f10679,f10683,f10687,f10710,f10714,f10718,f10722,f10726,f10730,f10734,f10738,f10742,f10746,f10754,f10758,f10762,f10766,f10770,f10774,f10778,f10782,f10786,f10790,f10800,f10804,f10808,f10812,f10816,f10820,f10824,f10828,f10832,f10836,f10878,f10882,f10886,f10890,f10894,f10898,f10902,f10906,f10910,f10914,f10919,f10923,f10927,f10931,f10935,f10939,f10943,f10947,f10951,f10955,f10959,f10982,f10986,f10990,f10994,f10998,f11002,f11006,f11010,f11014,f11018,f11043,f11146,f11312,f11471,f11496,f11518,f11537,f11584,f11588,f11592,f11596,f11600,f11604,f11623,f11627,f11631,f11635,f11639,f11643,f11647,f11651,f11655,f11659,f11682,f11686,f11690,f11694,f11698,f11702,f11706,f11710,f11714,f11718,f12308,f12312,f12316,f12320,f12325,f12329,f12333,f12337,f12341,f12345,f12349,f12353,f12357,f12361,f12365,f12388,f12392,f12396,f12400,f12404,f12408,f12412,f12416,f12420,f12424,f12484,f12488,f12492,f12496,f13001,f13005,f13009,f13013,f13017,f13021,f13025,f13029,f13034,f13038,f13042,f13046,f13050,f13054,f13058,f13062,f13066,f13070,f13074,f13091,f13095,f13099,f13103,f13107,f13111,f13115,f13119,f13123,f13127,f13131,f13135,f13139,f13143,f13147,f13151,f13155,f13159,f13163,f13167,f13171,f13176,f13180,f13184,f13188,f13192,f13196,f13200,f13204,f13208,f13212,f13216,f13221,f13225,f13229,f13233,f13237,f13241,f13245,f13249,f13253,f13257,f13261,f13265,f13269,f13273,f13277,f13281,f13285,f13289,f13293,f13297,f13301,f13305,f13309,f13313,f13317,f13321,f13325,f13329,f13333,f13337,f13341,f13345,f13349,f13353,f13357,f13361,f13365,f13369,f13373,f13377,f13381,f13385,f13389,f13393,f13397,f13401,f13405,f13409,f13413,f13417,f13421,f13425,f13429,f13433,f13437,f13441,f13445,f13449,f15507,f15716,f15748,f15752,f15756,f15760,f15764,f15768,f15772,f15776,f15780,f15784,f15788,f15792,f15796,f15800,f15804,f15808,f15812,f15816,f15820,f15824,f15845,f15849,f15853,f15857,f15861,f15865,f15869,f15873,f15877,f15881,f15885,f15889,f15893,f15897,f15901,f15905,f15909,f15913,f15917,f15921,f15925,f15944,f15948,f15952,f15956,f15960,f15964,f15968,f15972,f15976,f15980,f15985,f15989,f16373,f18167,f18171,f18175,f18179,f18183,f18187,f18191,f18195,f18199,f18203,f18207,f18211,f18215,f18219,f18223,f18227,f18231,f18235,f18239,f18243,f18247,f18251,f18255,f18259,f18263,f18267,f18271,f18275,f18279,f18313,f18897,f18901,f18905,f18909,f18913,f18934,f18938,f18942,f18946,f18950,f18954,f18958,f18962,f18966,f18970,f18994,f18998,f19100,f19198,f19216,f19220,f19224,f19228,f19232,f19236,f19240,f19331,f19435,f19439,f19443,f19447,f19451,f19455,f19527,f19531,f19535,f19539,f19543,f19547,f19551,f19555,f19559,f19563,f19567,f19571,f19575,f19579,f19583,f19622,f19899,f20069,f20073,f20077,f20081,f20217,f20266,f20270,f20274,f20278,f20282,f20286,f20290,f20294,f20298,f20356,f20360,f20364,f20368,f20372,f20376,f20380,f20384,f20388,f20392,f20396,f20400,f20404,f20408,f20790,f21413,f21673,f21677,f21681,f21685,f21874,f21878,f21882,f21886,f21890,f21894,f21898,f21909,f21913,f21917,f21921,f21925,f21929,f21933,f21937,f21941,f21945,f21955,f22528,f23080,f23084,f23088,f23092,f23096,f23100,f23104,f23108,f23112,f23116,f23120,f23124,f23128,f23658,f23662,f23666,f23680,f23684,f23688,f23729,f23733,f23743,f23748,f23760,f23772,f23776,f23929,f24003,f24028,f24053,f24093,f24133,f24209,f24285,f24449,f24453,f24458,f24463,f24507,f24599,f24603,f24607,f24611,f24615,f24639,f24643,f24648,f24666,f24679,f24781,f24887,f24918,f24923,f24947,f24967,f24982,f25020,f25024,f25092,f25177,f25262,f25315,f26027,f26031,f26035,f26043,f26052,f26056,f26060,f26078,f26092,f26097,f26101,f26105,f26109,f26113,f26304,f26309,f26337]) ).
fof(f26337,plain,
( ~ spl0_254
| ~ spl0_1311 ),
inference(avatar_contradiction_clause,[],[f26319]) ).
fof(f26319,plain,
( $false
| ~ spl0_254
| ~ spl0_1311 ),
inference(resolution,[],[f26308,f2682]) ).
fof(f2682,plain,
( ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_RealDef_Oreal)
| ~ spl0_254 ),
inference(avatar_component_clause,[],[f2681]) ).
fof(f2681,plain,
( spl0_254
<=> ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f26308,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_1311 ),
inference(avatar_component_clause,[],[f26306]) ).
fof(f26306,plain,
( spl0_1311
<=> c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f26309,plain,
( ~ spl0_257
| ~ spl0_13
| spl0_1311
| ~ spl0_8
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2624,f2615,f1376,f26306,f1401,f2699]) ).
fof(f2699,plain,
( spl0_257
<=> c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f1401,plain,
( spl0_13
<=> c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),v_x,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1376,plain,
( spl0_8
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Osin(v_x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f2615,plain,
( spl0_246
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Opi,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f2624,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),v_x,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_8
| ~ spl0_246 ),
inference(superposition,[],[f2616,f1378]) ).
fof(f1378,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Osin(v_x)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f1376]) ).
fof(f2616,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_246 ),
inference(avatar_component_clause,[],[f2615]) ).
fof(f26304,plain,
( spl0_1310
| ~ spl0_1098
| ~ spl0_1289 ),
inference(avatar_split_clause,[],[f24988,f24980,f15982,f26301]) ).
fof(f26301,plain,
( spl0_1310
<=> c_Transcendental_Opi = c_Lattices_Oupper__semilattice__class_Osup(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f15982,plain,
( spl0_1098
<=> c_Transcendental_Opi = c_Log_Opowr(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f24980,plain,
( spl0_1289
<=> ! [X0,X1] : c_Log_Opowr(X0,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Transcendental_Otan(c_Transcendental_Opi),c_Log_Opowr(X0,X1),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f24988,plain,
( c_Transcendental_Opi = c_Lattices_Oupper__semilattice__class_Osup(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_1098
| ~ spl0_1289 ),
inference(superposition,[],[f24981,f15984]) ).
fof(f15984,plain,
( c_Transcendental_Opi = c_Log_Opowr(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_1098 ),
inference(avatar_component_clause,[],[f15982]) ).
fof(f24981,plain,
( ! [X0,X1] : c_Log_Opowr(X0,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Transcendental_Otan(c_Transcendental_Opi),c_Log_Opowr(X0,X1),tc_RealDef_Oreal)
| ~ spl0_1289 ),
inference(avatar_component_clause,[],[f24980]) ).
fof(f26113,plain,
( ~ spl0_116
| ~ spl0_105
| spl0_1309
| ~ spl0_38
| ~ spl0_626 ),
inference(avatar_split_clause,[],[f7586,f7253,f1531,f26111,f1867,f1922]) ).
fof(f1922,plain,
( spl0_116
<=> class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1867,plain,
( spl0_105
<=> class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f26111,plain,
( spl0_1309
<=> ! [X0] :
( c_Transcendental_Otan(c_Transcendental_Opi) != c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f1531,plain,
( spl0_38
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f7253,plain,
( spl0_626
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| X1 = X2
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f7586,plain,
( ! [X0] :
( c_Transcendental_Otan(c_Transcendental_Opi) != c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0
| ~ class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) )
| ~ spl0_38
| ~ spl0_626 ),
inference(superposition,[],[f7254,f1533]) ).
fof(f1533,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f1531]) ).
fof(f7254,plain,
( ! [X2,X0,X1] :
( c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X2,X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| X1 = X2
| ~ class_Ring__and__Field_Odivision__ring(X0) )
| ~ spl0_626 ),
inference(avatar_component_clause,[],[f7253]) ).
fof(f26109,plain,
( spl0_1308
| ~ spl0_184
| ~ spl0_543 ),
inference(avatar_split_clause,[],[f5755,f5109,f2262,f26107]) ).
fof(f26107,plain,
( spl0_1308
<=> ! [X0,X3,X2,X1] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Odist__class_Odist(X1,X2,X3),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f2262,plain,
( spl0_184
<=> ! [X4,X0,X10] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Odist__class_Odist(X4,X10,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f5109,plain,
( spl0_543
<=> ! [X6,X39,X40] :
( ~ c_lessequals(X39,X40,tc_RealDef_Oreal)
| ~ c_lessequals(X40,X6,tc_RealDef_Oreal)
| c_lessequals(X39,X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f5755,plain,
( ! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Odist__class_Odist(X1,X2,X3),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X3) )
| ~ spl0_184
| ~ spl0_543 ),
inference(resolution,[],[f5110,f2263]) ).
fof(f2263,plain,
( ! [X10,X0,X4] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Odist__class_Odist(X4,X10,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f2262]) ).
fof(f5110,plain,
( ! [X40,X39,X6] :
( ~ c_lessequals(X40,X6,tc_RealDef_Oreal)
| ~ c_lessequals(X39,X40,tc_RealDef_Oreal)
| c_lessequals(X39,X6,tc_RealDef_Oreal) )
| ~ spl0_543 ),
inference(avatar_component_clause,[],[f5109]) ).
fof(f26105,plain,
( spl0_1307
| ~ spl0_185
| ~ spl0_543 ),
inference(avatar_split_clause,[],[f5743,f5109,f2266,f26103]) ).
fof(f26103,plain,
( spl0_1307
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_RealVector_Odist__class_Odist(X1,X1,X2),tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f2266,plain,
( spl0_185
<=> ! [X4,X0] :
( c_lessequals(c_RealVector_Odist__class_Odist(X4,X4,X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f5743,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_RealVector_Odist__class_Odist(X1,X1,X2),tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X2) )
| ~ spl0_185
| ~ spl0_543 ),
inference(resolution,[],[f5110,f2267]) ).
fof(f2267,plain,
( ! [X0,X4] :
( c_lessequals(c_RealVector_Odist__class_Odist(X4,X4,X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f2266]) ).
fof(f26101,plain,
( spl0_1306
| ~ spl0_189
| ~ spl0_543 ),
inference(avatar_split_clause,[],[f5741,f5109,f2282,f26099]) ).
fof(f26099,plain,
( spl0_1306
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1),tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f2282,plain,
( spl0_189
<=> ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f5741,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1),tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) )
| ~ spl0_189
| ~ spl0_543 ),
inference(resolution,[],[f5110,f2283]) ).
fof(f2283,plain,
( ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f2282]) ).
fof(f26097,plain,
( spl0_1305
| ~ spl0_222
| ~ spl0_523 ),
inference(avatar_split_clause,[],[f5407,f5018,f2479,f26095]) ).
fof(f26095,plain,
( spl0_1305
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = c_NthRoot_Osqrt(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f2479,plain,
( spl0_222
<=> ! [X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X4
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f5018,plain,
( spl0_523
<=> ! [X4,X10] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f5407,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = c_NthRoot_Osqrt(X0) )
| ~ spl0_222
| ~ spl0_523 ),
inference(superposition,[],[f2480,f5019]) ).
fof(f5019,plain,
( ! [X10,X4] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| ~ spl0_523 ),
inference(avatar_component_clause,[],[f5018]) ).
fof(f2480,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X4 )
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f2479]) ).
fof(f26092,plain,
( ~ spl0_125
| spl0_1304
| ~ spl0_125
| ~ spl0_167
| ~ spl0_479
| ~ spl0_520 ),
inference(avatar_split_clause,[],[f5330,f5006,f4519,f2174,f1967,f26090,f1967]) ).
fof(f26090,plain,
( spl0_1304
<=> ! [X0,X1] :
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Lattices_Olower__semilattice__class_Oinf(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Onorm__class_Onorm(X0,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f1967,plain,
( spl0_125
<=> class_Lattices_Olower__semilattice(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f2174,plain,
( spl0_167
<=> ! [X4,X0] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f4519,plain,
( spl0_479
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) = c_Lattices_Olower__semilattice__class_Oinf(X10,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f5006,plain,
( spl0_520
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X10,X4,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f5330,plain,
( ! [X0,X1] :
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Lattices_Olower__semilattice__class_Oinf(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Onorm__class_Onorm(X0,X1),tc_RealDef_Oreal)
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) )
| ~ spl0_125
| ~ spl0_167
| ~ spl0_479
| ~ spl0_520 ),
inference(forward_demodulation,[],[f5315,f4861]) ).
fof(f4861,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_RealDef_Oreal)
| ~ spl0_125
| ~ spl0_479 ),
inference(resolution,[],[f4520,f1969]) ).
fof(f1969,plain,
( class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1967]) ).
fof(f4520,plain,
( ! [X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) = c_Lattices_Olower__semilattice__class_Oinf(X10,X4,X0) )
| ~ spl0_479 ),
inference(avatar_component_clause,[],[f4519]) ).
fof(f5315,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = c_Lattices_Olower__semilattice__class_Oinf(c_RealVector_Onorm__class_Onorm(X0,X1),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) )
| ~ spl0_167
| ~ spl0_520 ),
inference(resolution,[],[f5007,f2175]) ).
fof(f2175,plain,
( ! [X0,X4] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f2174]) ).
fof(f5007,plain,
( ! [X10,X0,X4] :
( ~ c_lessequals(X10,X4,X0)
| ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) = X10 )
| ~ spl0_520 ),
inference(avatar_component_clause,[],[f5006]) ).
fof(f26078,plain,
( ~ spl0_150
| spl0_1303
| ~ spl0_222
| ~ spl0_432 ),
inference(avatar_split_clause,[],[f4285,f3964,f2479,f26076,f2092]) ).
fof(f2092,plain,
( spl0_150
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f26076,plain,
( spl0_1303
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f3964,plain,
( spl0_432
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f4285,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 )
| ~ spl0_222
| ~ spl0_432 ),
inference(resolution,[],[f3965,f2480]) ).
fof(f3965,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_432 ),
inference(avatar_component_clause,[],[f3964]) ).
fof(f26060,plain,
( ~ spl0_150
| spl0_1302
| ~ spl0_222
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f4110,f3912,f2479,f26058,f2092]) ).
fof(f26058,plain,
( spl0_1302
<=> ! [X0] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f3912,plain,
( spl0_419
<=> ! [X4,X0,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X10,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f4110,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 )
| ~ spl0_222
| ~ spl0_419 ),
inference(resolution,[],[f3913,f2480]) ).
fof(f3913,plain,
( ! [X10,X0,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| ~ c_lessequals(X10,X4,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_419 ),
inference(avatar_component_clause,[],[f3912]) ).
fof(f26056,plain,
( spl0_1301
| ~ spl0_251
| ~ spl0_326 ),
inference(avatar_split_clause,[],[f3207,f3179,f2648,f26054]) ).
fof(f26054,plain,
( spl0_1301
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal) != X0
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X1
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f2648,plain,
( spl0_251
<=> ! [X2,X1,X8] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X8
| X1 = X2
| c_HOL_Otimes__class_Otimes(X1,X8,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X2,X8,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f3179,plain,
( spl0_326
<=> ! [X14] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X14,tc_RealDef_Oreal) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f3207,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal) != X0
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X1
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 )
| ~ spl0_251
| ~ spl0_326 ),
inference(superposition,[],[f2649,f3180]) ).
fof(f3180,plain,
( ! [X14] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X14,tc_RealDef_Oreal) = X14
| ~ spl0_326 ),
inference(avatar_component_clause,[],[f3179]) ).
fof(f2649,plain,
( ! [X2,X1,X8] :
( c_HOL_Otimes__class_Otimes(X1,X8,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X2,X8,tc_RealDef_Oreal)
| X1 = X2
| c_Transcendental_Otan(c_Transcendental_Opi) = X8 )
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f2648]) ).
fof(f26052,plain,
( ~ spl0_1300
| ~ spl0_326
| ~ spl0_1298 ),
inference(avatar_split_clause,[],[f26036,f26033,f3179,f26049]) ).
fof(f26049,plain,
( spl0_1300
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f26033,plain,
( spl0_1298
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f26036,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_326
| ~ spl0_1298 ),
inference(superposition,[],[f26034,f3180]) ).
fof(f26034,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal)
| ~ spl0_1298 ),
inference(avatar_component_clause,[],[f26033]) ).
fof(f26043,plain,
( spl0_9
| spl0_1299
| ~ spl0_244
| ~ spl0_326 ),
inference(avatar_split_clause,[],[f3205,f3179,f2607,f26041,f1381]) ).
fof(f1381,plain,
( spl0_9
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Otan(c_Transcendental_Opi) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f26041,plain,
( spl0_1299
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f2607,plain,
( spl0_244
<=> ! [X4,X10] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X4
| c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f3205,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Otan(c_Transcendental_Opi) )
| ~ spl0_244
| ~ spl0_326 ),
inference(superposition,[],[f2608,f3180]) ).
fof(f2608,plain,
( ! [X10,X4] :
( c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X4 )
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f2607]) ).
fof(f26035,plain,
( spl0_9
| spl0_1298
| ~ spl0_245
| ~ spl0_326 ),
inference(avatar_split_clause,[],[f3202,f3179,f2611,f26033,f1381]) ).
fof(f2611,plain,
( spl0_245
<=> ! [X4,X10] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X10
| c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f3202,plain,
( ! [X0] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Otan(c_Transcendental_Opi) )
| ~ spl0_245
| ~ spl0_326 ),
inference(superposition,[],[f2612,f3180]) ).
fof(f2612,plain,
( ! [X10,X4] :
( c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X10 )
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f2611]) ).
fof(f26031,plain,
( spl0_1297
| ~ spl0_208
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2576,f2557,f2389,f26029]) ).
fof(f26029,plain,
( spl0_1297
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f2389,plain,
( spl0_208
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f2557,plain,
( spl0_238
<=> ! [X4,X0] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f2576,plain,
( ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal) )
| ~ spl0_208
| ~ spl0_238 ),
inference(resolution,[],[f2558,f2390]) ).
fof(f2390,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) )
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f2389]) ).
fof(f2558,plain,
( ! [X0,X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 )
| ~ spl0_238 ),
inference(avatar_component_clause,[],[f2557]) ).
fof(f26027,plain,
( spl0_1296
| ~ spl0_208
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2568,f2544,f2389,f26025]) ).
fof(f26025,plain,
( spl0_1296
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Ometric__space(X0)
| X1 = X2
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_RealVector_Odist__class_Odist(X1,X2,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f2544,plain,
( spl0_235
<=> ! [X4,X0,X10] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Odist__class_Odist(X4,X10,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f2568,plain,
( ! [X2,X0,X1] :
( ~ class_RealVector_Ometric__space(X0)
| X1 = X2
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_RealVector_Odist__class_Odist(X1,X2,X0),tc_RealDef_Oreal) )
| ~ spl0_208
| ~ spl0_235 ),
inference(resolution,[],[f2545,f2390]) ).
fof(f2545,plain,
( ! [X10,X0,X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Odist__class_Odist(X4,X10,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 )
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f2544]) ).
fof(f25315,plain,
( ~ spl0_153
| spl0_1295
| ~ spl0_40
| ~ spl0_690 ),
inference(avatar_split_clause,[],[f9020,f7542,f1540,f25313,f2107]) ).
fof(f2107,plain,
( spl0_153
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f25313,plain,
( spl0_1295
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Log_Opowr(X0,X1),X2,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X2,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f1540,plain,
( spl0_40
<=> ! [X4,X10] : c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_Log_Opowr(X4,X10),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f7542,plain,
( spl0_690
<=> ! [X4,X0,X14,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X4,X0)
| ~ c_lessequals(X14,X10,X0)
| c_lessequals(X14,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f9020,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Log_Opowr(X0,X1),X2,tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X2,tc_RealDef_Oreal) )
| ~ spl0_40
| ~ spl0_690 ),
inference(resolution,[],[f7543,f1541]) ).
fof(f1541,plain,
( ! [X10,X4] : c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_Log_Opowr(X4,X10),tc_RealDef_Oreal)
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f1540]) ).
fof(f7543,plain,
( ! [X10,X0,X14,X4] :
( ~ c_lessequals(X14,X10,X0)
| ~ c_lessequals(X10,X4,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X14,X4,X0) )
| ~ spl0_690 ),
inference(avatar_component_clause,[],[f7542]) ).
fof(f25262,plain,
( ~ spl0_150
| spl0_1294
| ~ spl0_41
| ~ spl0_686 ),
inference(avatar_split_clause,[],[f8764,f7526,f1544,f25260,f2092]) ).
fof(f25260,plain,
( spl0_1294
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Log_Opowr(X0,X1),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X2,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f1544,plain,
( spl0_41
<=> ! [X4,X1] : c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f7526,plain,
( spl0_686
<=> ! [X4,X0,X14,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X10,X14,X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| c_HOL_Oord__class_Oless(X4,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f8764,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Log_Opowr(X0,X1),X2,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X2,tc_RealDef_Oreal) )
| ~ spl0_41
| ~ spl0_686 ),
inference(resolution,[],[f7527,f1545]) ).
fof(f1545,plain,
( ! [X1,X4] : c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Log_Opowr(X4,X1),tc_RealDef_Oreal)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f1544]) ).
fof(f7527,plain,
( ! [X10,X0,X14,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| ~ c_lessequals(X10,X14,X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X4,X14,X0) )
| ~ spl0_686 ),
inference(avatar_component_clause,[],[f7526]) ).
fof(f25177,plain,
( ~ spl0_150
| spl0_1293
| ~ spl0_41
| ~ spl0_685 ),
inference(avatar_split_clause,[],[f8712,f7522,f1544,f25175,f2092]) ).
fof(f25175,plain,
( spl0_1293
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_Log_Opowr(X1,X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f7522,plain,
( spl0_685
<=> ! [X4,X0,X14,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X14,X0)
| c_HOL_Oord__class_Oless(X4,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f8712,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_Log_Opowr(X1,X2),tc_RealDef_Oreal) )
| ~ spl0_41
| ~ spl0_685 ),
inference(resolution,[],[f7523,f1545]) ).
fof(f7523,plain,
( ! [X10,X0,X14,X4] :
( ~ c_HOL_Oord__class_Oless(X10,X14,X0)
| ~ c_lessequals(X4,X10,X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X4,X14,X0) )
| ~ spl0_685 ),
inference(avatar_component_clause,[],[f7522]) ).
fof(f25092,plain,
( ~ spl0_150
| spl0_1292
| ~ spl0_41
| ~ spl0_661 ),
inference(avatar_split_clause,[],[f8297,f7426,f1544,f25090,f2092]) ).
fof(f25090,plain,
( spl0_1292
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_Log_Opowr(X1,X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f7426,plain,
( spl0_661
<=> ! [X4,X0,X14,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X14,X0)
| c_HOL_Oord__class_Oless(X4,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f8297,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_Log_Opowr(X1,X2),tc_RealDef_Oreal) )
| ~ spl0_41
| ~ spl0_661 ),
inference(resolution,[],[f7427,f1545]) ).
fof(f7427,plain,
( ! [X10,X0,X14,X4] :
( ~ c_HOL_Oord__class_Oless(X10,X14,X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X4,X14,X0) )
| ~ spl0_661 ),
inference(avatar_component_clause,[],[f7426]) ).
fof(f25024,plain,
( ~ spl0_153
| spl0_1291
| ~ spl0_41
| ~ spl0_660 ),
inference(avatar_split_clause,[],[f8249,f7422,f1544,f25022,f2107]) ).
fof(f25022,plain,
( spl0_1291
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Log_Opowr(X0,X1),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X2,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f7422,plain,
( spl0_660
<=> ! [X4,X0,X14,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X4,X0)
| ~ c_HOL_Oord__class_Oless(X14,X10,X0)
| c_HOL_Oord__class_Oless(X14,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f8249,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Log_Opowr(X0,X1),X2,tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X2,tc_RealDef_Oreal) )
| ~ spl0_41
| ~ spl0_660 ),
inference(resolution,[],[f7423,f1545]) ).
fof(f7423,plain,
( ! [X10,X0,X14,X4] :
( ~ c_HOL_Oord__class_Oless(X14,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X4,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X14,X4,X0) )
| ~ spl0_660 ),
inference(avatar_component_clause,[],[f7422]) ).
fof(f25020,plain,
( spl0_1290
| ~ spl0_167
| ~ spl0_543 ),
inference(avatar_split_clause,[],[f5754,f5109,f2174,f25018]) ).
fof(f25018,plain,
( spl0_1290
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(X1,X2),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f5754,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(X1,X2),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X2) )
| ~ spl0_167
| ~ spl0_543 ),
inference(resolution,[],[f5110,f2175]) ).
fof(f24982,plain,
( spl0_1289
| ~ spl0_124
| ~ spl0_40
| ~ spl0_531 ),
inference(avatar_split_clause,[],[f5585,f5061,f1540,f1962,f24980]) ).
fof(f1962,plain,
( spl0_124
<=> class_Lattices_Oupper__semilattice(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f5061,plain,
( spl0_531
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X4,X10,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f5585,plain,
( ! [X0,X1] :
( ~ class_Lattices_Oupper__semilattice(tc_RealDef_Oreal)
| c_Log_Opowr(X0,X1) = c_Lattices_Oupper__semilattice__class_Osup(c_Transcendental_Otan(c_Transcendental_Opi),c_Log_Opowr(X0,X1),tc_RealDef_Oreal) )
| ~ spl0_40
| ~ spl0_531 ),
inference(resolution,[],[f5062,f1541]) ).
fof(f5062,plain,
( ! [X10,X0,X4] :
( ~ c_lessequals(X4,X10,X0)
| ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) = X10 )
| ~ spl0_531 ),
inference(avatar_component_clause,[],[f5061]) ).
fof(f24967,plain,
( ~ spl0_150
| spl0_1288
| ~ spl0_210
| ~ spl0_432 ),
inference(avatar_split_clause,[],[f4291,f3964,f2397,f24965,f2092]) ).
fof(f24965,plain,
( spl0_1288
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f2397,plain,
( spl0_210
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f4291,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_210
| ~ spl0_432 ),
inference(resolution,[],[f3965,f2398]) ).
fof(f2398,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal) )
| ~ spl0_210 ),
inference(avatar_component_clause,[],[f2397]) ).
fof(f24947,plain,
( ~ spl0_150
| spl0_1287
| ~ spl0_207
| ~ spl0_432 ),
inference(avatar_split_clause,[],[f4280,f3964,f2385,f24945,f2092]) ).
fof(f24945,plain,
( spl0_1287
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f2385,plain,
( spl0_207
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f4280,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_207
| ~ spl0_432 ),
inference(resolution,[],[f3965,f2386]) ).
fof(f2386,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f2385]) ).
fof(f24923,plain,
( spl0_1286
| ~ spl0_13
| ~ spl0_1268 ),
inference(avatar_split_clause,[],[f24526,f24447,f1401,f24920]) ).
fof(f24920,plain,
( spl0_1286
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_NthRoot_Osqrt(v_x),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f24447,plain,
( spl0_1268
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_NthRoot_Osqrt(X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f24526,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_NthRoot_Osqrt(v_x),tc_RealDef_Oreal)
| ~ spl0_13
| ~ spl0_1268 ),
inference(resolution,[],[f24448,f1403]) ).
fof(f1403,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),v_x,tc_RealDef_Oreal)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f1401]) ).
fof(f24448,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_NthRoot_Osqrt(X0),tc_RealDef_Oreal) )
| ~ spl0_1268 ),
inference(avatar_component_clause,[],[f24447]) ).
fof(f24918,plain,
( ~ spl0_151
| spl0_1285
| ~ spl0_213
| ~ spl0_421 ),
inference(avatar_split_clause,[],[f4170,f3920,f2411,f24916,f2097]) ).
fof(f2097,plain,
( spl0_151
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f24916,plain,
( spl0_1285
<=> ! [X0] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f2411,plain,
( spl0_213
<=> ! [X4] :
( c_HOL_Oord__class_Oless(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f3920,plain,
( spl0_421
<=> ! [X4,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X10,X4,X0)
| c_HOL_Oord__class_Oless(X4,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f4170,plain,
( ! [X0] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_213
| ~ spl0_421 ),
inference(resolution,[],[f3921,f2412]) ).
fof(f2412,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2411]) ).
fof(f3921,plain,
( ! [X10,X0,X4] :
( c_HOL_Oord__class_Oless(X4,X10,X0)
| c_lessequals(X10,X4,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_421 ),
inference(avatar_component_clause,[],[f3920]) ).
fof(f24887,plain,
( ~ spl0_151
| spl0_1284
| ~ spl0_215
| ~ spl0_421 ),
inference(avatar_split_clause,[],[f4167,f3920,f2419,f24885,f2097]) ).
fof(f24885,plain,
( spl0_1284
<=> ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f2419,plain,
( spl0_215
<=> ! [X10] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f4167,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_215
| ~ spl0_421 ),
inference(resolution,[],[f3921,f2420]) ).
fof(f2420,plain,
( ! [X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal) )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f2419]) ).
fof(f24781,plain,
( ~ spl0_151
| spl0_1283
| ~ spl0_208
| ~ spl0_421 ),
inference(avatar_split_clause,[],[f4160,f3920,f2389,f24779,f2097]) ).
fof(f24779,plain,
( spl0_1283
<=> ! [X0] :
( c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f4160,plain,
( ! [X0] :
( c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal) )
| ~ spl0_208
| ~ spl0_421 ),
inference(resolution,[],[f3921,f2390]) ).
fof(f24679,plain,
( ~ spl0_151
| spl0_1282
| ~ spl0_209
| ~ spl0_421 ),
inference(avatar_split_clause,[],[f4159,f3920,f2393,f24677,f2097]) ).
fof(f24677,plain,
( spl0_1282
<=> ! [X0] :
( c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_Log_Opowr(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f2393,plain,
( spl0_209
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_Log_Opowr(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f4159,plain,
( ! [X0] :
( c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_Log_Opowr(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X0 )
| ~ spl0_209
| ~ spl0_421 ),
inference(resolution,[],[f3921,f2394]) ).
fof(f2394,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_Log_Opowr(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X4 )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f2393]) ).
fof(f24666,plain,
( ~ spl0_150
| spl0_1281
| ~ spl0_210
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f4116,f3912,f2397,f24664,f2092]) ).
fof(f24664,plain,
( spl0_1281
<=> ! [X0] :
( ~ c_lessequals(c_NthRoot_Osqrt(X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f4116,plain,
( ! [X0] :
( ~ c_lessequals(c_NthRoot_Osqrt(X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_210
| ~ spl0_419 ),
inference(resolution,[],[f3913,f2398]) ).
fof(f24648,plain,
( spl0_1280
| ~ spl0_14
| ~ spl0_1268 ),
inference(avatar_split_clause,[],[f24524,f24447,f1406,f24645]) ).
fof(f24645,plain,
( spl0_1280
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_NthRoot_Osqrt(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f1406,plain,
( spl0_14
<=> c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f24524,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_NthRoot_Osqrt(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_14
| ~ spl0_1268 ),
inference(resolution,[],[f24448,f1408]) ).
fof(f1408,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f1406]) ).
fof(f24643,plain,
( ~ spl0_150
| spl0_1279
| ~ spl0_207
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f4106,f3912,f2385,f24641,f2092]) ).
fof(f24641,plain,
( spl0_1279
<=> ! [X0] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f4106,plain,
( ! [X0] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_207
| ~ spl0_419 ),
inference(resolution,[],[f3913,f2386]) ).
fof(f24639,plain,
( spl0_1278
| ~ spl0_233
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f3719,f3535,f2536,f24637]) ).
fof(f24637,plain,
( spl0_1278
<=> ! [X0] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f2536,plain,
( spl0_233
<=> ! [X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X4
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f3535,plain,
( spl0_373
<=> ! [X29,X14] : c_HOL_Otimes__class_Otimes(X14,X29,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X29,X14,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f3719,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 )
| ~ spl0_233
| ~ spl0_373 ),
inference(superposition,[],[f3536,f2537]) ).
fof(f2537,plain,
( ! [X4] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X4 )
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2536]) ).
fof(f3536,plain,
( ! [X29,X14] : c_HOL_Otimes__class_Otimes(X14,X29,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X29,X14,tc_RealDef_Oreal)
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f3535]) ).
fof(f24615,plain,
( ~ spl0_107
| spl0_1277
| ~ spl0_233
| ~ spl0_370 ),
inference(avatar_split_clause,[],[f3712,f3523,f2536,f24613,f1877]) ).
fof(f1877,plain,
( spl0_107
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f24613,plain,
( spl0_1277
<=> ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f3523,plain,
( spl0_370
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f3712,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 )
| ~ spl0_233
| ~ spl0_370 ),
inference(superposition,[],[f3524,f2537]) ).
fof(f3524,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_370 ),
inference(avatar_component_clause,[],[f3523]) ).
fof(f24611,plain,
( spl0_1276
| ~ spl0_244
| ~ spl0_326 ),
inference(avatar_split_clause,[],[f3204,f3179,f2607,f24609]) ).
fof(f24609,plain,
( spl0_1276
<=> ! [X0] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f3204,plain,
( ! [X0] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 )
| ~ spl0_244
| ~ spl0_326 ),
inference(superposition,[],[f2608,f3180]) ).
fof(f24607,plain,
( spl0_1275
| ~ spl0_245
| ~ spl0_326 ),
inference(avatar_split_clause,[],[f3203,f3179,f2611,f24605]) ).
fof(f24605,plain,
( spl0_1275
<=> ! [X0] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f3203,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 )
| ~ spl0_245
| ~ spl0_326 ),
inference(superposition,[],[f2612,f3180]) ).
fof(f24603,plain,
( spl0_1274
| ~ spl0_208
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2496,f2479,f2389,f24601]) ).
fof(f24601,plain,
( spl0_1274
<=> ! [X0] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X0
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f2496,plain,
( ! [X0] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X0
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_208
| ~ spl0_222 ),
inference(resolution,[],[f2480,f2390]) ).
fof(f24599,plain,
( spl0_1273
| ~ spl0_209
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2441,f2397,f2393,f24597]) ).
fof(f24597,plain,
( spl0_1273
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X0) = c_Log_Opowr(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f2441,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X0) = c_Log_Opowr(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) )
| ~ spl0_209
| ~ spl0_210 ),
inference(resolution,[],[f2398,f2394]) ).
fof(f24507,plain,
( spl0_1272
| ~ spl0_1098
| ~ spl0_1271 ),
inference(avatar_split_clause,[],[f24469,f24461,f15982,f24504]) ).
fof(f24504,plain,
( spl0_1272
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_Lattices_Olower__semilattice__class_Oinf(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f24461,plain,
( spl0_1271
<=> ! [X0,X1] : c_Transcendental_Otan(c_Transcendental_Opi) = c_Lattices_Olower__semilattice__class_Oinf(c_Transcendental_Otan(c_Transcendental_Opi),c_Log_Opowr(X0,X1),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f24469,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Lattices_Olower__semilattice__class_Oinf(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_1098
| ~ spl0_1271 ),
inference(superposition,[],[f24462,f15984]) ).
fof(f24462,plain,
( ! [X0,X1] : c_Transcendental_Otan(c_Transcendental_Opi) = c_Lattices_Olower__semilattice__class_Oinf(c_Transcendental_Otan(c_Transcendental_Opi),c_Log_Opowr(X0,X1),tc_RealDef_Oreal)
| ~ spl0_1271 ),
inference(avatar_component_clause,[],[f24461]) ).
fof(f24463,plain,
( ~ spl0_125
| spl0_1271
| ~ spl0_40
| ~ spl0_125
| ~ spl0_479
| ~ spl0_520 ),
inference(avatar_split_clause,[],[f5333,f5006,f4519,f1967,f1540,f24461,f1967]) ).
fof(f5333,plain,
( ! [X0,X1] :
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Lattices_Olower__semilattice__class_Oinf(c_Transcendental_Otan(c_Transcendental_Opi),c_Log_Opowr(X0,X1),tc_RealDef_Oreal)
| ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal) )
| ~ spl0_40
| ~ spl0_125
| ~ spl0_479
| ~ spl0_520 ),
inference(forward_demodulation,[],[f5318,f4861]) ).
fof(f5318,plain,
( ! [X0,X1] :
( ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = c_Lattices_Olower__semilattice__class_Oinf(c_Log_Opowr(X0,X1),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_40
| ~ spl0_520 ),
inference(resolution,[],[f5007,f1541]) ).
fof(f24458,plain,
( ~ spl0_151
| spl0_1270
| spl0_181
| ~ spl0_421 ),
inference(avatar_split_clause,[],[f4163,f3920,f2249,f24455,f2097]) ).
fof(f24455,plain,
( spl0_1270
<=> c_lessequals(c_HOL_Otimes__class_Otimes(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f2249,plain,
( spl0_181
<=> c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f4163,plain,
( c_lessequals(c_HOL_Otimes__class_Otimes(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| spl0_181
| ~ spl0_421 ),
inference(resolution,[],[f3921,f2251]) ).
fof(f2251,plain,
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_181 ),
inference(avatar_component_clause,[],[f2249]) ).
fof(f24453,plain,
( spl0_1269
| ~ spl0_222
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f3321,f3280,f2479,f24451]) ).
fof(f24451,plain,
( spl0_1269
<=> ! [X0] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f3280,plain,
( spl0_338
<=> ! [X4,X10] :
( ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_lessequals(X4,X10,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f3321,plain,
( ! [X0] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 )
| ~ spl0_222
| ~ spl0_338 ),
inference(resolution,[],[f3281,f2480]) ).
fof(f3281,plain,
( ! [X10,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_lessequals(X4,X10,tc_RealDef_Oreal) )
| ~ spl0_338 ),
inference(avatar_component_clause,[],[f3280]) ).
fof(f24449,plain,
( spl0_1268
| ~ spl0_208
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2442,f2397,f2389,f24447]) ).
fof(f2442,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_NthRoot_Osqrt(X0),tc_RealDef_Oreal) )
| ~ spl0_208
| ~ spl0_210 ),
inference(resolution,[],[f2398,f2390]) ).
fof(f24285,plain,
( spl0_1267
| ~ spl0_338
| ~ spl0_1260 ),
inference(avatar_split_clause,[],[f23934,f23927,f3280,f24283]) ).
fof(f24283,plain,
( spl0_1267
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(v_x,X0,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f23927,plain,
( spl0_1260
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(v_x,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f23934,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(v_x,X0,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_338
| ~ spl0_1260 ),
inference(resolution,[],[f23928,f3281]) ).
fof(f23928,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_x,X0,tc_RealDef_Oreal) )
| ~ spl0_1260 ),
inference(avatar_component_clause,[],[f23927]) ).
fof(f24209,plain,
( ~ spl0_150
| spl0_1266
| ~ spl0_13
| ~ spl0_686 ),
inference(avatar_split_clause,[],[f8768,f7526,f1401,f24207,f2092]) ).
fof(f24207,plain,
( spl0_1266
<=> ! [X0] :
( ~ c_lessequals(v_x,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f8768,plain,
( ! [X0] :
( ~ c_lessequals(v_x,X0,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_13
| ~ spl0_686 ),
inference(resolution,[],[f7527,f1403]) ).
fof(f24133,plain,
( ~ spl0_150
| spl0_1265
| ~ spl0_14
| ~ spl0_686 ),
inference(avatar_split_clause,[],[f8767,f7526,f1406,f24131,f2092]) ).
fof(f24131,plain,
( spl0_1265
<=> ! [X0] :
( ~ c_lessequals(c_Transcendental_Opi,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f8767,plain,
( ! [X0] :
( ~ c_lessequals(c_Transcendental_Opi,X0,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_14
| ~ spl0_686 ),
inference(resolution,[],[f7527,f1408]) ).
fof(f24093,plain,
( ~ spl0_150
| spl0_1264
| ~ spl0_13
| ~ spl0_685 ),
inference(avatar_split_clause,[],[f8716,f7522,f1401,f24091,f2092]) ).
fof(f24091,plain,
( spl0_1264
<=> ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,v_x,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f8716,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,v_x,tc_RealDef_Oreal) )
| ~ spl0_13
| ~ spl0_685 ),
inference(resolution,[],[f7523,f1403]) ).
fof(f24053,plain,
( ~ spl0_150
| spl0_1263
| ~ spl0_14
| ~ spl0_685 ),
inference(avatar_split_clause,[],[f8715,f7522,f1406,f24051,f2092]) ).
fof(f24051,plain,
( spl0_1263
<=> ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_Transcendental_Opi,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f8715,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_14
| ~ spl0_685 ),
inference(resolution,[],[f7523,f1408]) ).
fof(f24028,plain,
( ~ spl0_150
| spl0_1262
| ~ spl0_13
| ~ spl0_661 ),
inference(avatar_split_clause,[],[f8301,f7426,f1401,f24026,f2092]) ).
fof(f24026,plain,
( spl0_1262
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,v_x,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f8301,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,v_x,tc_RealDef_Oreal) )
| ~ spl0_13
| ~ spl0_661 ),
inference(resolution,[],[f7427,f1403]) ).
fof(f24003,plain,
( ~ spl0_150
| spl0_1261
| ~ spl0_14
| ~ spl0_661 ),
inference(avatar_split_clause,[],[f8300,f7426,f1406,f24001,f2092]) ).
fof(f24001,plain,
( spl0_1261
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_Transcendental_Opi,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f8300,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_14
| ~ spl0_661 ),
inference(resolution,[],[f7427,f1408]) ).
fof(f23929,plain,
( ~ spl0_153
| spl0_1260
| ~ spl0_13
| ~ spl0_660 ),
inference(avatar_split_clause,[],[f8253,f7422,f1401,f23927,f2107]) ).
fof(f8253,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(v_x,X0,tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_13
| ~ spl0_660 ),
inference(resolution,[],[f7423,f1403]) ).
fof(f23776,plain,
spl0_1259,
inference(avatar_split_clause,[],[f576,f23774]) ).
fof(f23774,plain,
( spl0_1259
<=> ! [X2,X35,X36,X34,X0,X33,X1] :
( ~ class_Ring__and__Field_Olordered__ring(X0)
| ~ c_lessequals(X35,X1,X0)
| ~ c_lessequals(X1,X33,X0)
| ~ c_lessequals(X36,X2,X0)
| ~ c_lessequals(X2,X34,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X35,X0),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X34,X0),X0),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X33,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X34,X0),X0),X0),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X35,X0),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X36,X0),X0),X0),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X33,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X36,X0),X0),X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f576,axiom,
! [X2,X0,X36,X1,X34,X35,X33] :
( ~ class_Ring__and__Field_Olordered__ring(X0)
| ~ c_lessequals(X35,X1,X0)
| ~ c_lessequals(X1,X33,X0)
| ~ c_lessequals(X36,X2,X0)
| ~ c_lessequals(X2,X34,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X35,X0),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X34,X0),X0),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X33,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X34,X0),X0),X0),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X35,X0),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X36,X0),X0),X0),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X33,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X36,X0),X0),X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__ge__prts_0) ).
fof(f23772,plain,
spl0_1258,
inference(avatar_split_clause,[],[f506,f23770]) ).
fof(f23770,plain,
( spl0_1258
<=> ! [X2,X35,X36,X34,X0,X33,X1] :
( ~ class_Ring__and__Field_Olordered__ring(X0)
| ~ c_lessequals(X35,X1,X0)
| ~ c_lessequals(X1,X33,X0)
| ~ c_lessequals(X36,X2,X0)
| ~ c_lessequals(X2,X34,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X33,X0),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X34,X0),X0),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X35,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X34,X0),X0),X0),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X33,X0),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X36,X0),X0),X0),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X35,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X36,X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f506,axiom,
! [X2,X0,X36,X1,X34,X35,X33] :
( ~ class_Ring__and__Field_Olordered__ring(X0)
| ~ c_lessequals(X35,X1,X0)
| ~ c_lessequals(X1,X33,X0)
| ~ c_lessequals(X36,X2,X0)
| ~ c_lessequals(X2,X34,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X33,X0),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X34,X0),X0),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X35,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X34,X0),X0),X0),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X33,X0),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X36,X0),X0),X0),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X35,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X36,X0),X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__prts_0) ).
fof(f23760,plain,
spl0_1257,
inference(avatar_split_clause,[],[f651,f23758]) ).
fof(f23758,plain,
( spl0_1257
<=> ! [X4,X0,X10,X2,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X10,X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X0),c_HOL_Ominus__class_Ominus(X10,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X0),X2,X0),X0),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X10,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f651,axiom,
! [X2,X10,X0,X1,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X10,X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X0),c_HOL_Ominus__class_Ominus(X10,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X1,X0),X2,X0),X0),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X10,X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
fof(f23748,plain,
spl0_1256,
inference(avatar_split_clause,[],[f53,f23746]) ).
fof(f23746,plain,
( spl0_1256
<=> ! [X0,X16,X2,X1] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0),X16,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X16,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f53,axiom,
! [X2,X0,X1,X16] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0),X16,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X16,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__inverse__lemma_0) ).
fof(f23743,plain,
spl0_1255,
inference(avatar_split_clause,[],[f538,f23741]) ).
fof(f23741,plain,
( spl0_1255
<=> ! [X2,X0,X8,X16,X3,X1] :
( ~ class_RealVector_Oreal__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X8,X3,X0),X0),X16,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X0),X16,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X8,X0),X16,X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f538,axiom,
! [X2,X3,X0,X1,X8,X16] :
( ~ class_RealVector_Oreal__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X8,X3,X0),X0),X16,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X0),X16,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X8,X0),X16,X0),X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).
fof(f23733,plain,
spl0_1254,
inference(avatar_split_clause,[],[f733,f23731]) ).
fof(f23731,plain,
( spl0_1254
<=> ! [X10,X0,X14,X29,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Ozero__class_Ozero(X0) = X14
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X10,X0),c_HOL_Oinverse__class_Odivide(X29,X14,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X14,X0),c_HOL_Otimes__class_Otimes(X29,X10,X0),X0),c_HOL_Otimes__class_Otimes(X10,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f733,axiom,
! [X10,X0,X29,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Ozero__class_Ozero(X0) = X14
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X10,X0),c_HOL_Oinverse__class_Odivide(X29,X14,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X14,X0),c_HOL_Otimes__class_Otimes(X29,X10,X0),X0),c_HOL_Otimes__class_Otimes(X10,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).
fof(f23729,plain,
spl0_1253,
inference(avatar_split_clause,[],[f153,f23727]) ).
fof(f23727,plain,
( spl0_1253
<=> ! [X10,X0,X14,X29,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Ozero__class_Ozero(X0) = X14
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X10,X0),c_HOL_Oinverse__class_Odivide(X29,X14,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X14,X0),c_HOL_Otimes__class_Otimes(X29,X10,X0),X0),c_HOL_Otimes__class_Otimes(X10,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f153,axiom,
! [X10,X0,X29,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Ozero__class_Ozero(X0) = X14
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X10,X0),c_HOL_Oinverse__class_Odivide(X29,X14,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X14,X0),c_HOL_Otimes__class_Otimes(X29,X10,X0),X0),c_HOL_Otimes__class_Otimes(X10,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
fof(f23688,plain,
spl0_1252,
inference(avatar_split_clause,[],[f729,f23686]) ).
fof(f23686,plain,
( spl0_1252
<=> ! [X26,X2,X0,X8,X28,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X8,X0) != c_Divides_Odiv__class_Omod(X28,X8,X0)
| c_Divides_Odiv__class_Omod(X2,X8,X0) != c_Divides_Odiv__class_Omod(X26,X8,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X28,X26,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f729,axiom,
! [X2,X28,X0,X1,X8,X26] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X8,X0) != c_Divides_Odiv__class_Omod(X28,X8,X0)
| c_Divides_Odiv__class_Omod(X2,X8,X0) != c_Divides_Odiv__class_Omod(X26,X8,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X28,X26,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
fof(f23684,plain,
spl0_1251,
inference(avatar_split_clause,[],[f717,f23682]) ).
fof(f23682,plain,
( spl0_1251
<=> ! [X26,X2,X0,X8,X28,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X8,X0) != c_Divides_Odiv__class_Omod(X28,X8,X0)
| c_Divides_Odiv__class_Omod(X2,X8,X0) != c_Divides_Odiv__class_Omod(X26,X8,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X28,X26,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f717,axiom,
! [X2,X28,X0,X1,X8,X26] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X8,X0) != c_Divides_Odiv__class_Omod(X28,X8,X0)
| c_Divides_Odiv__class_Omod(X2,X8,X0) != c_Divides_Odiv__class_Omod(X26,X8,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X28,X26,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
fof(f23680,plain,
spl0_1250,
inference(avatar_split_clause,[],[f313,f23678]) ).
fof(f23678,plain,
( spl0_1250
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f313,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oinverse__diff__inverse_0) ).
fof(f23666,plain,
spl0_1249,
inference(avatar_split_clause,[],[f950,f23664]) ).
fof(f23664,plain,
( spl0_1249
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ominus__class_Ominus(X2,X1,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f950,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ominus__class_Ominus(X2,X1,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_division__ring__inverse__diff_0) ).
fof(f23662,plain,
spl0_1248,
inference(avatar_split_clause,[],[f302,f23660]) ).
fof(f23660,plain,
( spl0_1248
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f302,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_division__ring__inverse__add_0) ).
fof(f23658,plain,
spl0_1247,
inference(avatar_split_clause,[],[f301,f23656]) ).
fof(f23656,plain,
( spl0_1247
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f301,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__add_0) ).
fof(f23128,plain,
( spl0_1246
| ~ spl0_215
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f20307,f20215,f2419,f23126]) ).
fof(f23126,plain,
( spl0_1246
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f20215,plain,
( spl0_1185
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f20307,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_215
| ~ spl0_1185 ),
inference(resolution,[],[f20216,f2420]) ).
fof(f20216,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,X0,tc_RealDef_Oreal) )
| ~ spl0_1185 ),
inference(avatar_component_clause,[],[f20215]) ).
fof(f23124,plain,
spl0_1245,
inference(avatar_split_clause,[],[f725,f23122]) ).
fof(f23122,plain,
( spl0_1245
<=> ! [X4,X0,X14,X29,X10] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X4 = X29
| X10 = X14
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X29,X10,X0),c_HOL_Otimes__class_Otimes(X4,X14,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X29,X14,X0),c_HOL_Otimes__class_Otimes(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f725,axiom,
! [X10,X0,X29,X14,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X4 = X29
| X10 = X14
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X29,X10,X0),c_HOL_Otimes__class_Otimes(X4,X14,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X29,X14,X0),c_HOL_Otimes__class_Otimes(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
fof(f23120,plain,
spl0_1244,
inference(avatar_split_clause,[],[f715,f23118]) ).
fof(f23118,plain,
( spl0_1244
<=> ! [X2,X31,X0,X8,X3,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X31,X0),X3,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f715,axiom,
! [X2,X31,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X31,X0),X3,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
fof(f23116,plain,
spl0_1243,
inference(avatar_split_clause,[],[f714,f23114]) ).
fof(f23114,plain,
( spl0_1243
<=> ! [X2,X31,X0,X8,X3,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X31,X0),X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f714,axiom,
! [X2,X31,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X31,X0),X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
fof(f23112,plain,
spl0_1242,
inference(avatar_split_clause,[],[f713,f23110]) ).
fof(f23110,plain,
( spl0_1242
<=> ! [X2,X31,X0,X3,X8,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X31,X0),X8,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f713,axiom,
! [X2,X31,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X31,X0),X8,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
fof(f23108,plain,
spl0_1241,
inference(avatar_split_clause,[],[f712,f23106]) ).
fof(f23106,plain,
( spl0_1241
<=> ! [X2,X31,X0,X3,X8,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X31,X0),X8,X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f712,axiom,
! [X2,X31,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X31,X0),X8,X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
fof(f23104,plain,
spl0_1240,
inference(avatar_split_clause,[],[f453,f23102]) ).
fof(f23102,plain,
( spl0_1240
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X1,X0),c_HOL_Oinverse__class_Odivide(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f453,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X1,X0),c_HOL_Oinverse__class_Odivide(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).
fof(f23100,plain,
spl0_1239,
inference(avatar_split_clause,[],[f429,f23098]) ).
fof(f23098,plain,
( spl0_1239
<=> ! [X2,X31,X0,X3,X8,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X31,X0),X8,X0),X3,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f429,axiom,
! [X2,X31,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X31,X0),X8,X0),X3,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
fof(f23096,plain,
spl0_1238,
inference(avatar_split_clause,[],[f428,f23094]) ).
fof(f23094,plain,
( spl0_1238
<=> ! [X2,X31,X0,X3,X8,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X31,X0),X8,X0),X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f428,axiom,
! [X2,X31,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X31,X0),X8,X0),X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
fof(f23092,plain,
spl0_1237,
inference(avatar_split_clause,[],[f427,f23090]) ).
fof(f23090,plain,
( spl0_1237
<=> ! [X2,X31,X0,X8,X3,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X31,X0),X3,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f427,axiom,
! [X2,X31,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X31,X0),X3,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
fof(f23088,plain,
spl0_1236,
inference(avatar_split_clause,[],[f426,f23086]) ).
fof(f23086,plain,
( spl0_1236
<=> ! [X2,X31,X0,X8,X3,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X31,X0),X3,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f426,axiom,
! [X2,X31,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X31,X0),X3,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
fof(f23084,plain,
( spl0_1235
| ~ spl0_208
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f20301,f20215,f2389,f23082]) ).
fof(f23082,plain,
( spl0_1235
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,X0,tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f20301,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,X0,tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal) )
| ~ spl0_208
| ~ spl0_1185 ),
inference(resolution,[],[f20216,f2390]) ).
fof(f23080,plain,
spl0_1234,
inference(avatar_split_clause,[],[f193,f23078]) ).
fof(f23078,plain,
( spl0_1234
<=> ! [X4,X0,X14,X29,X10] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X29,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X4,X10,X0),c_Divides_Odiv__class_Odiv(X29,X14,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X4,X29,X0),c_HOL_Otimes__class_Otimes(X10,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f193,axiom,
! [X10,X0,X29,X14,X4] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X29,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X4,X10,X0),c_Divides_Odiv__class_Odiv(X29,X14,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X4,X29,X0),c_HOL_Otimes__class_Otimes(X10,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__div__if__dvd_0) ).
fof(f22528,plain,
( spl0_1233
| ~ spl0_209
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f20300,f20215,f2393,f22526]) ).
fof(f22526,plain,
( spl0_1233
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,X0,tc_RealDef_Oreal)
| c_Log_Opowr(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f20300,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,X0,tc_RealDef_Oreal)
| c_Log_Opowr(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X0 )
| ~ spl0_209
| ~ spl0_1185 ),
inference(resolution,[],[f20216,f2394]) ).
fof(f21955,plain,
spl0_1232,
inference(avatar_split_clause,[],[f891,f21953]) ).
fof(f21953,plain,
( spl0_1232
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X8,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f891,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X8,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
fof(f21945,plain,
spl0_1231,
inference(avatar_split_clause,[],[f890,f21943]) ).
fof(f21943,plain,
( spl0_1231
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f890,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
fof(f21941,plain,
spl0_1230,
inference(avatar_split_clause,[],[f849,f21939]) ).
fof(f21939,plain,
( spl0_1230
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f849,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).
fof(f21937,plain,
spl0_1229,
inference(avatar_split_clause,[],[f846,f21935]) ).
fof(f21935,plain,
( spl0_1229
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f846,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).
fof(f21933,plain,
spl0_1228,
inference(avatar_split_clause,[],[f781,f21931]) ).
fof(f21931,plain,
( spl0_1228
<=> ! [X10,X0,X14,X29,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X29,X14,X0)
| ~ c_lessequals(X4,X10,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X29,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X14,X0),c_HOL_Oinverse__class_Odivide(X10,X29,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f781,axiom,
! [X10,X0,X29,X14,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X29,X14,X0)
| ~ c_lessequals(X4,X10,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X29,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X14,X0),c_HOL_Oinverse__class_Odivide(X10,X29,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__le_0) ).
fof(f21929,plain,
spl0_1227,
inference(avatar_split_clause,[],[f541,f21927]) ).
fof(f21927,plain,
( spl0_1227
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X8,X3,X0),X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X8,X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f541,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X8,X3,X0),X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X8,X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__triangle__ineq_0) ).
fof(f21925,plain,
spl0_1226,
inference(avatar_split_clause,[],[f469,f21923]) ).
fof(f21923,plain,
( spl0_1226
<=> ! [X4,X0,X14,X10,X29] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,X10,X0)
| ~ c_HOL_Oord__class_Oless(X29,X14,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X29,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X14,X0),c_HOL_Oinverse__class_Odivide(X10,X29,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f469,axiom,
! [X10,X0,X29,X14,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,X10,X0)
| ~ c_HOL_Oord__class_Oless(X29,X14,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X29,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X14,X0),c_HOL_Oinverse__class_Odivide(X10,X29,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less2_0) ).
fof(f21921,plain,
spl0_1225,
inference(avatar_split_clause,[],[f449,f21919]) ).
fof(f21919,plain,
( spl0_1225
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f449,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
fof(f21917,plain,
spl0_1224,
inference(avatar_split_clause,[],[f270,f21915]) ).
fof(f21915,plain,
( spl0_1224
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f270,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).
fof(f21913,plain,
spl0_1223,
inference(avatar_split_clause,[],[f269,f21911]) ).
fof(f21911,plain,
( spl0_1223
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f269,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).
fof(f21909,plain,
spl0_1222,
inference(avatar_split_clause,[],[f178,f21907]) ).
fof(f21907,plain,
( spl0_1222
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f178,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).
fof(f21898,plain,
spl0_1221,
inference(avatar_split_clause,[],[f177,f21896]) ).
fof(f21896,plain,
( spl0_1221
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f177,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).
fof(f21894,plain,
spl0_1220,
inference(avatar_split_clause,[],[f174,f21892]) ).
fof(f21892,plain,
( spl0_1220
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f174,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).
fof(f21890,plain,
spl0_1219,
inference(avatar_split_clause,[],[f173,f21888]) ).
fof(f21888,plain,
( spl0_1219
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f173,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).
fof(f21886,plain,
spl0_1218,
inference(avatar_split_clause,[],[f166,f21884]) ).
fof(f21884,plain,
( spl0_1218
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f166,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
fof(f21882,plain,
spl0_1217,
inference(avatar_split_clause,[],[f165,f21880]) ).
fof(f21880,plain,
( spl0_1217
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f165,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
fof(f21878,plain,
spl0_1216,
inference(avatar_split_clause,[],[f132,f21876]) ).
fof(f21876,plain,
( spl0_1216
<=> ! [X10,X0,X14,X29,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X29,X14,X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X29,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X14,X0),c_HOL_Oinverse__class_Odivide(X10,X29,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f132,axiom,
! [X10,X0,X29,X14,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X29,X14,X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X29,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X14,X0),c_HOL_Oinverse__class_Odivide(X10,X29,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less_0) ).
fof(f21874,plain,
spl0_1215,
inference(avatar_split_clause,[],[f15,f21872]) ).
fof(f21872,plain,
( spl0_1215
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
fof(f21685,plain,
spl0_1214,
inference(avatar_split_clause,[],[f788,f21683]) ).
fof(f21683,plain,
( spl0_1214
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X1,X0),c_HOL_Oinverse__class_Odivide(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f788,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X1,X0),c_HOL_Oinverse__class_Odivide(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).
fof(f21681,plain,
spl0_1213,
inference(avatar_split_clause,[],[f787,f21679]) ).
fof(f21679,plain,
( spl0_1213
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X1,X0),c_HOL_Oinverse__class_Odivide(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f787,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X8,X1,X0),c_HOL_Oinverse__class_Odivide(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).
fof(f21677,plain,
spl0_1212,
inference(avatar_split_clause,[],[f564,f21675]) ).
fof(f21675,plain,
( spl0_1212
<=> ! [X2,X31,X0,X3,X8,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X31,X0),X3,X0) = X8
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f564,axiom,
! [X2,X31,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X31,X0),X3,X0) = X8
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),X8,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
fof(f21673,plain,
spl0_1211,
inference(avatar_split_clause,[],[f454,f21671]) ).
fof(f21671,plain,
( spl0_1211
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X1,X0),c_HOL_Oinverse__class_Odivide(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f454,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X8,X1,X0),c_HOL_Oinverse__class_Odivide(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).
fof(f21413,plain,
( spl0_1210
| ~ spl0_182
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f20306,f20215,f2254,f21411]) ).
fof(f21411,plain,
( spl0_1210
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_RealVector_Odist__class_Odist(X0,X0,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f2254,plain,
( spl0_182
<=> ! [X4,X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Odist__class_Odist(X4,X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f20306,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_RealVector_Odist__class_Odist(X0,X0,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) )
| ~ spl0_182
| ~ spl0_1185 ),
inference(resolution,[],[f20216,f2255]) ).
fof(f2255,plain,
( ! [X0,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Odist__class_Odist(X4,X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f2254]) ).
fof(f20790,plain,
( spl0_1209
| ~ spl0_187
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f20305,f20215,f2274,f20788]) ).
fof(f20788,plain,
( spl0_1209
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f2274,plain,
( spl0_187
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f20305,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_187
| ~ spl0_1185 ),
inference(resolution,[],[f20216,f2275]) ).
fof(f2275,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f2274]) ).
fof(f20408,plain,
spl0_1208,
inference(avatar_split_clause,[],[f967,f20406]) ).
fof(f20406,plain,
( spl0_1208
<=> ! [X10,X0,X14,X29,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Ozero__class_Ozero(X0) = X14
| c_HOL_Otimes__class_Otimes(X4,X14,X0) != c_HOL_Otimes__class_Otimes(X29,X10,X0)
| c_HOL_Oinverse__class_Odivide(X4,X10,X0) = c_HOL_Oinverse__class_Odivide(X29,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f967,axiom,
! [X10,X0,X29,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Ozero__class_Ozero(X0) = X14
| c_HOL_Otimes__class_Otimes(X4,X14,X0) != c_HOL_Otimes__class_Otimes(X29,X10,X0)
| c_HOL_Oinverse__class_Odivide(X4,X10,X0) = c_HOL_Oinverse__class_Odivide(X29,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
fof(f20404,plain,
spl0_1207,
inference(avatar_split_clause,[],[f966,f20402]) ).
fof(f20402,plain,
( spl0_1207
<=> ! [X10,X0,X14,X29,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Ozero__class_Ozero(X0) = X14
| c_HOL_Oinverse__class_Odivide(X4,X10,X0) != c_HOL_Oinverse__class_Odivide(X29,X14,X0)
| c_HOL_Otimes__class_Otimes(X4,X14,X0) = c_HOL_Otimes__class_Otimes(X29,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f966,axiom,
! [X10,X0,X29,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Ozero__class_Ozero(X0) = X14
| c_HOL_Oinverse__class_Odivide(X4,X10,X0) != c_HOL_Oinverse__class_Odivide(X29,X14,X0)
| c_HOL_Otimes__class_Otimes(X4,X14,X0) = c_HOL_Otimes__class_Otimes(X29,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
fof(f20400,plain,
spl0_1206,
inference(avatar_split_clause,[],[f920,f20398]) ).
fof(f20398,plain,
( spl0_1206
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f920,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).
fof(f20396,plain,
( spl0_1205
| ~ spl0_338
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f20303,f20215,f3280,f20394]) ).
fof(f20394,plain,
( spl0_1205
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,X0,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f20303,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,X0,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_338
| ~ spl0_1185 ),
inference(resolution,[],[f20216,f3281]) ).
fof(f20392,plain,
spl0_1204,
inference(avatar_split_clause,[],[f919,f20390]) ).
fof(f20390,plain,
( spl0_1204
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f919,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).
fof(f20388,plain,
spl0_1203,
inference(avatar_split_clause,[],[f918,f20386]) ).
fof(f20386,plain,
( spl0_1203
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f918,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).
fof(f20384,plain,
spl0_1202,
inference(avatar_split_clause,[],[f917,f20382]) ).
fof(f20382,plain,
( spl0_1202
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f917,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).
fof(f20380,plain,
spl0_1201,
inference(avatar_split_clause,[],[f707,f20378]) ).
fof(f20378,plain,
( spl0_1201
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f707,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).
fof(f20376,plain,
spl0_1200,
inference(avatar_split_clause,[],[f706,f20374]) ).
fof(f20374,plain,
( spl0_1200
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f706,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).
fof(f20372,plain,
spl0_1199,
inference(avatar_split_clause,[],[f705,f20370]) ).
fof(f20370,plain,
( spl0_1199
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f705,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).
fof(f20368,plain,
spl0_1198,
inference(avatar_split_clause,[],[f704,f20366]) ).
fof(f20366,plain,
( spl0_1198
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f704,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).
fof(f20364,plain,
spl0_1197,
inference(avatar_split_clause,[],[f703,f20362]) ).
fof(f20362,plain,
( spl0_1197
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f703,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).
fof(f20360,plain,
spl0_1196,
inference(avatar_split_clause,[],[f702,f20358]) ).
fof(f20358,plain,
( spl0_1196
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f702,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).
fof(f20356,plain,
spl0_1195,
inference(avatar_split_clause,[],[f701,f20354]) ).
fof(f20354,plain,
( spl0_1195
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f701,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).
fof(f20298,plain,
spl0_1194,
inference(avatar_split_clause,[],[f700,f20296]) ).
fof(f20296,plain,
( spl0_1194
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f700,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).
fof(f20294,plain,
spl0_1193,
inference(avatar_split_clause,[],[f478,f20292]) ).
fof(f20292,plain,
( spl0_1193
<=> ! [X2,X0,X8,X3,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Otimes__class_Otimes(X8,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f478,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Otimes__class_Otimes(X8,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).
fof(f20290,plain,
spl0_1192,
inference(avatar_split_clause,[],[f444,f20288]) ).
fof(f20288,plain,
( spl0_1192
<=> ! [X4,X0,X14,X10] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X10,X0)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X4,X10,X0),X14,X0) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X4,X14,X0),c_Divides_Odiv__class_Odiv(X10,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f444,axiom,
! [X10,X0,X14,X4] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X10,X0)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X4,X10,X0),X14,X0) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X4,X14,X0),c_Divides_Odiv__class_Odiv(X10,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__add_0) ).
fof(f20286,plain,
spl0_1191,
inference(avatar_split_clause,[],[f380,f20284]) ).
fof(f20284,plain,
( spl0_1191
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f380,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).
fof(f20282,plain,
spl0_1190,
inference(avatar_split_clause,[],[f379,f20280]) ).
fof(f20280,plain,
( spl0_1190
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f379,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).
fof(f20278,plain,
spl0_1189,
inference(avatar_split_clause,[],[f378,f20276]) ).
fof(f20276,plain,
( spl0_1189
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f378,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).
fof(f20274,plain,
spl0_1188,
inference(avatar_split_clause,[],[f377,f20272]) ).
fof(f20272,plain,
( spl0_1188
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f377,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).
fof(f20270,plain,
spl0_1187,
inference(avatar_split_clause,[],[f4,f20268]) ).
fof(f20268,plain,
( spl0_1187
<=> ! [X6,X4,X0,X5,X3,X7] :
( ~ class_Ring__and__Field_Ocomm__ring(X0)
| ~ class_Ring__and__Field_Odvd(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Oplus__class_Oplus(X4,X5,X0),X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X7,X0),X0),X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f4,axiom,
! [X3,X0,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__ring(X0)
| ~ class_Ring__and__Field_Odvd(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Oplus__class_Oplus(X4,X5,X0),X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X7,X0),X0),X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).
fof(f20266,plain,
spl0_1186,
inference(avatar_split_clause,[],[f3,f20264]) ).
fof(f20264,plain,
( spl0_1186
<=> ! [X6,X4,X0,X5,X3,X7] :
( ~ class_Ring__and__Field_Ocomm__ring(X0)
| ~ class_Ring__and__Field_Odvd(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Oplus__class_Oplus(X4,X5,X0),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X7,X0),X0),X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f3,axiom,
! [X3,X0,X6,X7,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__ring(X0)
| ~ class_Ring__and__Field_Odvd(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Oplus__class_Oplus(X4,X5,X0),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Otimes__class_Otimes(X6,X7,X0),X0),X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).
fof(f20217,plain,
( ~ spl0_153
| spl0_1185
| ~ spl0_14
| ~ spl0_660 ),
inference(avatar_split_clause,[],[f8252,f7422,f1406,f20215,f2107]) ).
fof(f8252,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,X0,tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_14
| ~ spl0_660 ),
inference(resolution,[],[f7423,f1408]) ).
fof(f20081,plain,
spl0_1184,
inference(avatar_split_clause,[],[f207,f20079]) ).
fof(f20079,plain,
( spl0_1184
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f207,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_0) ).
fof(f20077,plain,
spl0_1183,
inference(avatar_split_clause,[],[f206,f20075]) ).
fof(f20075,plain,
( spl0_1183
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f206,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_1) ).
fof(f20073,plain,
spl0_1182,
inference(avatar_split_clause,[],[f205,f20071]) ).
fof(f20071,plain,
( spl0_1182
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f205,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_2) ).
fof(f20069,plain,
spl0_1181,
inference(avatar_split_clause,[],[f204,f20067]) ).
fof(f20067,plain,
( spl0_1181
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f204,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).
fof(f19899,plain,
( spl0_1180
| ~ spl0_40
| ~ spl0_543 ),
inference(avatar_split_clause,[],[f5757,f5109,f1540,f19897]) ).
fof(f19897,plain,
( spl0_1180
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_Log_Opowr(X1,X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f5757,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_Log_Opowr(X1,X2),tc_RealDef_Oreal) )
| ~ spl0_40
| ~ spl0_543 ),
inference(resolution,[],[f5110,f1541]) ).
fof(f19622,plain,
( spl0_1179
| ~ spl0_26
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f4096,f3908,f1469,f19620]) ).
fof(f19620,plain,
( spl0_1179
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f1469,plain,
( spl0_26
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Oarctan(c_Transcendental_Otan(c_Transcendental_Opi)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f3908,plain,
( spl0_418
<=> ! [X4,X10] :
( ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(X4),c_Transcendental_Oarctan(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f4096,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_26
| ~ spl0_418 ),
inference(superposition,[],[f3909,f1471]) ).
fof(f1471,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Oarctan(c_Transcendental_Otan(c_Transcendental_Opi))
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f1469]) ).
fof(f3909,plain,
( ! [X10,X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(X4),c_Transcendental_Oarctan(X10),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal) )
| ~ spl0_418 ),
inference(avatar_component_clause,[],[f3908]) ).
fof(f19583,plain,
spl0_1178,
inference(avatar_split_clause,[],[f851,f19581]) ).
fof(f19581,plain,
( spl0_1178
<=> ! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f851,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).
fof(f19579,plain,
spl0_1177,
inference(avatar_split_clause,[],[f850,f19577]) ).
fof(f19577,plain,
( spl0_1177
<=> ! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f850,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).
fof(f19575,plain,
spl0_1176,
inference(avatar_split_clause,[],[f848,f19573]) ).
fof(f19573,plain,
( spl0_1176
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f848,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
fof(f19571,plain,
spl0_1175,
inference(avatar_split_clause,[],[f847,f19569]) ).
fof(f19569,plain,
( spl0_1175
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f847,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
fof(f19567,plain,
spl0_1174,
inference(avatar_split_clause,[],[f661,f19565]) ).
fof(f19565,plain,
( spl0_1174
<=> ! [X31,X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X31,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f661,axiom,
! [X31,X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X31,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
fof(f19563,plain,
spl0_1173,
inference(avatar_split_clause,[],[f443,f19561]) ).
fof(f19561,plain,
( spl0_1173
<=> ! [X2,X31,X0,X3,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X31,X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f443,axiom,
! [X2,X31,X3,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X31,X0),X3,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X31,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X31,X0),X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
fof(f19559,plain,
spl0_1172,
inference(avatar_split_clause,[],[f309,f19557]) ).
fof(f19557,plain,
( spl0_1172
<=> ! [X4,X0,X14,X10] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X14,X10,X0),X0),X10,X0) = c_HOL_Oplus__class_Oplus(X14,c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f309,axiom,
! [X10,X0,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X14,X10,X0),X0),X10,X0) = c_HOL_Oplus__class_Oplus(X14,c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
fof(f19555,plain,
spl0_1171,
inference(avatar_split_clause,[],[f308,f19553]) ).
fof(f19553,plain,
( spl0_1171
<=> ! [X4,X0,X14,X10] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X10,X0),X14,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X14,X10,X0),X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f308,axiom,
! [X10,X0,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X10,X0),X14,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X14,X10,X0),X0),X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
fof(f19551,plain,
spl0_1170,
inference(avatar_split_clause,[],[f176,f19549]) ).
fof(f19549,plain,
( spl0_1170
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f176,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
fof(f19547,plain,
( spl0_1169
| ~ spl0_26
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f4094,f3908,f1469,f19545]) ).
fof(f19545,plain,
( spl0_1169
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Oarctan(X0),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f4094,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Oarctan(X0),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_26
| ~ spl0_418 ),
inference(superposition,[],[f3909,f1471]) ).
fof(f19543,plain,
spl0_1168,
inference(avatar_split_clause,[],[f175,f19541]) ).
fof(f19541,plain,
( spl0_1168
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f175,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
fof(f19539,plain,
spl0_1167,
inference(avatar_split_clause,[],[f172,f19537]) ).
fof(f19537,plain,
( spl0_1167
<=> ! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f172,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
fof(f19535,plain,
spl0_1166,
inference(avatar_split_clause,[],[f171,f19533]) ).
fof(f19533,plain,
( spl0_1166
<=> ! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f171,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
fof(f19531,plain,
spl0_1165,
inference(avatar_split_clause,[],[f111,f19529]) ).
fof(f19529,plain,
( spl0_1165
<=> ! [X17,X4,X0,X10,X15] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X0),X15,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X10,X0),X17,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X4,X10,X0),X0),c_HOL_Otimes__class_Otimes(X15,X17,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f111,axiom,
! [X10,X0,X4,X17,X15] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X0),X15,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X10,X0),X17,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X4,X10,X0),X0),c_HOL_Otimes__class_Otimes(X15,X17,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult__less_0) ).
fof(f19527,plain,
spl0_1164,
inference(avatar_split_clause,[],[f41,f19525]) ).
fof(f19525,plain,
( spl0_1164
<=> ! [X15,X4,X0,X3,X8] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X3 = X8
| c_HOL_Ozero__class_Ozero(X0) = X15
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X15,X8,X0),X0) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X15,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f41,axiom,
! [X3,X0,X8,X4,X15] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X3 = X8
| c_HOL_Ozero__class_Ozero(X0) = X15
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X15,X8,X0),X0) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X15,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(f19455,plain,
( spl0_1163
| ~ spl0_26
| ~ spl0_413 ),
inference(avatar_split_clause,[],[f4065,f3887,f1469,f19453]) ).
fof(f19453,plain,
( spl0_1163
<=> ! [X0] :
( c_lessequals(c_Transcendental_Oarctan(X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f3887,plain,
( spl0_413
<=> ! [X4,X10] :
( ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Oarctan(X4),c_Transcendental_Oarctan(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f4065,plain,
( ! [X0] :
( c_lessequals(c_Transcendental_Oarctan(X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_26
| ~ spl0_413 ),
inference(superposition,[],[f3888,f1471]) ).
fof(f3888,plain,
( ! [X10,X4] :
( c_lessequals(c_Transcendental_Oarctan(X4),c_Transcendental_Oarctan(X10),tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal) )
| ~ spl0_413 ),
inference(avatar_component_clause,[],[f3887]) ).
fof(f19451,plain,
spl0_1162,
inference(avatar_split_clause,[],[f856,f19449]) ).
fof(f19449,plain,
( spl0_1162
<=> ! [X15,X4,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X15,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X15,X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X0),X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f856,axiom,
! [X0,X1,X4,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X15,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X15,X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X0),X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).
fof(f19447,plain,
spl0_1161,
inference(avatar_split_clause,[],[f474,f19445]) ).
fof(f19445,plain,
( spl0_1161
<=> ! [X4,X0,X14,X10] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X10,X0),c_HOL_Otimes__class_Otimes(X4,X14,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X14,X0),c_HOL_Otimes__class_Otimes(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f474,axiom,
! [X10,X0,X14,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X10,X0),c_HOL_Otimes__class_Otimes(X4,X14,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X14,X0),c_HOL_Otimes__class_Otimes(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
fof(f19443,plain,
spl0_1160,
inference(avatar_split_clause,[],[f359,f19441]) ).
fof(f19441,plain,
( spl0_1160
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f359,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
fof(f19439,plain,
spl0_1159,
inference(avatar_split_clause,[],[f203,f19437]) ).
fof(f19437,plain,
( spl0_1159
<=> ! [X10,X0,X14,X29,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X4,X10,X0),c_HOL_Oinverse__class_Odivide(X14,X29,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X14,X0),c_HOL_Otimes__class_Otimes(X10,X29,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f203,axiom,
! [X10,X0,X29,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X4,X10,X0),c_HOL_Oinverse__class_Odivide(X14,X29,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X14,X0),c_HOL_Otimes__class_Otimes(X10,X29,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
fof(f19435,plain,
spl0_1158,
inference(avatar_split_clause,[],[f181,f19433]) ).
fof(f19433,plain,
( spl0_1158
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f181,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
fof(f19331,plain,
( spl0_1157
| ~ spl0_26
| ~ spl0_413 ),
inference(avatar_split_clause,[],[f4063,f3887,f1469,f19329]) ).
fof(f19329,plain,
( spl0_1157
<=> ! [X0] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Oarctan(X0),tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f4063,plain,
( ! [X0] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Oarctan(X0),tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_26
| ~ spl0_413 ),
inference(superposition,[],[f3888,f1471]) ).
fof(f19240,plain,
spl0_1156,
inference(avatar_split_clause,[],[f914,f19238]) ).
fof(f19238,plain,
( spl0_1156
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X9,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f914,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X9,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
fof(f19236,plain,
spl0_1155,
inference(avatar_split_clause,[],[f721,f19234]) ).
fof(f19234,plain,
( spl0_1155
<=> ! [X4,X0,X9,X10] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X4,X0)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X4,X10,X0),X9,X0) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X4,X9,X0),c_Power_Opower__class_Opower(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f721,axiom,
! [X10,X0,X9,X4] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X4,X0)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X4,X10,X0),X9,X0) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X4,X9,X0),c_Power_Opower__class_Opower(X10,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__power_0) ).
fof(f19232,plain,
spl0_1154,
inference(avatar_split_clause,[],[f699,f19230]) ).
fof(f19230,plain,
( spl0_1154
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(X8,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f699,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(X8,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self2_0) ).
fof(f19228,plain,
spl0_1153,
inference(avatar_split_clause,[],[f698,f19226]) ).
fof(f19226,plain,
( spl0_1153
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X8,X2,X0),X0),X2,X0) = c_HOL_Oplus__class_Oplus(X8,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f698,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X8,X2,X0),X0),X2,X0) = c_HOL_Oplus__class_Oplus(X8,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self1_0) ).
fof(f19224,plain,
spl0_1152,
inference(avatar_split_clause,[],[f339,f19222]) ).
fof(f19222,plain,
( spl0_1152
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X10,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X10,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f339,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X10,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X10,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
fof(f19220,plain,
spl0_1151,
inference(avatar_split_clause,[],[f338,f19218]) ).
fof(f19218,plain,
( spl0_1151
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X10,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f338,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X10,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X10,X4,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
fof(f19216,plain,
spl0_1150,
inference(avatar_split_clause,[],[f320,f19214]) ).
fof(f19214,plain,
( spl0_1150
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X8,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X0),c_Divides_Odiv__class_Odiv(X8,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f320,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X8,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X0),c_Divides_Odiv__class_Odiv(X8,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__dvd__div_1) ).
fof(f19198,plain,
spl0_1149,
inference(avatar_split_clause,[],[f319,f19196]) ).
fof(f19196,plain,
( spl0_1149
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X8,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X0),c_Divides_Odiv__class_Odiv(X8,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f319,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X8,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X0),c_Divides_Odiv__class_Odiv(X8,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__dvd__div_0) ).
fof(f19100,plain,
( ~ spl0_107
| spl0_1148
| ~ spl0_233
| ~ spl0_369 ),
inference(avatar_split_clause,[],[f3710,f3519,f2536,f19098,f1877]) ).
fof(f19098,plain,
( spl0_1148
<=> ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f3519,plain,
( spl0_369
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f3710,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = X0 )
| ~ spl0_233
| ~ spl0_369 ),
inference(superposition,[],[f3520,f2537]) ).
fof(f3520,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_369 ),
inference(avatar_component_clause,[],[f3519]) ).
fof(f18998,plain,
spl0_1147,
inference(avatar_split_clause,[],[f812,f18996]) ).
fof(f18996,plain,
( spl0_1147
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f812,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
fof(f18994,plain,
spl0_1146,
inference(avatar_split_clause,[],[f811,f18992]) ).
fof(f18992,plain,
( spl0_1146
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f811,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
fof(f18970,plain,
spl0_1145,
inference(avatar_split_clause,[],[f695,f18968]) ).
fof(f18968,plain,
( spl0_1145
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X8,X0),c_Divides_Odiv__class_Omod(X2,X8,X0),X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f695,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X8,X0),c_Divides_Odiv__class_Omod(X2,X8,X0),X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
fof(f18966,plain,
spl0_1144,
inference(avatar_split_clause,[],[f673,f18964]) ).
fof(f18964,plain,
( spl0_1144
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ominus__class_Ominus(X8,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f673,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ominus__class_Ominus(X8,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
fof(f18962,plain,
spl0_1143,
inference(avatar_split_clause,[],[f590,f18960]) ).
fof(f18960,plain,
( spl0_1143
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X8,X0),c_Divides_Odiv__class_Omod(X2,X8,X0),X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f590,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X8,X0),c_Divides_Odiv__class_Omod(X2,X8,X0),X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
fof(f18958,plain,
spl0_1142,
inference(avatar_split_clause,[],[f566,f18956]) ).
fof(f18956,plain,
( spl0_1142
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(X1,X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f566,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(X1,X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mod__equality2_0) ).
fof(f18954,plain,
spl0_1141,
inference(avatar_split_clause,[],[f565,f18952]) ).
fof(f18952,plain,
( spl0_1141
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(X1,X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X0),X2,X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f565,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(X1,X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X0),X2,X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mod__equality_0) ).
fof(f18950,plain,
spl0_1140,
inference(avatar_split_clause,[],[f411,f18948]) ).
fof(f18948,plain,
( spl0_1140
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f411,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).
fof(f18946,plain,
spl0_1139,
inference(avatar_split_clause,[],[f409,f18944]) ).
fof(f18944,plain,
( spl0_1139
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f409,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).
fof(f18942,plain,
spl0_1138,
inference(avatar_split_clause,[],[f393,f18940]) ).
fof(f18940,plain,
( spl0_1138
<=> ! [X4,X0,X10] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X4,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f393,axiom,
! [X10,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X4,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
fof(f18938,plain,
spl0_1137,
inference(avatar_split_clause,[],[f392,f18936]) ).
fof(f18936,plain,
( spl0_1137
<=> ! [X4,X0,X10] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X4,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f392,axiom,
! [X10,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X4,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
fof(f18934,plain,
spl0_1136,
inference(avatar_split_clause,[],[f312,f18932]) ).
fof(f18932,plain,
( spl0_1136
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X8,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f312,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X8,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f18913,plain,
spl0_1135,
inference(avatar_split_clause,[],[f256,f18911]) ).
fof(f18911,plain,
( spl0_1135
<=> ! [X18,X19,X20,X0,X21] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X19,X0),c_HOL_Otimes__class_Otimes(X20,X21,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X20,X0),c_HOL_Otimes__class_Otimes(X19,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f256,axiom,
! [X21,X0,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X19,X0),c_HOL_Otimes__class_Otimes(X20,X21,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X20,X0),c_HOL_Otimes__class_Otimes(X19,X21,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f18909,plain,
spl0_1134,
inference(avatar_split_clause,[],[f101,f18907]) ).
fof(f18907,plain,
( spl0_1134
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),c_HOL_Oinverse__class_Odivide(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f101,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X8,X0),c_HOL_Oinverse__class_Odivide(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
fof(f18905,plain,
spl0_1133,
inference(avatar_split_clause,[],[f100,f18903]) ).
fof(f18903,plain,
( spl0_1133
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X8,X0),c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f100,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X8,X0),c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
fof(f18901,plain,
spl0_1132,
inference(avatar_split_clause,[],[f36,f18899]) ).
fof(f18899,plain,
( spl0_1132
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f36,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).
fof(f18897,plain,
spl0_1131,
inference(avatar_split_clause,[],[f34,f18895]) ).
fof(f18895,plain,
( spl0_1131
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f34,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).
fof(f18313,plain,
( spl0_1130
| ~ spl0_185
| ~ spl0_1046 ),
inference(avatar_split_clause,[],[f16985,f15714,f2266,f18311]) ).
fof(f18311,plain,
( spl0_1130
<=> ! [X0,X1] :
( c_lessequals(c_NthRoot_Osqrt(c_RealVector_Odist__class_Odist(X0,X0,X1)),v_x,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f15714,plain,
( spl0_1046
<=> ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),v_x,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f16985,plain,
( ! [X0,X1] :
( c_lessequals(c_NthRoot_Osqrt(c_RealVector_Odist__class_Odist(X0,X0,X1)),v_x,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) )
| ~ spl0_185
| ~ spl0_1046 ),
inference(resolution,[],[f15715,f2267]) ).
fof(f15715,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X0),v_x,tc_RealDef_Oreal) )
| ~ spl0_1046 ),
inference(avatar_component_clause,[],[f15714]) ).
fof(f18279,plain,
spl0_1129,
inference(avatar_split_clause,[],[f808,f18277]) ).
fof(f18277,plain,
( spl0_1129
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f808,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
fof(f18275,plain,
spl0_1128,
inference(avatar_split_clause,[],[f807,f18273]) ).
fof(f18273,plain,
( spl0_1128
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f807,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
fof(f18271,plain,
spl0_1127,
inference(avatar_split_clause,[],[f806,f18269]) ).
fof(f18269,plain,
( spl0_1127
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f806,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
fof(f18267,plain,
spl0_1126,
inference(avatar_split_clause,[],[f805,f18265]) ).
fof(f18265,plain,
( spl0_1126
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f805,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
fof(f18263,plain,
spl0_1125,
inference(avatar_split_clause,[],[f779,f18261]) ).
fof(f18261,plain,
( spl0_1125
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f779,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
fof(f18259,plain,
spl0_1124,
inference(avatar_split_clause,[],[f778,f18257]) ).
fof(f18257,plain,
( spl0_1124
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f778,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).
fof(f18255,plain,
spl0_1123,
inference(avatar_split_clause,[],[f626,f18253]) ).
fof(f18253,plain,
( spl0_1123
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f626,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
fof(f18251,plain,
spl0_1122,
inference(avatar_split_clause,[],[f625,f18249]) ).
fof(f18249,plain,
( spl0_1122
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f625,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
fof(f18247,plain,
( spl0_1121
| ~ spl0_189
| ~ spl0_1046 ),
inference(avatar_split_clause,[],[f16984,f15714,f2282,f18245]) ).
fof(f18245,plain,
( spl0_1121
<=> ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0)),v_x,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f16984,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0)),v_x,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_189
| ~ spl0_1046 ),
inference(resolution,[],[f15715,f2283]) ).
fof(f18243,plain,
spl0_1120,
inference(avatar_split_clause,[],[f624,f18241]) ).
fof(f18241,plain,
( spl0_1120
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f624,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
fof(f18239,plain,
spl0_1119,
inference(avatar_split_clause,[],[f623,f18237]) ).
fof(f18237,plain,
( spl0_1119
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f623,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
fof(f18235,plain,
spl0_1118,
inference(avatar_split_clause,[],[f584,f18233]) ).
fof(f18233,plain,
( spl0_1118
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X9,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X9,X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f584,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X9,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X9,X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus_0) ).
fof(f18231,plain,
spl0_1117,
inference(avatar_split_clause,[],[f583,f18229]) ).
fof(f18229,plain,
( spl0_1117
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f583,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
fof(f18227,plain,
spl0_1116,
inference(avatar_split_clause,[],[f582,f18225]) ).
fof(f18225,plain,
( spl0_1116
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f582,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
fof(f18223,plain,
spl0_1115,
inference(avatar_split_clause,[],[f581,f18221]) ).
fof(f18221,plain,
( spl0_1115
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f581,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
fof(f18219,plain,
spl0_1114,
inference(avatar_split_clause,[],[f580,f18217]) ).
fof(f18217,plain,
( spl0_1114
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f580,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
fof(f18215,plain,
spl0_1113,
inference(avatar_split_clause,[],[f431,f18213]) ).
fof(f18213,plain,
( spl0_1113
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f431,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
fof(f18211,plain,
spl0_1112,
inference(avatar_split_clause,[],[f430,f18209]) ).
fof(f18209,plain,
( spl0_1112
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f430,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
fof(f18207,plain,
spl0_1111,
inference(avatar_split_clause,[],[f268,f18205]) ).
fof(f18205,plain,
( spl0_1111
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X4,X0),X10,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f268,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X4,X0),X10,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__div__pos_0) ).
fof(f18203,plain,
( spl0_1110
| ~ spl0_212
| ~ spl0_659 ),
inference(avatar_split_clause,[],[f7549,f7418,f2407,f18201]) ).
fof(f18201,plain,
( spl0_1110
<=> ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),v_x,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f2407,plain,
( spl0_212
<=> ! [X10] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f7418,plain,
( spl0_659
<=> ! [X0] :
( c_lessequals(X0,v_x,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f7549,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),v_x,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_212
| ~ spl0_659 ),
inference(resolution,[],[f7419,f2408]) ).
fof(f2408,plain,
( ! [X10] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal) )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2407]) ).
fof(f7419,plain,
( ! [X0] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal)
| c_lessequals(X0,v_x,tc_RealDef_Oreal) )
| ~ spl0_659 ),
inference(avatar_component_clause,[],[f7418]) ).
fof(f18199,plain,
spl0_1109,
inference(avatar_split_clause,[],[f235,f18197]) ).
fof(f18197,plain,
( spl0_1109
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X9,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f235,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X9,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__divide_0) ).
fof(f18195,plain,
spl0_1108,
inference(avatar_split_clause,[],[f184,f18193]) ).
fof(f18193,plain,
( spl0_1108
<=> ! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f184,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
fof(f18191,plain,
spl0_1107,
inference(avatar_split_clause,[],[f182,f18189]) ).
fof(f18189,plain,
( spl0_1107
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f182,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
fof(f18187,plain,
spl0_1106,
inference(avatar_split_clause,[],[f150,f18185]) ).
fof(f18185,plain,
( spl0_1106
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f150,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__add__self2_0) ).
fof(f18183,plain,
spl0_1105,
inference(avatar_split_clause,[],[f149,f18181]) ).
fof(f18181,plain,
( spl0_1105
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X1,X0),X2,X0) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f149,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X1,X0),X2,X0) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
fof(f18179,plain,
spl0_1104,
inference(avatar_split_clause,[],[f23,f18177]) ).
fof(f18177,plain,
( spl0_1104
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f23,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
fof(f18175,plain,
spl0_1103,
inference(avatar_split_clause,[],[f22,f18173]) ).
fof(f18173,plain,
( spl0_1103
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
fof(f18171,plain,
spl0_1102,
inference(avatar_split_clause,[],[f21,f18169]) ).
fof(f18169,plain,
( spl0_1102
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
fof(f18167,plain,
spl0_1101,
inference(avatar_split_clause,[],[f20,f18165]) ).
fof(f18165,plain,
( spl0_1101
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f20,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
fof(f16373,plain,
( spl0_1100
| ~ spl0_459
| ~ spl0_880
| ~ spl0_987 ),
inference(avatar_split_clause,[],[f14149,f13218,f11534,f4438,f16370]) ).
fof(f16370,plain,
( spl0_1100
<=> v_x = c_Log_Opowr(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f4438,plain,
( spl0_459
<=> ! [X4,X1] : c_Log_Opowr(X4,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_Log_Opowr(X4,X1),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f11534,plain,
( spl0_880
<=> v_x = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f13218,plain,
( spl0_987
<=> c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal) = c_Log_Opowr(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f14149,plain,
( v_x = c_Log_Opowr(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_459
| ~ spl0_880
| ~ spl0_987 ),
inference(forward_demodulation,[],[f14133,f11536]) ).
fof(f11536,plain,
( v_x = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_880 ),
inference(avatar_component_clause,[],[f11534]) ).
fof(f14133,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Log_Opowr(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_459
| ~ spl0_987 ),
inference(superposition,[],[f4439,f13220]) ).
fof(f13220,plain,
( c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal) = c_Log_Opowr(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_987 ),
inference(avatar_component_clause,[],[f13218]) ).
fof(f4439,plain,
( ! [X1,X4] : c_Log_Opowr(X4,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_Log_Opowr(X4,X1),tc_RealDef_Oreal)
| ~ spl0_459 ),
inference(avatar_component_clause,[],[f4438]) ).
fof(f15989,plain,
spl0_1099,
inference(avatar_split_clause,[],[f958,f15987]) ).
fof(f15987,plain,
( spl0_1099
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f958,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
fof(f15985,plain,
( spl0_1098
| ~ spl0_459
| ~ spl0_800
| ~ spl0_976 ),
inference(avatar_split_clause,[],[f13973,f13173,f10509,f4438,f15982]) ).
fof(f10509,plain,
( spl0_800
<=> c_Transcendental_Opi = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f13173,plain,
( spl0_976
<=> c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal) = c_Log_Opowr(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f13973,plain,
( c_Transcendental_Opi = c_Log_Opowr(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_459
| ~ spl0_800
| ~ spl0_976 ),
inference(forward_demodulation,[],[f13957,f10511]) ).
fof(f10511,plain,
( c_Transcendental_Opi = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_800 ),
inference(avatar_component_clause,[],[f10509]) ).
fof(f13957,plain,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Log_Opowr(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_459
| ~ spl0_976 ),
inference(superposition,[],[f4439,f13175]) ).
fof(f13175,plain,
( c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal) = c_Log_Opowr(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_976 ),
inference(avatar_component_clause,[],[f13173]) ).
fof(f15980,plain,
spl0_1097,
inference(avatar_split_clause,[],[f957,f15978]) ).
fof(f15978,plain,
( spl0_1097
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f957,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
fof(f15976,plain,
spl0_1096,
inference(avatar_split_clause,[],[f956,f15974]) ).
fof(f15974,plain,
( spl0_1096
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f956,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
fof(f15972,plain,
spl0_1095,
inference(avatar_split_clause,[],[f955,f15970]) ).
fof(f15970,plain,
( spl0_1095
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f955,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
fof(f15968,plain,
spl0_1094,
inference(avatar_split_clause,[],[f916,f15966]) ).
fof(f15966,plain,
( spl0_1094
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f916,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
fof(f15964,plain,
spl0_1093,
inference(avatar_split_clause,[],[f836,f15962]) ).
fof(f15962,plain,
( spl0_1093
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f836,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
fof(f15960,plain,
spl0_1092,
inference(avatar_split_clause,[],[f835,f15958]) ).
fof(f15958,plain,
( spl0_1092
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f835,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
fof(f15956,plain,
spl0_1091,
inference(avatar_split_clause,[],[f834,f15954]) ).
fof(f15954,plain,
( spl0_1091
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f834,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
fof(f15952,plain,
spl0_1090,
inference(avatar_split_clause,[],[f833,f15950]) ).
fof(f15950,plain,
( spl0_1090
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f833,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
fof(f15948,plain,
spl0_1089,
inference(avatar_split_clause,[],[f831,f15946]) ).
fof(f15946,plain,
( spl0_1089
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f831,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
fof(f15944,plain,
spl0_1088,
inference(avatar_split_clause,[],[f828,f15942]) ).
fof(f15942,plain,
( spl0_1088
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f828,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
fof(f15925,plain,
spl0_1087,
inference(avatar_split_clause,[],[f827,f15923]) ).
fof(f15923,plain,
( spl0_1087
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f827,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
fof(f15921,plain,
spl0_1086,
inference(avatar_split_clause,[],[f826,f15919]) ).
fof(f15919,plain,
( spl0_1086
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f826,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
fof(f15917,plain,
spl0_1085,
inference(avatar_split_clause,[],[f824,f15915]) ).
fof(f15915,plain,
( spl0_1085
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f824,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
fof(f15913,plain,
spl0_1084,
inference(avatar_split_clause,[],[f776,f15911]) ).
fof(f15911,plain,
( spl0_1084
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f776,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).
fof(f15909,plain,
spl0_1083,
inference(avatar_split_clause,[],[f682,f15907]) ).
fof(f15907,plain,
( spl0_1083
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f682,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_0) ).
fof(f15905,plain,
spl0_1082,
inference(avatar_split_clause,[],[f678,f15903]) ).
fof(f15903,plain,
( spl0_1082
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X0),X8,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f678,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X0),X8,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X8,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__div__mult_0) ).
fof(f15901,plain,
spl0_1081,
inference(avatar_split_clause,[],[f640,f15899]) ).
fof(f15899,plain,
( spl0_1081
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f640,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
fof(f15897,plain,
spl0_1080,
inference(avatar_split_clause,[],[f639,f15895]) ).
fof(f15895,plain,
( spl0_1080
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f639,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
fof(f15893,plain,
spl0_1079,
inference(avatar_split_clause,[],[f638,f15891]) ).
fof(f15891,plain,
( spl0_1079
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f638,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
fof(f15889,plain,
spl0_1078,
inference(avatar_split_clause,[],[f637,f15887]) ).
fof(f15887,plain,
( spl0_1078
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f637,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
fof(f15885,plain,
( ~ spl0_152
| spl0_1077
| ~ spl0_351
| ~ spl0_625 ),
inference(avatar_split_clause,[],[f7367,f7163,f3429,f15883,f2102]) ).
fof(f2102,plain,
( spl0_152
<=> class_Lattices_Olattice(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f15883,plain,
( spl0_1077
<=> ! [X0] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f3429,plain,
( spl0_351
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f7163,plain,
( spl0_625
<=> ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,v_x,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f7367,plain,
( ! [X0] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal),v_x,tc_RealDef_Oreal)
| ~ class_Lattices_Olattice(tc_RealDef_Oreal) )
| ~ spl0_351
| ~ spl0_625 ),
inference(resolution,[],[f7164,f3430]) ).
fof(f3430,plain,
( ! [X10,X0,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X4,X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_351 ),
inference(avatar_component_clause,[],[f3429]) ).
fof(f7164,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,v_x,tc_RealDef_Oreal) )
| ~ spl0_625 ),
inference(avatar_component_clause,[],[f7163]) ).
fof(f15881,plain,
spl0_1076,
inference(avatar_split_clause,[],[f636,f15879]) ).
fof(f15879,plain,
( spl0_1076
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f636,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
fof(f15877,plain,
spl0_1075,
inference(avatar_split_clause,[],[f635,f15875]) ).
fof(f15875,plain,
( spl0_1075
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f635,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
fof(f15873,plain,
spl0_1074,
inference(avatar_split_clause,[],[f631,f15871]) ).
fof(f15871,plain,
( spl0_1074
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),X4,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f631,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),X4,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_0) ).
fof(f15869,plain,
spl0_1073,
inference(avatar_split_clause,[],[f628,f15867]) ).
fof(f15867,plain,
( spl0_1073
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f628,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
fof(f15865,plain,
spl0_1072,
inference(avatar_split_clause,[],[f500,f15863]) ).
fof(f15863,plain,
( spl0_1072
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f500,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__divide_0) ).
fof(f15861,plain,
spl0_1071,
inference(avatar_split_clause,[],[f470,f15859]) ).
fof(f15859,plain,
( spl0_1071
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f470,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0),X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__over_0) ).
fof(f15857,plain,
spl0_1070,
inference(avatar_split_clause,[],[f407,f15855]) ).
fof(f15855,plain,
( spl0_1070
<=> ! [X4,X0,X14,X10] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X14,X10,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X10,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f407,axiom,
! [X10,X0,X14,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X14,X10,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X10,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).
fof(f15853,plain,
spl0_1069,
inference(avatar_split_clause,[],[f406,f15851]) ).
fof(f15851,plain,
( spl0_1069
<=> ! [X4,X0,X14,X10] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X14,X10,X0),X4,X0)
| c_lessequals(X14,c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f406,axiom,
! [X10,X0,X14,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X14,X10,X0),X4,X0)
| c_lessequals(X14,c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).
fof(f15849,plain,
spl0_1068,
inference(avatar_split_clause,[],[f405,f15847]) ).
fof(f15847,plain,
( spl0_1068
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f405,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
fof(f15845,plain,
spl0_1067,
inference(avatar_split_clause,[],[f404,f15843]) ).
fof(f15843,plain,
( spl0_1067
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f404,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
fof(f15824,plain,
spl0_1066,
inference(avatar_split_clause,[],[f403,f15822]) ).
fof(f15822,plain,
( spl0_1066
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f403,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
fof(f15820,plain,
spl0_1065,
inference(avatar_split_clause,[],[f402,f15818]) ).
fof(f15818,plain,
( spl0_1065
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f402,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
fof(f15816,plain,
spl0_1064,
inference(avatar_split_clause,[],[f368,f15814]) ).
fof(f15814,plain,
( spl0_1064
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X10,X14,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f368,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X10,X14,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
fof(f15812,plain,
spl0_1063,
inference(avatar_split_clause,[],[f334,f15810]) ).
fof(f15810,plain,
( spl0_1063
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X8,X0),c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f334,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X8,X0),c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
fof(f15808,plain,
spl0_1062,
inference(avatar_split_clause,[],[f333,f15806]) ).
fof(f15806,plain,
( spl0_1062
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X8,X0),c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f333,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X8,X0),c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
fof(f15804,plain,
spl0_1061,
inference(avatar_split_clause,[],[f306,f15802]) ).
fof(f15802,plain,
( spl0_1061
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f306,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
fof(f15800,plain,
spl0_1060,
inference(avatar_split_clause,[],[f305,f15798]) ).
fof(f15798,plain,
( spl0_1060
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f305,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
fof(f15796,plain,
spl0_1059,
inference(avatar_split_clause,[],[f279,f15794]) ).
fof(f15794,plain,
( spl0_1059
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f279,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
fof(f15792,plain,
spl0_1058,
inference(avatar_split_clause,[],[f247,f15790]) ).
fof(f15790,plain,
( spl0_1058
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),c_Lattices_Oupper__semilattice__class_Osup(X4,X14,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f247,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),c_Lattices_Oupper__semilattice__class_Osup(X4,X14,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
fof(f15788,plain,
spl0_1057,
inference(avatar_split_clause,[],[f168,f15786]) ).
fof(f15786,plain,
( spl0_1057
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Divides_Odiv__class_Odiv(X1,X2,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f168,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Divides_Odiv__class_Odiv(X1,X2,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).
fof(f15784,plain,
( ~ spl0_152
| spl0_1056
| ~ spl0_350
| ~ spl0_625 ),
inference(avatar_split_clause,[],[f7365,f7163,f3425,f15782,f2102]) ).
fof(f15782,plain,
( spl0_1056
<=> ! [X0] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f3425,plain,
( spl0_350
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f7365,plain,
( ! [X0] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),v_x,tc_RealDef_Oreal)
| ~ class_Lattices_Olattice(tc_RealDef_Oreal) )
| ~ spl0_350
| ~ spl0_625 ),
inference(resolution,[],[f7164,f3426]) ).
fof(f3426,plain,
( ! [X10,X0,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X10,X0)
| ~ class_Lattices_Olattice(X0) )
| ~ spl0_350 ),
inference(avatar_component_clause,[],[f3425]) ).
fof(f15780,plain,
spl0_1055,
inference(avatar_split_clause,[],[f167,f15778]) ).
fof(f15778,plain,
( spl0_1055
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Divides_Odiv__class_Odiv(X1,X2,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f167,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Divides_Odiv__class_Odiv(X1,X2,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).
fof(f15776,plain,
spl0_1054,
inference(avatar_split_clause,[],[f141,f15774]) ).
fof(f15774,plain,
( spl0_1054
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f141,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_2) ).
fof(f15772,plain,
spl0_1053,
inference(avatar_split_clause,[],[f49,f15770]) ).
fof(f15770,plain,
( spl0_1053
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f49,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
fof(f15768,plain,
spl0_1052,
inference(avatar_split_clause,[],[f48,f15766]) ).
fof(f15766,plain,
( spl0_1052
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f48,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
fof(f15764,plain,
spl0_1051,
inference(avatar_split_clause,[],[f47,f15762]) ).
fof(f15762,plain,
( spl0_1051
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f47,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
fof(f15760,plain,
spl0_1050,
inference(avatar_split_clause,[],[f46,f15758]) ).
fof(f15758,plain,
( spl0_1050
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f46,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
fof(f15756,plain,
spl0_1049,
inference(avatar_split_clause,[],[f45,f15754]) ).
fof(f15754,plain,
( spl0_1049
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f45,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
fof(f15752,plain,
spl0_1048,
inference(avatar_split_clause,[],[f32,f15750]) ).
fof(f15750,plain,
( spl0_1048
<=> ! [X4,X0,X14,X10] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X14,X10,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X10,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f32,axiom,
! [X10,X0,X14,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X14,X10,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X10,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).
fof(f15748,plain,
spl0_1047,
inference(avatar_split_clause,[],[f31,f15746]) ).
fof(f15746,plain,
( spl0_1047
<=> ! [X4,X0,X14,X10] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X10,X0),X4,X0)
| c_HOL_Oord__class_Oless(X14,c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f31,axiom,
! [X10,X0,X14,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X10,X0),X4,X0)
| c_HOL_Oord__class_Oless(X14,c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
fof(f15716,plain,
( spl0_1046
| ~ spl0_205
| ~ spl0_625 ),
inference(avatar_split_clause,[],[f7359,f7163,f2377,f15714]) ).
fof(f2377,plain,
( spl0_205
<=> ! [X4] :
( ~ c_lessequals(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f7359,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),v_x,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_205
| ~ spl0_625 ),
inference(resolution,[],[f7164,f2378]) ).
fof(f2378,plain,
( ! [X4] :
( c_lessequals(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f2377]) ).
fof(f15507,plain,
( spl0_1045
| ~ spl0_364
| ~ spl0_625 ),
inference(avatar_split_clause,[],[f7358,f7163,f3499,f15505]) ).
fof(f15505,plain,
( spl0_1045
<=> ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),v_x,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f3499,plain,
( spl0_364
<=> ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f7358,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),v_x,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_364
| ~ spl0_625 ),
inference(resolution,[],[f7164,f3500]) ).
fof(f3500,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_364 ),
inference(avatar_component_clause,[],[f3499]) ).
fof(f13449,plain,
spl0_1044,
inference(avatar_split_clause,[],[f1008,f13447]) ).
fof(f13447,plain,
( spl0_1044
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f1008,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
fof(f13445,plain,
spl0_1043,
inference(avatar_split_clause,[],[f972,f13443]) ).
fof(f13443,plain,
( spl0_1043
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f972,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
fof(f13441,plain,
( spl0_1042
| ~ spl0_185
| ~ spl0_754 ),
inference(avatar_split_clause,[],[f12968,f9322,f2266,f13439]) ).
fof(f13439,plain,
( spl0_1042
<=> ! [X0,X1] :
( c_lessequals(c_NthRoot_Osqrt(c_RealVector_Odist__class_Odist(X0,X0,X1)),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f9322,plain,
( spl0_754
<=> ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f12968,plain,
( ! [X0,X1] :
( c_lessequals(c_NthRoot_Osqrt(c_RealVector_Odist__class_Odist(X0,X0,X1)),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) )
| ~ spl0_185
| ~ spl0_754 ),
inference(resolution,[],[f9323,f2267]) ).
fof(f9323,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X0),c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_754 ),
inference(avatar_component_clause,[],[f9322]) ).
fof(f13437,plain,
spl0_1041,
inference(avatar_split_clause,[],[f971,f13435]) ).
fof(f13435,plain,
( spl0_1041
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X8,c_Divides_Odiv__class_Omod(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f971,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X8,c_Divides_Odiv__class_Omod(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
fof(f13433,plain,
spl0_1040,
inference(avatar_split_clause,[],[f942,f13431]) ).
fof(f13431,plain,
( spl0_1040
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f942,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f13429,plain,
spl0_1039,
inference(avatar_split_clause,[],[f940,f13427]) ).
fof(f13427,plain,
( spl0_1039
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X8,X3,X0)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f940,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X8,X3,X0)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
fof(f13425,plain,
spl0_1038,
inference(avatar_split_clause,[],[f925,f13423]) ).
fof(f13423,plain,
( spl0_1038
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X10,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f925,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X10,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
fof(f13421,plain,
spl0_1037,
inference(avatar_split_clause,[],[f924,f13419]) ).
fof(f13419,plain,
( spl0_1037
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X10,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f924,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X10,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
fof(f13417,plain,
spl0_1036,
inference(avatar_split_clause,[],[f915,f13415]) ).
fof(f13415,plain,
( spl0_1036
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f915,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X3,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
fof(f13413,plain,
spl0_1035,
inference(avatar_split_clause,[],[f866,f13411]) ).
fof(f13411,plain,
( spl0_1035
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f866,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
fof(f13409,plain,
spl0_1034,
inference(avatar_split_clause,[],[f865,f13407]) ).
fof(f13407,plain,
( spl0_1034
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X8,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f865,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X8,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
fof(f13405,plain,
spl0_1033,
inference(avatar_split_clause,[],[f857,f13403]) ).
fof(f13403,plain,
( spl0_1033
<=> ! [X9,X0,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X30,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X30,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f857,axiom,
! [X0,X9,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X30,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X30,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
fof(f13401,plain,
spl0_1032,
inference(avatar_split_clause,[],[f855,f13399]) ).
fof(f13399,plain,
( spl0_1032
<=> ! [X4,X0,X27,X10] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X10,X0),X27,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X27,X0),c_HOL_Oinverse__class_Odivide(X10,X27,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f855,axiom,
! [X10,X0,X27,X4] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X10,X0),X27,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X27,X0),c_HOL_Oinverse__class_Odivide(X10,X27,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
fof(f13397,plain,
( spl0_1031
| ~ spl0_189
| ~ spl0_754 ),
inference(avatar_split_clause,[],[f12967,f9322,f2282,f13395]) ).
fof(f13395,plain,
( spl0_1031
<=> ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0)),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f12967,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0)),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_189
| ~ spl0_754 ),
inference(resolution,[],[f9323,f2283]) ).
fof(f13393,plain,
spl0_1030,
inference(avatar_split_clause,[],[f854,f13391]) ).
fof(f13391,plain,
( spl0_1030
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X8,X0),c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f854,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X8,X0),c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
fof(f13389,plain,
spl0_1029,
inference(avatar_split_clause,[],[f845,f13387]) ).
fof(f13387,plain,
( spl0_1029
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f845,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
fof(f13385,plain,
spl0_1028,
inference(avatar_split_clause,[],[f844,f13383]) ).
fof(f13383,plain,
( spl0_1028
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f844,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
fof(f13381,plain,
spl0_1027,
inference(avatar_split_clause,[],[f799,f13379]) ).
fof(f13379,plain,
( spl0_1027
<=> ! [X26,X0,X2,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Oplus__class_Oplus(X2,X26,X0),X0) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),c_RealVector_OscaleR__class_OscaleR(X1,X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f799,axiom,
! [X2,X0,X1,X26] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Oplus__class_Oplus(X2,X26,X0),X0) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),c_RealVector_OscaleR__class_OscaleR(X1,X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Oadd__right_0) ).
fof(f13377,plain,
spl0_1026,
inference(avatar_split_clause,[],[f798,f13375]) ).
fof(f13375,plain,
( spl0_1026
<=> ! [X4,X0,X10,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Oplus__class_Oplus(X4,X10,X0),X0) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),c_RealVector_OscaleR__class_OscaleR(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f798,axiom,
! [X10,X0,X1,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Oplus__class_Oplus(X4,X10,X0),X0) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),c_RealVector_OscaleR__class_OscaleR(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Oadd_0) ).
fof(f13373,plain,
spl0_1025,
inference(avatar_split_clause,[],[f797,f13371]) ).
fof(f13371,plain,
( spl0_1025
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f797,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
fof(f13369,plain,
spl0_1024,
inference(avatar_split_clause,[],[f796,f13367]) ).
fof(f13367,plain,
( spl0_1024
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f796,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
fof(f13365,plain,
spl0_1023,
inference(avatar_split_clause,[],[f795,f13363]) ).
fof(f13363,plain,
( spl0_1023
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X8,X0),X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f795,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X8,X0),X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
fof(f13361,plain,
spl0_1022,
inference(avatar_split_clause,[],[f794,f13359]) ).
fof(f13359,plain,
( spl0_1022
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X8,X0),X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f794,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X8,X0),X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
fof(f13357,plain,
spl0_1021,
inference(avatar_split_clause,[],[f765,f13355]) ).
fof(f13355,plain,
( spl0_1021
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f765,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f13353,plain,
( spl0_1020
| ~ spl0_185
| ~ spl0_732 ),
inference(avatar_split_clause,[],[f12558,f9234,f2266,f13351]) ).
fof(f13351,plain,
( spl0_1020
<=> ! [X0,X1] :
( c_lessequals(c_RealVector_Odist__class_Odist(X0,X0,X1),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f9234,plain,
( spl0_732
<=> ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f12558,plain,
( ! [X0,X1] :
( c_lessequals(c_RealVector_Odist__class_Odist(X0,X0,X1),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) )
| ~ spl0_185
| ~ spl0_732 ),
inference(resolution,[],[f9235,f2267]) ).
fof(f9235,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_732 ),
inference(avatar_component_clause,[],[f9234]) ).
fof(f13349,plain,
spl0_1019,
inference(avatar_split_clause,[],[f757,f13347]) ).
fof(f13347,plain,
( spl0_1019
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f757,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f13345,plain,
spl0_1018,
inference(avatar_split_clause,[],[f745,f13343]) ).
fof(f13343,plain,
( spl0_1018
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X10,X0),X4,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X10,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f745,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X10,X0),X4,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X10,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).
fof(f13341,plain,
spl0_1017,
inference(avatar_split_clause,[],[f671,f13339]) ).
fof(f13339,plain,
( spl0_1017
<=> ! [X28,X0,X2,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X28,X0),X2,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X28,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f671,axiom,
! [X2,X28,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X28,X0),X2,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X28,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
fof(f13337,plain,
spl0_1016,
inference(avatar_split_clause,[],[f670,f13335]) ).
fof(f13335,plain,
( spl0_1016
<=> ! [X26,X0,X2,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X26,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f670,axiom,
! [X2,X0,X1,X26] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X26,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
fof(f13333,plain,
spl0_1015,
inference(avatar_split_clause,[],[f668,f13331]) ).
fof(f13331,plain,
( spl0_1015
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f668,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
fof(f13329,plain,
spl0_1014,
inference(avatar_split_clause,[],[f667,f13327]) ).
fof(f13327,plain,
( spl0_1014
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f667,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
fof(f13325,plain,
spl0_1013,
inference(avatar_split_clause,[],[f666,f13323]) ).
fof(f13323,plain,
( spl0_1013
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f666,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f13321,plain,
spl0_1012,
inference(avatar_split_clause,[],[f627,f13319]) ).
fof(f13319,plain,
( spl0_1012
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X2,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f627,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X2,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
fof(f13317,plain,
spl0_1011,
inference(avatar_split_clause,[],[f622,f13315]) ).
fof(f13315,plain,
( spl0_1011
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X8,X0),X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f622,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X8,X0),X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
fof(f13313,plain,
spl0_1010,
inference(avatar_split_clause,[],[f621,f13311]) ).
fof(f13311,plain,
( spl0_1010
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X8,X0),X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f621,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X8,X0),X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
fof(f13309,plain,
( spl0_1009
| ~ spl0_189
| ~ spl0_732 ),
inference(avatar_split_clause,[],[f12557,f9234,f2282,f13307]) ).
fof(f13307,plain,
( spl0_1009
<=> ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f12557,plain,
( ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_189
| ~ spl0_732 ),
inference(resolution,[],[f9235,f2283]) ).
fof(f13305,plain,
spl0_1008,
inference(avatar_split_clause,[],[f594,f13303]) ).
fof(f13303,plain,
( spl0_1008
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f594,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).
fof(f13301,plain,
spl0_1007,
inference(avatar_split_clause,[],[f593,f13299]) ).
fof(f13299,plain,
( spl0_1007
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X8,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f593,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X8,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).
fof(f13297,plain,
spl0_1006,
inference(avatar_split_clause,[],[f592,f13295]) ).
fof(f13295,plain,
( spl0_1006
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X8,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f592,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X8,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__sup__distrib__left_0) ).
fof(f13293,plain,
spl0_1005,
inference(avatar_split_clause,[],[f591,f13291]) ).
fof(f13291,plain,
( spl0_1005
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f591,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X8,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__sup__distrib__right_0) ).
fof(f13289,plain,
spl0_1004,
inference(avatar_split_clause,[],[f542,f13287]) ).
fof(f13287,plain,
( spl0_1004
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X2,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f542,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X2,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
fof(f13285,plain,
spl0_1003,
inference(avatar_split_clause,[],[f523,f13283]) ).
fof(f13283,plain,
( spl0_1003
<=> ! [X0,X8,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f523,axiom,
! [X2,X3,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X8,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f13281,plain,
spl0_1002,
inference(avatar_split_clause,[],[f518,f13279]) ).
fof(f13279,plain,
( spl0_1002
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f518,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f13277,plain,
spl0_1001,
inference(avatar_split_clause,[],[f505,f13275]) ).
fof(f13275,plain,
( spl0_1001
<=> ! [X4,X0,X14,X10,X32] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X4,X14,X0) = X32
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X10,X14,X0),X0) != c_HOL_Oplus__class_Oplus(X10,X32,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f505,axiom,
! [X10,X0,X14,X4,X32] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X4,X14,X0) = X32
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X10,X14,X0),X0) != c_HOL_Oplus__class_Oplus(X10,X32,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
fof(f13273,plain,
spl0_1000,
inference(avatar_split_clause,[],[f485,f13271]) ).
fof(f13271,plain,
( spl0_1000
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X10,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f485,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X10,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
fof(f13269,plain,
spl0_999,
inference(avatar_split_clause,[],[f484,f13267]) ).
fof(f13267,plain,
( spl0_999
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X10,X14,X0),X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X10,X4,X0),c_Lattices_Olower__semilattice__class_Oinf(X14,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f484,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X10,X14,X0),X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X10,X4,X0),c_Lattices_Olower__semilattice__class_Oinf(X14,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
fof(f13265,plain,
( spl0_998
| ~ spl0_341
| ~ spl0_732 ),
inference(avatar_split_clause,[],[f12555,f9234,f3292,f13263]) ).
fof(f13263,plain,
( spl0_998
<=> ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f3292,plain,
( spl0_341
<=> ! [X29,X14] :
( c_lessequals(X14,X29,tc_RealDef_Oreal)
| c_lessequals(X29,X14,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f12555,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_341
| ~ spl0_732 ),
inference(resolution,[],[f9235,f3293]) ).
fof(f3293,plain,
( ! [X29,X14] :
( c_lessequals(X14,X29,tc_RealDef_Oreal)
| c_lessequals(X29,X14,tc_RealDef_Oreal) )
| ~ spl0_341 ),
inference(avatar_component_clause,[],[f3292]) ).
fof(f13261,plain,
spl0_997,
inference(avatar_split_clause,[],[f477,f13259]) ).
fof(f13259,plain,
( spl0_997
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f477,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).
fof(f13257,plain,
spl0_996,
inference(avatar_split_clause,[],[f435,f13255]) ).
fof(f13255,plain,
( spl0_996
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X2,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f435,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X2,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f13253,plain,
spl0_995,
inference(avatar_split_clause,[],[f434,f13251]) ).
fof(f13251,plain,
( spl0_995
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f434,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f13249,plain,
spl0_994,
inference(avatar_split_clause,[],[f391,f13247]) ).
fof(f13247,plain,
( spl0_994
<=> ! [X4,X0,X27,X10] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X4,X10,X0),X27,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X27,X0),c_HOL_Oinverse__class_Odivide(X10,X27,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f391,axiom,
! [X10,X0,X27,X4] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X4,X10,X0),X27,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X27,X0),c_HOL_Oinverse__class_Odivide(X10,X27,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
fof(f13245,plain,
spl0_993,
inference(avatar_split_clause,[],[f390,f13243]) ).
fof(f13243,plain,
( spl0_993
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X8,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X8,X0),c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f390,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X8,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X8,X0),c_HOL_Oinverse__class_Odivide(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
fof(f13241,plain,
spl0_992,
inference(avatar_split_clause,[],[f389,f13239]) ).
fof(f13239,plain,
( spl0_992
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X8,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f389,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X8,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).
fof(f13237,plain,
spl0_991,
inference(avatar_split_clause,[],[f388,f13235]) ).
fof(f13235,plain,
( spl0_991
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X8,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f388,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X8,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).
fof(f13233,plain,
spl0_990,
inference(avatar_split_clause,[],[f387,f13231]) ).
fof(f13231,plain,
( spl0_990
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X8,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f387,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X8,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).
fof(f13229,plain,
spl0_989,
inference(avatar_split_clause,[],[f386,f13227]) ).
fof(f13227,plain,
( spl0_989
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X8,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f386,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X8,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).
fof(f13225,plain,
spl0_988,
inference(avatar_split_clause,[],[f363,f13223]) ).
fof(f13223,plain,
( spl0_988
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f363,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
fof(f13221,plain,
( spl0_987
| ~ spl0_345
| ~ spl0_710 ),
inference(avatar_split_clause,[],[f11030,f9145,f3374,f13218]) ).
fof(f3374,plain,
( spl0_345
<=> ! [X0,X1] : c_Log_Opowr(X0,X1) = c_Log_Opowr(c_Log_Opowr(X0,X1),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f9145,plain,
( spl0_710
<=> c_Log_Opowr(v_x,c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f11030,plain,
( c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal) = c_Log_Opowr(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_345
| ~ spl0_710 ),
inference(superposition,[],[f3375,f9147]) ).
fof(f9147,plain,
( c_Log_Opowr(v_x,c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal)
| ~ spl0_710 ),
inference(avatar_component_clause,[],[f9145]) ).
fof(f3375,plain,
( ! [X0,X1] : c_Log_Opowr(X0,X1) = c_Log_Opowr(c_Log_Opowr(X0,X1),c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_345 ),
inference(avatar_component_clause,[],[f3374]) ).
fof(f13216,plain,
spl0_986,
inference(avatar_split_clause,[],[f362,f13214]) ).
fof(f13214,plain,
( spl0_986
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f362,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
fof(f13212,plain,
spl0_985,
inference(avatar_split_clause,[],[f357,f13210]) ).
fof(f13210,plain,
( spl0_985
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f357,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
fof(f13208,plain,
spl0_984,
inference(avatar_split_clause,[],[f353,f13206]) ).
fof(f13206,plain,
( spl0_984
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f353,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
fof(f13204,plain,
spl0_983,
inference(avatar_split_clause,[],[f352,f13202]) ).
fof(f13202,plain,
( spl0_983
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f352,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
fof(f13200,plain,
spl0_982,
inference(avatar_split_clause,[],[f351,f13198]) ).
fof(f13198,plain,
( spl0_982
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f351,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
fof(f13196,plain,
spl0_981,
inference(avatar_split_clause,[],[f337,f13194]) ).
fof(f13194,plain,
( spl0_981
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f337,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
fof(f13192,plain,
spl0_980,
inference(avatar_split_clause,[],[f336,f13190]) ).
fof(f13190,plain,
( spl0_980
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f336,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
fof(f13188,plain,
spl0_979,
inference(avatar_split_clause,[],[f292,f13186]) ).
fof(f13186,plain,
( spl0_979
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f292,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
fof(f13184,plain,
spl0_978,
inference(avatar_split_clause,[],[f291,f13182]) ).
fof(f13182,plain,
( spl0_978
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f291,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
fof(f13180,plain,
spl0_977,
inference(avatar_split_clause,[],[f283,f13178]) ).
fof(f13178,plain,
( spl0_977
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f283,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
fof(f13176,plain,
( spl0_976
| ~ spl0_345
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f9810,f9100,f3374,f13173]) ).
fof(f9100,plain,
( spl0_699
<=> c_Log_Opowr(c_Transcendental_Opi,c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f9810,plain,
( c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal) = c_Log_Opowr(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_345
| ~ spl0_699 ),
inference(superposition,[],[f3375,f9102]) ).
fof(f9102,plain,
( c_Log_Opowr(c_Transcendental_Opi,c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_699 ),
inference(avatar_component_clause,[],[f9100]) ).
fof(f13171,plain,
spl0_975,
inference(avatar_split_clause,[],[f282,f13169]) ).
fof(f13169,plain,
( spl0_975
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f282,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
fof(f13167,plain,
spl0_974,
inference(avatar_split_clause,[],[f281,f13165]) ).
fof(f13165,plain,
( spl0_974
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f281,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
fof(f13163,plain,
spl0_973,
inference(avatar_split_clause,[],[f280,f13161]) ).
fof(f13161,plain,
( spl0_973
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f280,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
fof(f13159,plain,
spl0_972,
inference(avatar_split_clause,[],[f263,f13157]) ).
fof(f13157,plain,
( spl0_972
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f263,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
fof(f13155,plain,
spl0_971,
inference(avatar_split_clause,[],[f262,f13153]) ).
fof(f13153,plain,
( spl0_971
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f262,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
fof(f13151,plain,
spl0_970,
inference(avatar_split_clause,[],[f259,f13149]) ).
fof(f13149,plain,
( spl0_970
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f259,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
fof(f13147,plain,
spl0_969,
inference(avatar_split_clause,[],[f220,f13145]) ).
fof(f13145,plain,
( spl0_969
<=> ! [X26,X0,X2,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ominus__class_Ominus(X2,X26,X0),X0) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),c_RealVector_OscaleR__class_OscaleR(X1,X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f220,axiom,
! [X2,X0,X1,X26] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ominus__class_Ominus(X2,X26,X0),X0) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),c_RealVector_OscaleR__class_OscaleR(X1,X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Odiff__right_0) ).
fof(f13143,plain,
spl0_968,
inference(avatar_split_clause,[],[f219,f13141]) ).
fof(f13141,plain,
( spl0_968
<=> ! [X4,X0,X10,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ominus__class_Ominus(X4,X10,X0),X0) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),c_RealVector_OscaleR__class_OscaleR(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f219,axiom,
! [X10,X0,X1,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ominus__class_Ominus(X4,X10,X0),X0) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),c_RealVector_OscaleR__class_OscaleR(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Odiff_0) ).
fof(f13139,plain,
spl0_967,
inference(avatar_split_clause,[],[f185,f13137]) ).
fof(f13137,plain,
( spl0_967
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f185,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
fof(f13135,plain,
spl0_966,
inference(avatar_split_clause,[],[f183,f13133]) ).
fof(f13133,plain,
( spl0_966
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f183,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
fof(f13131,plain,
( spl0_965
| ~ spl0_212
| ~ spl0_589 ),
inference(avatar_split_clause,[],[f6276,f5994,f2407,f13129]) ).
fof(f13129,plain,
( spl0_965
<=> ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f5994,plain,
( spl0_589
<=> ! [X0] :
( c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f6276,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_212
| ~ spl0_589 ),
inference(resolution,[],[f5995,f2408]) ).
fof(f5995,plain,
( ! [X0] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_589 ),
inference(avatar_component_clause,[],[f5994]) ).
fof(f13127,plain,
spl0_964,
inference(avatar_split_clause,[],[f147,f13125]) ).
fof(f13125,plain,
( spl0_964
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f147,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
fof(f13123,plain,
spl0_963,
inference(avatar_split_clause,[],[f145,f13121]) ).
fof(f13121,plain,
( spl0_963
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f145,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
fof(f13119,plain,
spl0_962,
inference(avatar_split_clause,[],[f144,f13117]) ).
fof(f13117,plain,
( spl0_962
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f144,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
fof(f13115,plain,
spl0_961,
inference(avatar_split_clause,[],[f143,f13113]) ).
fof(f13113,plain,
( spl0_961
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f143,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
fof(f13111,plain,
spl0_960,
inference(avatar_split_clause,[],[f142,f13109]) ).
fof(f13109,plain,
( spl0_960
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f142,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
fof(f13107,plain,
spl0_959,
inference(avatar_split_clause,[],[f131,f13105]) ).
fof(f13105,plain,
( spl0_959
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f131,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
fof(f13103,plain,
spl0_958,
inference(avatar_split_clause,[],[f130,f13101]) ).
fof(f13101,plain,
( spl0_958
<=> ! [X4,X0,X14,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oplus__class_Oplus(X10,X14,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X10,X0),c_HOL_Otimes__class_Otimes(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f130,axiom,
! [X10,X0,X14,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oplus__class_Oplus(X10,X14,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X10,X0),c_HOL_Otimes__class_Otimes(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
fof(f13099,plain,
spl0_957,
inference(avatar_split_clause,[],[f128,f13097]) ).
fof(f13097,plain,
( spl0_957
<=> ! [X4,X0,X27,X10] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X10,X0),X27,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),c_HOL_Otimes__class_Otimes(X10,X27,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f128,axiom,
! [X10,X0,X27,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X10,X0),X27,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),c_HOL_Otimes__class_Otimes(X10,X27,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
fof(f13095,plain,
spl0_956,
inference(avatar_split_clause,[],[f126,f13093]) ).
fof(f13093,plain,
( spl0_956
<=> ! [X4,X0,X10,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Oplus__class_Oplus(X4,X10,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X4,X0),c_HOL_Otimes__class_Otimes(X25,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f126,axiom,
! [X10,X0,X4,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Oplus__class_Oplus(X4,X10,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X4,X0),c_HOL_Otimes__class_Otimes(X25,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
fof(f13091,plain,
spl0_955,
inference(avatar_split_clause,[],[f125,f13089]) ).
fof(f13089,plain,
( spl0_955
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f125,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f13074,plain,
spl0_954,
inference(avatar_split_clause,[],[f110,f13072]) ).
fof(f13072,plain,
( spl0_954
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f110,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
fof(f13070,plain,
spl0_953,
inference(avatar_split_clause,[],[f109,f13068]) ).
fof(f13068,plain,
( spl0_953
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f109,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
fof(f13066,plain,
spl0_952,
inference(avatar_split_clause,[],[f108,f13064]) ).
fof(f13064,plain,
( spl0_952
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f108,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
fof(f13062,plain,
spl0_951,
inference(avatar_split_clause,[],[f106,f13060]) ).
fof(f13060,plain,
( spl0_951
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f106,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
fof(f13058,plain,
spl0_950,
inference(avatar_split_clause,[],[f104,f13056]) ).
fof(f13056,plain,
( spl0_950
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f104,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
fof(f13054,plain,
spl0_949,
inference(avatar_split_clause,[],[f76,f13052]) ).
fof(f13052,plain,
( spl0_949
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f76,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
fof(f13050,plain,
spl0_948,
inference(avatar_split_clause,[],[f75,f13048]) ).
fof(f13048,plain,
( spl0_948
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f75,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
fof(f13046,plain,
spl0_947,
inference(avatar_split_clause,[],[f74,f13044]) ).
fof(f13044,plain,
( spl0_947
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f74,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
fof(f13042,plain,
spl0_946,
inference(avatar_split_clause,[],[f73,f13040]) ).
fof(f13040,plain,
( spl0_946
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f73,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
fof(f13038,plain,
spl0_945,
inference(avatar_split_clause,[],[f72,f13036]) ).
fof(f13036,plain,
( spl0_945
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f72,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
fof(f13034,plain,
( spl0_944
| ~ spl0_125
| ~ spl0_295
| ~ spl0_520 ),
inference(avatar_split_clause,[],[f5323,f5006,f2937,f1967,f13031]) ).
fof(f13031,plain,
( spl0_944
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_Lattices_Olower__semilattice__class_Oinf(v_x,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f2937,plain,
( spl0_295
<=> c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),v_x,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f5323,plain,
( ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = c_Lattices_Olower__semilattice__class_Oinf(v_x,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_295
| ~ spl0_520 ),
inference(resolution,[],[f5007,f2939]) ).
fof(f2939,plain,
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),v_x,tc_RealDef_Oreal)
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f2937]) ).
fof(f13029,plain,
spl0_943,
inference(avatar_split_clause,[],[f71,f13027]) ).
fof(f13027,plain,
( spl0_943
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f71,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
fof(f13025,plain,
spl0_942,
inference(avatar_split_clause,[],[f66,f13023]) ).
fof(f13023,plain,
( spl0_942
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),c_Lattices_Oupper__semilattice__class_Osup(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f66,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),c_Lattices_Oupper__semilattice__class_Osup(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
fof(f13021,plain,
spl0_941,
inference(avatar_split_clause,[],[f65,f13019]) ).
fof(f13019,plain,
( spl0_941
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X10,X4,X0),c_Lattices_Oupper__semilattice__class_Osup(X14,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f65,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X10,X4,X0),c_Lattices_Oupper__semilattice__class_Osup(X14,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
fof(f13017,plain,
spl0_940,
inference(avatar_split_clause,[],[f51,f13015]) ).
fof(f13015,plain,
( spl0_940
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f51,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X9,X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
fof(f13013,plain,
spl0_939,
inference(avatar_split_clause,[],[f19,f13011]) ).
fof(f13011,plain,
( spl0_939
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X10,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f19,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(X10,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X10,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).
fof(f13009,plain,
spl0_938,
inference(avatar_split_clause,[],[f18,f13007]) ).
fof(f13007,plain,
( spl0_938
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X10,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f18,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X10,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
fof(f13005,plain,
spl0_937,
inference(avatar_split_clause,[],[f8,f13003]) ).
fof(f13003,plain,
( spl0_937
<=> ! [X4,X11,X0,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X4,X10,X0),X11,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X4,X11,X0),c_Power_Opower__class_Opower(X10,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f8,axiom,
! [X10,X0,X11,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X4,X10,X0),X11,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X4,X11,X0),c_Power_Opower__class_Opower(X10,X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
fof(f13001,plain,
spl0_936,
inference(avatar_split_clause,[],[f7,f12999]) ).
fof(f12999,plain,
( spl0_936
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f7,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X9,X0),c_Power_Opower__class_Opower(X2,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
fof(f12496,plain,
spl0_935,
inference(avatar_split_clause,[],[f1011,f12494]) ).
fof(f12494,plain,
( spl0_935
<=> ! [X9,X0,X1] :
( ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X9,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f1011,axiom,
! [X0,X1,X9] :
( ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X9,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
fof(f12492,plain,
spl0_934,
inference(avatar_split_clause,[],[f954,f12490]) ).
fof(f12490,plain,
( spl0_934
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f954,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
fof(f12488,plain,
spl0_933,
inference(avatar_split_clause,[],[f892,f12486]) ).
fof(f12486,plain,
( spl0_933
<=> ! [X0,X9,X1,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X9 = X30
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_Power_Opower__class_Opower(X1,X9,X0) != c_Power_Opower__class_Opower(X1,X30,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f892,axiom,
! [X0,X1,X9,X30] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X9 = X30
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_Power_Opower__class_Opower(X1,X9,X0) != c_Power_Opower__class_Opower(X1,X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
fof(f12484,plain,
spl0_932,
inference(avatar_split_clause,[],[f818,f12482]) ).
fof(f12482,plain,
( spl0_932
<=> ! [X4,X0,X14,X10] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X4,X10,X0),X14,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X14,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f818,axiom,
! [X10,X0,X14,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X4,X10,X0),X14,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X14,X0),X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
fof(f12424,plain,
spl0_931,
inference(avatar_split_clause,[],[f815,f12422]) ).
fof(f12422,plain,
( spl0_931
<=> ! [X4,X0,X10] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X4,X0),c_Transcendental_Oexp(X10,X0),X0) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f815,axiom,
! [X10,X0,X4] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X4,X0),c_Transcendental_Oexp(X10,X0),X0) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__add_0) ).
fof(f12420,plain,
spl0_930,
inference(avatar_split_clause,[],[f727,f12418]) ).
fof(f12418,plain,
( spl0_930
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X9,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f727,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X9,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
fof(f12416,plain,
spl0_929,
inference(avatar_split_clause,[],[f689,f12414]) ).
fof(f12414,plain,
( spl0_929
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f689,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__divide_0) ).
fof(f12412,plain,
spl0_928,
inference(avatar_split_clause,[],[f634,f12410]) ).
fof(f12410,plain,
( spl0_928
<=> ! [X4,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X4,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f634,axiom,
! [X0,X9,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X4,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
fof(f12408,plain,
spl0_927,
inference(avatar_split_clause,[],[f588,f12406]) ).
fof(f12406,plain,
( spl0_927
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f588,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le__neg_0) ).
fof(f12404,plain,
spl0_926,
inference(avatar_split_clause,[],[f587,f12402]) ).
fof(f12402,plain,
( spl0_926
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f587,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le__neg_0) ).
fof(f12400,plain,
spl0_925,
inference(avatar_split_clause,[],[f586,f12398]) ).
fof(f12398,plain,
( spl0_925
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f586,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le_0) ).
fof(f12396,plain,
spl0_924,
inference(avatar_split_clause,[],[f585,f12394]) ).
fof(f12394,plain,
( spl0_924
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f585,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le_0) ).
fof(f12392,plain,
spl0_923,
inference(avatar_split_clause,[],[f530,f12390]) ).
fof(f12390,plain,
( spl0_923
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f530,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__if_0) ).
fof(f12388,plain,
spl0_922,
inference(avatar_split_clause,[],[f516,f12386]) ).
fof(f12386,plain,
( spl0_922
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f516,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).
fof(f12365,plain,
spl0_921,
inference(avatar_split_clause,[],[f515,f12363]) ).
fof(f12363,plain,
( spl0_921
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f515,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).
fof(f12361,plain,
spl0_920,
inference(avatar_split_clause,[],[f514,f12359]) ).
fof(f12359,plain,
( spl0_920
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f514,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).
fof(f12357,plain,
spl0_919,
inference(avatar_split_clause,[],[f513,f12355]) ).
fof(f12355,plain,
( spl0_919
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f513,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).
fof(f12353,plain,
spl0_918,
inference(avatar_split_clause,[],[f508,f12351]) ).
fof(f12351,plain,
( spl0_918
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Osgn__class_Osgn(X4,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f508,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Osgn__class_Osgn(X4,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__if_2) ).
fof(f12349,plain,
spl0_917,
inference(avatar_split_clause,[],[f471,f12347]) ).
fof(f12347,plain,
( spl0_917
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f471,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
fof(f12345,plain,
spl0_916,
inference(avatar_split_clause,[],[f455,f12343]) ).
fof(f12343,plain,
( spl0_916
<=> ! [X4,X0,X10] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(X4,X10,X0),X0) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X4,X0),c_Transcendental_Oexp(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f455,axiom,
! [X10,X0,X4] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(X4,X10,X0),X0) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X4,X0),c_Transcendental_Oexp(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__diff_0) ).
fof(f12341,plain,
spl0_915,
inference(avatar_split_clause,[],[f401,f12339]) ).
fof(f12339,plain,
( spl0_915
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Otimes__class_Otimes(X1,X1,X0) != c_HOL_Otimes__class_Otimes(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f401,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Otimes__class_Otimes(X1,X1,X0) != c_HOL_Otimes__class_Otimes(X2,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
fof(f12337,plain,
spl0_914,
inference(avatar_split_clause,[],[f358,f12335]) ).
fof(f12335,plain,
( spl0_914
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f358,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
fof(f12333,plain,
spl0_913,
inference(avatar_split_clause,[],[f318,f12331]) ).
fof(f12331,plain,
( spl0_913
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f318,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
fof(f12329,plain,
spl0_912,
inference(avatar_split_clause,[],[f267,f12327]) ).
fof(f12327,plain,
( spl0_912
<=> ! [X4,X0,X1] :
( ~ class_RealVector_Oreal__div__algebra(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f267,axiom,
! [X0,X1,X4] :
( ~ class_RealVector_Oreal__div__algebra(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__scaleR__distrib_0) ).
fof(f12325,plain,
( spl0_911
| ~ spl0_330
| ~ spl0_710 ),
inference(avatar_split_clause,[],[f11029,f9145,f3195,f12322]) ).
fof(f12322,plain,
( spl0_911
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f3195,plain,
( spl0_330
<=> ! [X0,X1] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_Log_Opowr(X0,X1),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f11029,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_330
| ~ spl0_710 ),
inference(superposition,[],[f3196,f9147]) ).
fof(f3196,plain,
( ! [X0,X1] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_Log_Opowr(X0,X1),tc_RealDef_Oreal)
| ~ spl0_330 ),
inference(avatar_component_clause,[],[f3195]) ).
fof(f12320,plain,
spl0_910,
inference(avatar_split_clause,[],[f40,f12318]) ).
fof(f12318,plain,
( spl0_910
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f40,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
fof(f12316,plain,
spl0_909,
inference(avatar_split_clause,[],[f39,f12314]) ).
fof(f12314,plain,
( spl0_909
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f39,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
fof(f12312,plain,
spl0_908,
inference(avatar_split_clause,[],[f11,f12310]) ).
fof(f12310,plain,
( spl0_908
<=> ! [X4,X13,X0,X12,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| c_HOL_Oord__class_Oless(X12,X13,X0)
| c_HOL_Ominus__class_Ominus(X4,X10,X0) != c_HOL_Ominus__class_Ominus(X12,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f11,axiom,
! [X10,X0,X4,X12,X13] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| c_HOL_Oord__class_Oless(X12,X13,X0)
| c_HOL_Ominus__class_Ominus(X4,X10,X0) != c_HOL_Ominus__class_Ominus(X12,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
fof(f12308,plain,
spl0_907,
inference(avatar_split_clause,[],[f9,f12306]) ).
fof(f12306,plain,
( spl0_907
<=> ! [X4,X0,X13,X12,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X10,X4,X0)
| c_lessequals(X13,X12,X0)
| c_HOL_Ominus__class_Ominus(X4,X10,X0) != c_HOL_Ominus__class_Ominus(X12,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f9,axiom,
! [X10,X0,X4,X12,X13] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X10,X4,X0)
| c_lessequals(X13,X12,X0)
| c_HOL_Ominus__class_Ominus(X4,X10,X0) != c_HOL_Ominus__class_Ominus(X12,X13,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
fof(f11718,plain,
spl0_906,
inference(avatar_split_clause,[],[f959,f11716]) ).
fof(f11716,plain,
( spl0_906
<=> ! [X15,X4,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X15,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X0),X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f959,axiom,
! [X0,X1,X4,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X1,X15,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X0),X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).
fof(f11714,plain,
spl0_905,
inference(avatar_split_clause,[],[f907,f11712]) ).
fof(f11712,plain,
( spl0_905
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f907,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
fof(f11710,plain,
spl0_904,
inference(avatar_split_clause,[],[f906,f11708]) ).
fof(f11708,plain,
( spl0_904
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f906,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
fof(f11706,plain,
spl0_903,
inference(avatar_split_clause,[],[f905,f11704]) ).
fof(f11704,plain,
( spl0_903
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X2,X0)
| c_Divides_Odiv__class_Omod(X1,X8,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f905,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X8,X2,X0)
| c_Divides_Odiv__class_Omod(X1,X8,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).
fof(f11702,plain,
spl0_902,
inference(avatar_split_clause,[],[f896,f11700]) ).
fof(f11700,plain,
( spl0_902
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f896,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq4_0) ).
fof(f11698,plain,
spl0_901,
inference(avatar_split_clause,[],[f876,f11696]) ).
fof(f11696,plain,
( spl0_901
<=> ! [X4,X0,X2,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_RealVector_OscaleR__class_OscaleR(X1,X4,X0) != c_RealVector_OscaleR__class_OscaleR(X2,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f876,axiom,
! [X2,X0,X1,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_RealVector_OscaleR__class_OscaleR(X1,X4,X0) != c_RealVector_OscaleR__class_OscaleR(X2,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__right_0) ).
fof(f11694,plain,
spl0_900,
inference(avatar_split_clause,[],[f740,f11692]) ).
fof(f11692,plain,
( spl0_900
<=> ! [X0,X1,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X30,X0) = c_HOL_Oplus__class_Oplus(X30,c_HOL_Otimes__class_Otimes(X1,X30,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f740,axiom,
! [X0,X1,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X30,X0) = c_HOL_Oplus__class_Oplus(X30,c_HOL_Otimes__class_Otimes(X1,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(f11690,plain,
spl0_899,
inference(avatar_split_clause,[],[f739,f11688]) ).
fof(f11688,plain,
( spl0_899
<=> ! [X0,X1,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X30,X0),X30,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X30,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f739,axiom,
! [X0,X1,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X30,X0),X30,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(f11686,plain,
spl0_898,
inference(avatar_split_clause,[],[f687,f11684]) ).
fof(f11684,plain,
( spl0_898
<=> ! [X15,X4,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X15,X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X0),X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f687,axiom,
! [X0,X1,X4,X15] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X15,X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X1,X0),X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).
fof(f11682,plain,
spl0_897,
inference(avatar_split_clause,[],[f608,f11680]) ).
fof(f11680,plain,
( spl0_897
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f608,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
fof(f11659,plain,
spl0_896,
inference(avatar_split_clause,[],[f537,f11657]) ).
fof(f11657,plain,
( spl0_896
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f537,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
fof(f11655,plain,
spl0_895,
inference(avatar_split_clause,[],[f536,f11653]) ).
fof(f11653,plain,
( spl0_895
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f536,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
fof(f11651,plain,
spl0_894,
inference(avatar_split_clause,[],[f501,f11649]) ).
fof(f11649,plain,
( spl0_894
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f501,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).
fof(f11647,plain,
spl0_893,
inference(avatar_split_clause,[],[f447,f11645]) ).
fof(f11645,plain,
( spl0_893
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Olordered__ring(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f447,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Olordered__ring(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).
fof(f11643,plain,
spl0_892,
inference(avatar_split_clause,[],[f420,f11641]) ).
fof(f11641,plain,
( spl0_892
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f420,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).
fof(f11639,plain,
spl0_891,
inference(avatar_split_clause,[],[f419,f11637]) ).
fof(f11637,plain,
( spl0_891
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f419,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
fof(f11635,plain,
spl0_890,
inference(avatar_split_clause,[],[f416,f11633]) ).
fof(f11633,plain,
( spl0_890
<=> ! [X4,X0,X10] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X4,X10,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X4,X0),c_RealVector_Onorm__class_Onorm(X10,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f416,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X4,X10,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X4,X0),c_RealVector_Onorm__class_Onorm(X10,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult__ineq_0) ).
fof(f11631,plain,
spl0_889,
inference(avatar_split_clause,[],[f343,f11629]) ).
fof(f11629,plain,
( spl0_889
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f343,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__iff_2) ).
fof(f11627,plain,
spl0_888,
inference(avatar_split_clause,[],[f246,f11625]) ).
fof(f11625,plain,
( spl0_888
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f246,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
fof(f11623,plain,
spl0_887,
inference(avatar_split_clause,[],[f245,f11621]) ).
fof(f11621,plain,
( spl0_887
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f245,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).
fof(f11604,plain,
spl0_886,
inference(avatar_split_clause,[],[f242,f11602]) ).
fof(f11602,plain,
( spl0_886
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X8,c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f242,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X8,c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).
fof(f11600,plain,
spl0_885,
inference(avatar_split_clause,[],[f234,f11598]) ).
fof(f11598,plain,
( spl0_885
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f234,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
fof(f11596,plain,
spl0_884,
inference(avatar_split_clause,[],[f115,f11594]) ).
fof(f11594,plain,
( spl0_884
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f115,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).
fof(f11592,plain,
spl0_883,
inference(avatar_split_clause,[],[f80,f11590]) ).
fof(f11590,plain,
( spl0_883
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f80,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
fof(f11588,plain,
spl0_882,
inference(avatar_split_clause,[],[f56,f11586]) ).
fof(f11586,plain,
( spl0_882
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f56,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f11584,plain,
spl0_881,
inference(avatar_split_clause,[],[f52,f11582]) ).
fof(f11582,plain,
( spl0_881
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f52,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).
fof(f11537,plain,
( spl0_880
| ~ spl0_140
| ~ spl0_242
| ~ spl0_380
| ~ spl0_459
| ~ spl0_710 ),
inference(avatar_split_clause,[],[f11037,f9145,f4438,f3563,f2596,f2042,f11534]) ).
fof(f2042,plain,
( spl0_140
<=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f2596,plain,
( spl0_242
<=> v_x = c_Log_Opowr(v_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f3563,plain,
( spl0_380
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f11037,plain,
( v_x = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_140
| ~ spl0_242
| ~ spl0_380
| ~ spl0_459
| ~ spl0_710 ),
inference(forward_demodulation,[],[f11036,f2598]) ).
fof(f2598,plain,
( v_x = c_Log_Opowr(v_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f2596]) ).
fof(f11036,plain,
( c_Log_Opowr(v_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_140
| ~ spl0_380
| ~ spl0_459
| ~ spl0_710 ),
inference(forward_demodulation,[],[f11031,f3794]) ).
fof(f3794,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_140
| ~ spl0_380 ),
inference(resolution,[],[f3564,f2044]) ).
fof(f2044,plain,
( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f2042]) ).
fof(f3564,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 )
| ~ spl0_380 ),
inference(avatar_component_clause,[],[f3563]) ).
fof(f11031,plain,
( c_Log_Opowr(v_x,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_459
| ~ spl0_710 ),
inference(superposition,[],[f4439,f9147]) ).
fof(f11518,plain,
( ~ spl0_879
| ~ spl0_540
| ~ spl0_710 ),
inference(avatar_split_clause,[],[f11035,f9145,f5097,f11515]) ).
fof(f11515,plain,
( spl0_879
<=> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f5097,plain,
( spl0_540
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Log_Opowr(X0,X1),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f11035,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_540
| ~ spl0_710 ),
inference(superposition,[],[f5098,f9147]) ).
fof(f5098,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Log_Opowr(X0,X1),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_540 ),
inference(avatar_component_clause,[],[f5097]) ).
fof(f11496,plain,
( ~ spl0_878
| ~ spl0_519
| ~ spl0_710 ),
inference(avatar_split_clause,[],[f11034,f9145,f5002,f11493]) ).
fof(f11493,plain,
( spl0_878
<=> c_lessequals(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f5002,plain,
( spl0_519
<=> ! [X0,X1] : ~ c_lessequals(c_Log_Opowr(X0,X1),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f11034,plain,
( ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_519
| ~ spl0_710 ),
inference(superposition,[],[f5003,f9147]) ).
fof(f5003,plain,
( ! [X0,X1] : ~ c_lessequals(c_Log_Opowr(X0,X1),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_519 ),
inference(avatar_component_clause,[],[f5002]) ).
fof(f11471,plain,
( spl0_877
| ~ spl0_41
| ~ spl0_710 ),
inference(avatar_split_clause,[],[f11021,f9145,f1544,f11468]) ).
fof(f11468,plain,
( spl0_877
<=> c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f11021,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_41
| ~ spl0_710 ),
inference(superposition,[],[f1545,f9147]) ).
fof(f11312,plain,
( spl0_876
| ~ spl0_40
| ~ spl0_710 ),
inference(avatar_split_clause,[],[f11020,f9145,f1540,f11309]) ).
fof(f11309,plain,
( spl0_876
<=> c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f11020,plain,
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_40
| ~ spl0_710 ),
inference(superposition,[],[f1541,f9147]) ).
fof(f11146,plain,
( ~ spl0_875
| ~ spl0_23
| ~ spl0_710 ),
inference(avatar_split_clause,[],[f11019,f9145,f1455,f11143]) ).
fof(f11143,plain,
( spl0_875
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f1455,plain,
( spl0_23
<=> ! [X4,X1] : c_Log_Opowr(X4,X1) != c_Transcendental_Otan(c_Transcendental_Opi) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f11019,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) != c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal)
| ~ spl0_23
| ~ spl0_710 ),
inference(superposition,[],[f1456,f9147]) ).
fof(f1456,plain,
( ! [X1,X4] : c_Log_Opowr(X4,X1) != c_Transcendental_Otan(c_Transcendental_Opi)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f1455]) ).
fof(f11043,plain,
spl0_874,
inference(avatar_split_clause,[],[f1206,f11041]) ).
fof(f11041,plain,
( spl0_874
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f1206,plain,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
inference(duplicate_literal_removal,[],[f486]) ).
fof(f486,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f11018,plain,
spl0_873,
inference(avatar_split_clause,[],[f1016,f11016]) ).
fof(f11016,plain,
( spl0_873
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f1016,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
fof(f11014,plain,
spl0_872,
inference(avatar_split_clause,[],[f1014,f11012]) ).
fof(f11012,plain,
( spl0_872
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f1014,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
fof(f11010,plain,
spl0_871,
inference(avatar_split_clause,[],[f983,f11008]) ).
fof(f11008,plain,
( spl0_871
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f983,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
fof(f11006,plain,
spl0_870,
inference(avatar_split_clause,[],[f982,f11004]) ).
fof(f11004,plain,
( spl0_870
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f982,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).
fof(f11002,plain,
spl0_869,
inference(avatar_split_clause,[],[f969,f11000]) ).
fof(f11000,plain,
( spl0_869
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Osgn__class_Osgn(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f969,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Osgn__class_Osgn(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__times_0) ).
fof(f10998,plain,
spl0_868,
inference(avatar_split_clause,[],[f968,f10996]) ).
fof(f10996,plain,
( spl0_868
<=> ! [X4,X0,X10] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X4,X10,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X4,X0),c_HOL_Osgn__class_Osgn(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f968,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X4,X10,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X4,X0),c_HOL_Osgn__class_Osgn(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__mult_0) ).
fof(f10994,plain,
spl0_867,
inference(avatar_split_clause,[],[f962,f10992]) ).
fof(f10992,plain,
( spl0_867
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f962,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).
fof(f10990,plain,
spl0_866,
inference(avatar_split_clause,[],[f952,f10988]) ).
fof(f10988,plain,
( spl0_866
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X0),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X0),X2,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f952,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X0),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X0),X2,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).
fof(f10986,plain,
spl0_865,
inference(avatar_split_clause,[],[f913,f10984]) ).
fof(f10984,plain,
( spl0_865
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f913,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
fof(f10982,plain,
spl0_864,
inference(avatar_split_clause,[],[f897,f10980]) ).
fof(f10980,plain,
( spl0_864
<=> ! [X4,X0,X15] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Osgn__class_Osgn(c_RealVector_OscaleR__class_OscaleR(X15,X4,X0),X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Osgn__class_Osgn(X15,tc_RealDef_Oreal),c_HOL_Osgn__class_Osgn(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f897,axiom,
! [X0,X4,X15] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Osgn__class_Osgn(c_RealVector_OscaleR__class_OscaleR(X15,X4,X0),X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Osgn__class_Osgn(X15,tc_RealDef_Oreal),c_HOL_Osgn__class_Osgn(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__scaleR_0) ).
fof(f10959,plain,
spl0_863,
inference(avatar_split_clause,[],[f843,f10957]) ).
fof(f10957,plain,
( spl0_863
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X8,X2,X0),X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f843,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X8,X2,X0),X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
fof(f10955,plain,
spl0_862,
inference(avatar_split_clause,[],[f842,f10953]) ).
fof(f10953,plain,
( spl0_862
<=> ! [X0,X8,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f842,axiom,
! [X2,X0,X1,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
fof(f10951,plain,
spl0_861,
inference(avatar_split_clause,[],[f803,f10949]) ).
fof(f10949,plain,
( spl0_861
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f803,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).
fof(f10947,plain,
spl0_860,
inference(avatar_split_clause,[],[f800,f10945]) ).
fof(f10945,plain,
( spl0_860
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f800,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).
fof(f10943,plain,
spl0_859,
inference(avatar_split_clause,[],[f737,f10941]) ).
fof(f10941,plain,
( spl0_859
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X9,X0),X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f737,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X9,X0),X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).
fof(f10939,plain,
spl0_858,
inference(avatar_split_clause,[],[f735,f10937]) ).
fof(f10937,plain,
( spl0_858
<=> ! [X2,X0,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X8,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f735,axiom,
! [X2,X0,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X8,X0),X8,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
fof(f10935,plain,
spl0_857,
inference(avatar_split_clause,[],[f728,f10933]) ).
fof(f10933,plain,
( spl0_857
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f728,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
fof(f10931,plain,
spl0_856,
inference(avatar_split_clause,[],[f696,f10929]) ).
fof(f10929,plain,
( spl0_856
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X9,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f696,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X9,X0),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X9,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).
fof(f10927,plain,
spl0_855,
inference(avatar_split_clause,[],[f693,f10925]) ).
fof(f10925,plain,
( spl0_855
<=> ! [X4,X0,X10] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X4,X10,X0),X0) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X4,X0),c_RealVector_Onorm__class_Onorm(X10,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f693,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X4,X10,X0),X0) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X4,X0),c_RealVector_Onorm__class_Onorm(X10,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult_0) ).
fof(f10923,plain,
spl0_854,
inference(avatar_split_clause,[],[f652,f10921]) ).
fof(f10921,plain,
( spl0_854
<=> ! [X4,X0,X2,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_RealVector_OscaleR__class_OscaleR(X2,X4,X0),X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f652,axiom,
! [X2,X0,X1,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_RealVector_OscaleR__class_OscaleR(X2,X4,X0),X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__vector_Oscale__scale_0) ).
fof(f10919,plain,
( spl0_853
| ~ spl0_330
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f9809,f9100,f3195,f10916]) ).
fof(f10916,plain,
( spl0_853
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f9809,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_330
| ~ spl0_699 ),
inference(superposition,[],[f3196,f9102]) ).
fof(f10914,plain,
spl0_852,
inference(avatar_split_clause,[],[f649,f10912]) ).
fof(f10912,plain,
( spl0_852
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f649,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
fof(f10910,plain,
spl0_851,
inference(avatar_split_clause,[],[f648,f10908]) ).
fof(f10908,plain,
( spl0_851
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X10,X14,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f648,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X10,X14,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
fof(f10906,plain,
spl0_850,
inference(avatar_split_clause,[],[f647,f10904]) ).
fof(f10904,plain,
( spl0_850
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X10,X14,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f647,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X10,X14,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
fof(f10902,plain,
spl0_849,
inference(avatar_split_clause,[],[f646,f10900]) ).
fof(f10900,plain,
( spl0_849
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X10,X14,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f646,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X10,X14,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
fof(f10898,plain,
spl0_848,
inference(avatar_split_clause,[],[f645,f10896]) ).
fof(f10896,plain,
( spl0_848
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X10,X14,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f645,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X10,X14,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X10,c_Lattices_Oupper__semilattice__class_Osup(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
fof(f10894,plain,
spl0_847,
inference(avatar_split_clause,[],[f605,f10892]) ).
fof(f10892,plain,
( spl0_847
<=> ! [X0,X8,X3,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X8,X3,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f605,axiom,
! [X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X8,X3,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f10890,plain,
spl0_846,
inference(avatar_split_clause,[],[f604,f10888]) ).
fof(f10888,plain,
( spl0_846
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f604,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f10886,plain,
spl0_845,
inference(avatar_split_clause,[],[f602,f10884]) ).
fof(f10884,plain,
( spl0_845
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f602,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f10882,plain,
spl0_844,
inference(avatar_split_clause,[],[f601,f10880]) ).
fof(f10880,plain,
( spl0_844
<=> ! [X4,X0,X14,X10] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X10,X14,X0),X0) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f601,axiom,
! [X10,X0,X14,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X10,X14,X0),X0) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f10878,plain,
spl0_843,
inference(avatar_split_clause,[],[f600,f10876]) ).
fof(f10876,plain,
( spl0_843
<=> ! [X4,X0,X14,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X10,X14,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X10,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f600,axiom,
! [X10,X0,X14,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X10,X14,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X10,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
fof(f10836,plain,
spl0_842,
inference(avatar_split_clause,[],[f599,f10834]) ).
fof(f10834,plain,
( spl0_842
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f599,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f10832,plain,
spl0_841,
inference(avatar_split_clause,[],[f598,f10830]) ).
fof(f10830,plain,
( spl0_841
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f598,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f10828,plain,
spl0_840,
inference(avatar_split_clause,[],[f573,f10826]) ).
fof(f10826,plain,
( spl0_840
<=> ! [X2,X4,X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_RealVector_OscaleR__class_OscaleR(X2,X4,X0),X0) = c_RealVector_OscaleR__class_OscaleR(X2,c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f573,axiom,
! [X2,X0,X1,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_RealVector_OscaleR__class_OscaleR(X2,X4,X0),X0) = c_RealVector_OscaleR__class_OscaleR(X2,c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__left__commute_0) ).
fof(f10824,plain,
spl0_839,
inference(avatar_split_clause,[],[f572,f10822]) ).
fof(f10822,plain,
( spl0_839
<=> ! [X15,X0,X2,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_RealVector_OscaleR__class_OscaleR(X15,X2,X0),X0) = c_RealVector_OscaleR__class_OscaleR(X15,c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f572,axiom,
! [X2,X0,X1,X15] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_RealVector_OscaleR__class_OscaleR(X15,X2,X0),X0) = c_RealVector_OscaleR__class_OscaleR(X15,c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_OscaleR__right_0) ).
fof(f10820,plain,
spl0_838,
inference(avatar_split_clause,[],[f533,f10818]) ).
fof(f10818,plain,
( spl0_838
<=> ! [X2,X1,X4] :
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_Log_Opowr(X4,X1),c_Log_Opowr(X4,X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f533,axiom,
! [X2,X1,X4] :
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_Log_Opowr(X4,X1),c_Log_Opowr(X4,X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__le__cancel__iff_0) ).
fof(f10816,plain,
spl0_837,
inference(avatar_split_clause,[],[f532,f10814]) ).
fof(f10814,plain,
( spl0_837
<=> ! [X2,X1,X4] :
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_Log_Opowr(X4,X1),c_Log_Opowr(X4,X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f532,axiom,
! [X2,X1,X4] :
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_Log_Opowr(X4,X1),c_Log_Opowr(X4,X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__le__cancel__iff_1) ).
fof(f10812,plain,
spl0_836,
inference(avatar_split_clause,[],[f526,f10810]) ).
fof(f10810,plain,
( spl0_836
<=> ! [X2,X1,X4] :
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Log_Opowr(X4,X1),c_Log_Opowr(X4,X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f526,axiom,
! [X2,X1,X4] :
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Log_Opowr(X4,X1),c_Log_Opowr(X4,X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__less__cancel_0) ).
fof(f10808,plain,
spl0_835,
inference(avatar_split_clause,[],[f524,f10806]) ).
fof(f10806,plain,
( spl0_835
<=> ! [X2,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X4,X1),c_Log_Opowr(X4,X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f524,axiom,
! [X2,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X4,X1),c_Log_Opowr(X4,X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__less__cancel__iff_1) ).
fof(f10804,plain,
spl0_834,
inference(avatar_split_clause,[],[f522,f10802]) ).
fof(f10802,plain,
( spl0_834
<=> ! [X4,X0,X10,X15] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X15,X4,X0),X10,X0) = c_RealVector_OscaleR__class_OscaleR(X15,c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f522,axiom,
! [X10,X0,X4,X15] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X15,X4,X0),X10,X0) = c_RealVector_OscaleR__class_OscaleR(X15,c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_OscaleR_0) ).
fof(f10800,plain,
spl0_833,
inference(avatar_split_clause,[],[f498,f10798]) ).
fof(f10798,plain,
( spl0_833
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f498,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__inverse_0) ).
fof(f10790,plain,
spl0_832,
inference(avatar_split_clause,[],[f497,f10788]) ).
fof(f10788,plain,
( spl0_832
<=> ! [X4,X0,X10,X1] :
( ~ class_RealVector_Oreal__algebra(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Otimes__class_Otimes(X4,X10,X0),X0) = c_HOL_Otimes__class_Otimes(X4,c_RealVector_OscaleR__class_OscaleR(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f497,axiom,
! [X10,X0,X1,X4] :
( ~ class_RealVector_Oreal__algebra(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Otimes__class_Otimes(X4,X10,X0),X0) = c_HOL_Otimes__class_Otimes(X4,c_RealVector_OscaleR__class_OscaleR(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__scaleR__right_0) ).
fof(f10786,plain,
spl0_831,
inference(avatar_split_clause,[],[f496,f10784]) ).
fof(f10784,plain,
( spl0_831
<=> ! [X4,X0,X10,X1] :
( ~ class_RealVector_Oreal__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X10,X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Otimes__class_Otimes(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f496,axiom,
! [X10,X0,X1,X4] :
( ~ class_RealVector_Oreal__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X10,X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Otimes__class_Otimes(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__scaleR__left_0) ).
fof(f10782,plain,
spl0_830,
inference(avatar_split_clause,[],[f494,f10780]) ).
fof(f10780,plain,
( spl0_830
<=> ! [X15,X0,X2,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_RealVector_OscaleR__class_OscaleR(X15,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_RealVector_OscaleR__class_OscaleR(X15,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f494,axiom,
! [X2,X0,X1,X15] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_RealVector_OscaleR__class_OscaleR(X15,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_RealVector_OscaleR__class_OscaleR(X15,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_OscaleR__right_0) ).
fof(f10778,plain,
spl0_829,
inference(avatar_split_clause,[],[f492,f10776]) ).
fof(f10776,plain,
( spl0_829
<=> ! [X15,X0,X2,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X15,X1,X0),X2,X0) = c_RealVector_OscaleR__class_OscaleR(X15,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f492,axiom,
! [X2,X0,X1,X15] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X15,X1,X0),X2,X0) = c_RealVector_OscaleR__class_OscaleR(X15,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_OscaleR__left_0) ).
fof(f10774,plain,
spl0_828,
inference(avatar_split_clause,[],[f433,f10772]) ).
fof(f10772,plain,
( spl0_828
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f433,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__inf__sup_0) ).
fof(f10770,plain,
spl0_827,
inference(avatar_split_clause,[],[f424,f10768]) ).
fof(f10768,plain,
( spl0_827
<=> ! [X9,X0,X6,X30] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X6,X30,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,c_Divides_Odiv__class_Omod(X30,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f424,axiom,
! [X0,X6,X9,X30] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X6,X30,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,c_Divides_Odiv__class_Omod(X30,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).
fof(f10766,plain,
spl0_826,
inference(avatar_split_clause,[],[f423,f10764]) ).
fof(f10764,plain,
( spl0_826
<=> ! [X9,X0,X6,X30] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X30,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X6,c_Divides_Odiv__class_Omod(X30,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f423,axiom,
! [X0,X6,X9,X30] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X30,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X6,c_Divides_Odiv__class_Omod(X30,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).
fof(f10762,plain,
spl0_825,
inference(avatar_split_clause,[],[f397,f10760]) ).
fof(f10760,plain,
( spl0_825
<=> ! [X4,X0,X14,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X10,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X14,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ominus__class_Ominus(X10,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f397,axiom,
! [X10,X0,X14,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X10,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X14,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ominus__class_Ominus(X10,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
fof(f10758,plain,
spl0_824,
inference(avatar_split_clause,[],[f371,f10756]) ).
fof(f10756,plain,
( spl0_824
<=> ! [X2,X4,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X4,X0)
| ~ c_lessequals(X2,X4,X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f371,axiom,
! [X2,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X1,X4,X0)
| ~ c_lessequals(X2,X4,X0)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
fof(f10754,plain,
spl0_823,
inference(avatar_split_clause,[],[f367,f10752]) ).
fof(f10752,plain,
( spl0_823
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f367,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__norm__inverse_0) ).
fof(f10746,plain,
spl0_822,
inference(avatar_split_clause,[],[f340,f10744]) ).
fof(f10744,plain,
( spl0_822
<=> ! [X2,X1,X4] :
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_Log_Opowr(X4,X1),c_Log_Opowr(X4,X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f340,axiom,
! [X2,X1,X4] :
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_Log_Opowr(X4,X1),c_Log_Opowr(X4,X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__mono_0) ).
fof(f10742,plain,
spl0_821,
inference(avatar_split_clause,[],[f300,f10740]) ).
fof(f10740,plain,
( spl0_821
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f300,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__add_0) ).
fof(f10738,plain,
spl0_820,
inference(avatar_split_clause,[],[f290,f10736]) ).
fof(f10736,plain,
( spl0_820
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f290,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).
fof(f10734,plain,
spl0_819,
inference(avatar_split_clause,[],[f277,f10732]) ).
fof(f10732,plain,
( spl0_819
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f277,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
fof(f10730,plain,
spl0_818,
inference(avatar_split_clause,[],[f276,f10728]) ).
fof(f10728,plain,
( spl0_818
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f276,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
fof(f10726,plain,
spl0_817,
inference(avatar_split_clause,[],[f275,f10724]) ).
fof(f10724,plain,
( spl0_817
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f275,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
fof(f10722,plain,
spl0_816,
inference(avatar_split_clause,[],[f274,f10720]) ).
fof(f10720,plain,
( spl0_816
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f274,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X10,c_Lattices_Olower__semilattice__class_Oinf(X4,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
fof(f10718,plain,
spl0_815,
inference(avatar_split_clause,[],[f272,f10716]) ).
fof(f10716,plain,
( spl0_815
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Osgn__class_Osgn(X4,X0) = c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f272,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Osgn__class_Osgn(X4,X0) = c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__if_1) ).
fof(f10714,plain,
spl0_814,
inference(avatar_split_clause,[],[f208,f10712]) ).
fof(f10712,plain,
( spl0_814
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f208,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult_0) ).
fof(f10710,plain,
spl0_813,
inference(avatar_split_clause,[],[f190,f10708]) ).
fof(f10708,plain,
( spl0_813
<=> ! [X4] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X4
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X4
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f190,axiom,
! [X4] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X4
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X4
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__is__one_0) ).
fof(f10687,plain,
spl0_812,
inference(avatar_split_clause,[],[f139,f10685]) ).
fof(f10685,plain,
( spl0_812
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f139,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
fof(f10683,plain,
spl0_811,
inference(avatar_split_clause,[],[f124,f10681]) ).
fof(f10681,plain,
( spl0_811
<=> ! [X4,X0,X14,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(X10,X14,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X4,X10,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f124,axiom,
! [X10,X0,X14,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(X10,X14,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X4,X10,X0),X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
fof(f10679,plain,
spl0_810,
inference(avatar_split_clause,[],[f122,f10677]) ).
fof(f10677,plain,
( spl0_810
<=> ! [X18,X20,X0,X21] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X18,c_HOL_Otimes__class_Otimes(X20,X21,X0),X0) = c_HOL_Otimes__class_Otimes(X20,c_HOL_Otimes__class_Otimes(X18,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f122,axiom,
! [X21,X0,X18,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X18,c_HOL_Otimes__class_Otimes(X20,X21,X0),X0) = c_HOL_Otimes__class_Otimes(X20,c_HOL_Otimes__class_Otimes(X18,X21,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f10675,plain,
spl0_809,
inference(avatar_split_clause,[],[f119,f10673]) ).
fof(f10673,plain,
( spl0_809
<=> ! [X18,X20,X0,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X19,X0),X20,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X20,X0),X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f119,axiom,
! [X0,X18,X19,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X19,X0),X20,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X18,X20,X0),X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f10671,plain,
spl0_808,
inference(avatar_split_clause,[],[f118,f10669]) ).
fof(f10669,plain,
( spl0_808
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f118,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f10667,plain,
spl0_807,
inference(avatar_split_clause,[],[f102,f10665]) ).
fof(f10665,plain,
( spl0_807
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X9,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f102,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X9,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inverse_0) ).
fof(f10663,plain,
spl0_806,
inference(avatar_split_clause,[],[f90,f10661]) ).
fof(f10661,plain,
( spl0_806
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f90,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__equality2_0) ).
fof(f10659,plain,
spl0_805,
inference(avatar_split_clause,[],[f83,f10657]) ).
fof(f10657,plain,
( spl0_805
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X4,X10,X0)
| ~ c_lessequals(X4,X14,X0)
| c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f83,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X4,X10,X0)
| ~ c_lessequals(X4,X14,X0)
| c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
fof(f10655,plain,
spl0_804,
inference(avatar_split_clause,[],[f81,f10653]) ).
fof(f10653,plain,
( spl0_804
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f81,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
fof(f10651,plain,
spl0_803,
inference(avatar_split_clause,[],[f44,f10649]) ).
fof(f10649,plain,
( spl0_803
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f44,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__if_1) ).
fof(f10632,plain,
spl0_802,
inference(avatar_split_clause,[],[f13,f10630]) ).
fof(f10630,plain,
( spl0_802
<=> ! [X4,X0,X10] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),X0) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X4,X0),c_RealVector_Oof__real(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f13,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),X0) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X4,X0),c_RealVector_Oof__real(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__mult_0) ).
fof(f10628,plain,
spl0_801,
inference(avatar_split_clause,[],[f1,f10626]) ).
fof(f10626,plain,
( spl0_801
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X0),X2,X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X0),X2,X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__equality_0) ).
fof(f10512,plain,
( spl0_800
| ~ spl0_140
| ~ spl0_237
| ~ spl0_380
| ~ spl0_459
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f9817,f9100,f4438,f3563,f2552,f2042,f10509]) ).
fof(f2552,plain,
( spl0_237
<=> c_Transcendental_Opi = c_Log_Opowr(c_Transcendental_Opi,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f9817,plain,
( c_Transcendental_Opi = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_140
| ~ spl0_237
| ~ spl0_380
| ~ spl0_459
| ~ spl0_699 ),
inference(forward_demodulation,[],[f9816,f2554]) ).
fof(f2554,plain,
( c_Transcendental_Opi = c_Log_Opowr(c_Transcendental_Opi,c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_237 ),
inference(avatar_component_clause,[],[f2552]) ).
fof(f9816,plain,
( c_Log_Opowr(c_Transcendental_Opi,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_140
| ~ spl0_380
| ~ spl0_459
| ~ spl0_699 ),
inference(forward_demodulation,[],[f9811,f3794]) ).
fof(f9811,plain,
( c_Log_Opowr(c_Transcendental_Opi,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_459
| ~ spl0_699 ),
inference(superposition,[],[f4439,f9102]) ).
fof(f10364,plain,
( ~ spl0_799
| ~ spl0_540
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f9815,f9100,f5097,f10361]) ).
fof(f10361,plain,
( spl0_799
<=> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f9815,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_540
| ~ spl0_699 ),
inference(superposition,[],[f5098,f9102]) ).
fof(f10148,plain,
( ~ spl0_798
| ~ spl0_519
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f9814,f9100,f5002,f10145]) ).
fof(f10145,plain,
( spl0_798
<=> c_lessequals(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f9814,plain,
( ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_519
| ~ spl0_699 ),
inference(superposition,[],[f5003,f9102]) ).
fof(f10016,plain,
( spl0_797
| ~ spl0_41
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f9801,f9100,f1544,f10013]) ).
fof(f10013,plain,
( spl0_797
<=> c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f9801,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_41
| ~ spl0_699 ),
inference(superposition,[],[f1545,f9102]) ).
fof(f10011,plain,
spl0_796,
inference(avatar_split_clause,[],[f946,f10009]) ).
fof(f10009,plain,
( spl0_796
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f946,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).
fof(f10007,plain,
spl0_795,
inference(avatar_split_clause,[],[f933,f10005]) ).
fof(f10005,plain,
( spl0_795
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f933,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f10003,plain,
spl0_794,
inference(avatar_split_clause,[],[f932,f10001]) ).
fof(f10001,plain,
( spl0_794
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f932,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f9999,plain,
spl0_793,
inference(avatar_split_clause,[],[f931,f9997]) ).
fof(f9997,plain,
( spl0_793
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f931,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f9995,plain,
spl0_792,
inference(avatar_split_clause,[],[f930,f9993]) ).
fof(f9993,plain,
( spl0_792
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f930,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f9991,plain,
spl0_791,
inference(avatar_split_clause,[],[f929,f9989]) ).
fof(f9989,plain,
( spl0_791
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f929,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f9987,plain,
spl0_790,
inference(avatar_split_clause,[],[f928,f9985]) ).
fof(f9985,plain,
( spl0_790
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f928,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f9983,plain,
spl0_789,
inference(avatar_split_clause,[],[f810,f9981]) ).
fof(f9981,plain,
( spl0_789
<=> ! [X4,X0,X14,X10] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X14,X0) = X4
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X10,X14,X0),X0) != X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f810,axiom,
! [X10,X0,X14,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X14,X0) = X4
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X10,X14,X0),X0) != X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
fof(f9979,plain,
spl0_788,
inference(avatar_split_clause,[],[f793,f9977]) ).
fof(f9977,plain,
( spl0_788
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f793,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).
fof(f9975,plain,
spl0_787,
inference(avatar_split_clause,[],[f759,f9973]) ).
fof(f9973,plain,
( spl0_787
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f759,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).
fof(f9971,plain,
( spl0_786
| ~ spl0_40
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f9800,f9100,f1540,f9968]) ).
fof(f9968,plain,
( spl0_786
<=> c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f9800,plain,
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_40
| ~ spl0_699 ),
inference(superposition,[],[f1541,f9102]) ).
fof(f9966,plain,
spl0_785,
inference(avatar_split_clause,[],[f746,f9964]) ).
fof(f9964,plain,
( spl0_785
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f746,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_1) ).
fof(f9962,plain,
spl0_784,
inference(avatar_split_clause,[],[f709,f9960]) ).
fof(f9960,plain,
( spl0_784
<=> ! [X0,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X30,X30,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X30,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f709,axiom,
! [X0,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X30,X30,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(f9958,plain,
spl0_783,
inference(avatar_split_clause,[],[f708,f9956]) ).
fof(f9956,plain,
( spl0_783
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X4,X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f708,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X4,X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_2) ).
fof(f9954,plain,
spl0_782,
inference(avatar_split_clause,[],[f686,f9952]) ).
fof(f9952,plain,
( spl0_782
<=> ! [X4,X0,X9,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X10,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X4,X9,X0),c_Power_Opower__class_Opower(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f686,axiom,
! [X10,X0,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X10,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X4,X9,X0),c_Power_Opower__class_Opower(X10,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
fof(f9950,plain,
spl0_781,
inference(avatar_split_clause,[],[f677,f9948]) ).
fof(f9948,plain,
( spl0_781
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f677,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).
fof(f9946,plain,
spl0_780,
inference(avatar_split_clause,[],[f676,f9944]) ).
fof(f9944,plain,
( spl0_780
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f676,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_1) ).
fof(f9942,plain,
spl0_779,
inference(avatar_split_clause,[],[f658,f9940]) ).
fof(f9940,plain,
( spl0_779
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f658,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_0) ).
fof(f9938,plain,
spl0_778,
inference(avatar_split_clause,[],[f560,f9936]) ).
fof(f9936,plain,
( spl0_778
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f560,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
fof(f9934,plain,
spl0_777,
inference(avatar_split_clause,[],[f559,f9932]) ).
fof(f9932,plain,
( spl0_777
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f559,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
fof(f9930,plain,
spl0_776,
inference(avatar_split_clause,[],[f529,f9928]) ).
fof(f9928,plain,
( spl0_776
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f529,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).
fof(f9926,plain,
spl0_775,
inference(avatar_split_clause,[],[f528,f9924]) ).
fof(f9924,plain,
( spl0_775
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f528,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).
fof(f9922,plain,
spl0_774,
inference(avatar_split_clause,[],[f417,f9920]) ).
fof(f9920,plain,
( spl0_774
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f417,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
fof(f9918,plain,
spl0_773,
inference(avatar_split_clause,[],[f415,f9916]) ).
fof(f9916,plain,
( spl0_773
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f415,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_1) ).
fof(f9914,plain,
spl0_772,
inference(avatar_split_clause,[],[f400,f9912]) ).
fof(f9912,plain,
( spl0_772
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f400,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).
fof(f9910,plain,
spl0_771,
inference(avatar_split_clause,[],[f345,f9908]) ).
fof(f9908,plain,
( spl0_771
<=> ! [X4,X0,X14,X10] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X10 = X14
| c_HOL_Oplus__class_Oplus(X4,X10,X0) != c_HOL_Oplus__class_Oplus(X4,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f345,axiom,
! [X10,X0,X14,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X10 = X14
| c_HOL_Oplus__class_Oplus(X4,X10,X0) != c_HOL_Oplus__class_Oplus(X4,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f9906,plain,
spl0_770,
inference(avatar_split_clause,[],[f299,f9904]) ).
fof(f9904,plain,
( spl0_770
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f299,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).
fof(f9902,plain,
spl0_769,
inference(avatar_split_clause,[],[f271,f9900]) ).
fof(f9900,plain,
( spl0_769
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f271,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X10,X10,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
fof(f9898,plain,
spl0_768,
inference(avatar_split_clause,[],[f252,f9896]) ).
fof(f9896,plain,
( spl0_768
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f252,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_1) ).
fof(f9894,plain,
spl0_767,
inference(avatar_split_clause,[],[f214,f9892]) ).
fof(f9892,plain,
( spl0_767
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f214,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f9890,plain,
spl0_766,
inference(avatar_split_clause,[],[f213,f9888]) ).
fof(f9888,plain,
( spl0_766
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f213,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f9886,plain,
( ~ spl0_765
| ~ spl0_23
| ~ spl0_699 ),
inference(avatar_split_clause,[],[f9799,f9100,f1455,f9883]) ).
fof(f9883,plain,
( spl0_765
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f9799,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) != c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_23
| ~ spl0_699 ),
inference(superposition,[],[f1456,f9102]) ).
fof(f9881,plain,
spl0_764,
inference(avatar_split_clause,[],[f212,f9879]) ).
fof(f9879,plain,
( spl0_764
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f212,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f9877,plain,
spl0_763,
inference(avatar_split_clause,[],[f211,f9875]) ).
fof(f9875,plain,
( spl0_763
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f211,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f9873,plain,
spl0_762,
inference(avatar_split_clause,[],[f210,f9871]) ).
fof(f9871,plain,
( spl0_762
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f210,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f9869,plain,
spl0_761,
inference(avatar_split_clause,[],[f209,f9867]) ).
fof(f9867,plain,
( spl0_761
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f209,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f9865,plain,
spl0_760,
inference(avatar_split_clause,[],[f198,f9863]) ).
fof(f9863,plain,
( spl0_760
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f198,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
fof(f9861,plain,
spl0_759,
inference(avatar_split_clause,[],[f197,f9859]) ).
fof(f9859,plain,
( spl0_759
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f197,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
fof(f9857,plain,
spl0_758,
inference(avatar_split_clause,[],[f194,f9855]) ).
fof(f9855,plain,
( spl0_758
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f194,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).
fof(f9853,plain,
spl0_757,
inference(avatar_split_clause,[],[f112,f9851]) ).
fof(f9851,plain,
( spl0_757
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f112,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
fof(f9566,plain,
( ~ spl0_152
| spl0_756
| ~ spl0_351
| ~ spl0_557 ),
inference(avatar_split_clause,[],[f5904,f5850,f3429,f9564,f2102]) ).
fof(f9564,plain,
( spl0_756
<=> ! [X0] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f5850,plain,
( spl0_557
<=> ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f5904,plain,
( ! [X0] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_Lattices_Olattice(tc_RealDef_Oreal) )
| ~ spl0_351
| ~ spl0_557 ),
inference(resolution,[],[f5851,f3430]) ).
fof(f5851,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_557 ),
inference(avatar_component_clause,[],[f5850]) ).
fof(f9444,plain,
( ~ spl0_152
| spl0_755
| ~ spl0_350
| ~ spl0_557 ),
inference(avatar_split_clause,[],[f5902,f5850,f3425,f9442,f2102]) ).
fof(f9442,plain,
( spl0_755
<=> ! [X0] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f5902,plain,
( ! [X0] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_Lattices_Olattice(tc_RealDef_Oreal) )
| ~ spl0_350
| ~ spl0_557 ),
inference(resolution,[],[f5851,f3426]) ).
fof(f9324,plain,
( spl0_754
| ~ spl0_205
| ~ spl0_557 ),
inference(avatar_split_clause,[],[f5899,f5850,f2377,f9322]) ).
fof(f5899,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_205
| ~ spl0_557 ),
inference(resolution,[],[f5851,f2378]) ).
fof(f9320,plain,
spl0_753,
inference(avatar_split_clause,[],[f949,f9318]) ).
fof(f9318,plain,
( spl0_753
<=> ! [X4,X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f949,axiom,
! [X0,X4] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__minus_0) ).
fof(f9316,plain,
spl0_752,
inference(avatar_split_clause,[],[f910,f9314]) ).
fof(f9314,plain,
( spl0_752
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f910,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f9312,plain,
spl0_751,
inference(avatar_split_clause,[],[f909,f9310]) ).
fof(f9310,plain,
( spl0_751
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f909,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f9308,plain,
spl0_750,
inference(avatar_split_clause,[],[f895,f9306]) ).
fof(f9306,plain,
( spl0_750
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f895,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
fof(f9304,plain,
spl0_749,
inference(avatar_split_clause,[],[f894,f9302]) ).
fof(f9302,plain,
( spl0_749
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) != c_HOL_Osgn__class_Osgn(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f894,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) != c_HOL_Osgn__class_Osgn(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__1__neg_0) ).
fof(f9300,plain,
spl0_748,
inference(avatar_split_clause,[],[f893,f9298]) ).
fof(f9298,plain,
( spl0_748
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f893,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__neg_0) ).
fof(f9296,plain,
spl0_747,
inference(avatar_split_clause,[],[f840,f9294]) ).
fof(f9294,plain,
( spl0_747
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f840,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__commute_0) ).
fof(f9292,plain,
spl0_746,
inference(avatar_split_clause,[],[f821,f9290]) ).
fof(f9290,plain,
( spl0_746
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X0),X1,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f821,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X0),X1,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).
fof(f9288,plain,
spl0_745,
inference(avatar_split_clause,[],[f820,f9286]) ).
fof(f9286,plain,
( spl0_745
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f820,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).
fof(f9284,plain,
spl0_744,
inference(avatar_split_clause,[],[f726,f9282]) ).
fof(f9282,plain,
( spl0_744
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(X1,X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f726,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(X1,X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
fof(f9280,plain,
( spl0_743
| ~ spl0_364
| ~ spl0_557 ),
inference(avatar_split_clause,[],[f5898,f5850,f3499,f9278]) ).
fof(f9278,plain,
( spl0_743
<=> ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f5898,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_364
| ~ spl0_557 ),
inference(resolution,[],[f5851,f3500]) ).
fof(f9276,plain,
spl0_742,
inference(avatar_split_clause,[],[f718,f9274]) ).
fof(f9274,plain,
( spl0_742
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f718,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
fof(f9272,plain,
spl0_741,
inference(avatar_split_clause,[],[f716,f9270]) ).
fof(f9270,plain,
( spl0_741
<=> ! [X0,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X8,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f716,axiom,
! [X0,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X8,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
fof(f9268,plain,
spl0_740,
inference(avatar_split_clause,[],[f688,f9266]) ).
fof(f9266,plain,
( spl0_740
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f688,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__inverse_0) ).
fof(f9264,plain,
spl0_739,
inference(avatar_split_clause,[],[f685,f9262]) ).
fof(f9262,plain,
( spl0_739
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X9,X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f685,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X9,X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__abs_0) ).
fof(f9260,plain,
spl0_738,
inference(avatar_split_clause,[],[f650,f9258]) ).
fof(f9258,plain,
( spl0_738
<=> ! [X4,X0,X10] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X0),X10,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f650,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X0),X10,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
fof(f9256,plain,
spl0_737,
inference(avatar_split_clause,[],[f632,f9254]) ).
fof(f9254,plain,
( spl0_737
<=> ! [X4,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f632,axiom,
! [X0,X9,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X4,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
fof(f9252,plain,
spl0_736,
inference(avatar_split_clause,[],[f561,f9250]) ).
fof(f9250,plain,
( spl0_736
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f561,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
fof(f9248,plain,
spl0_735,
inference(avatar_split_clause,[],[f548,f9246]) ).
fof(f9246,plain,
( spl0_735
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f548,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
fof(f9244,plain,
spl0_734,
inference(avatar_split_clause,[],[f547,f9242]) ).
fof(f9242,plain,
( spl0_734
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f547,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
fof(f9240,plain,
spl0_733,
inference(avatar_split_clause,[],[f535,f9238]) ).
fof(f9238,plain,
( spl0_733
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f535,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f9236,plain,
( spl0_732
| ~ spl0_47
| ~ spl0_543 ),
inference(avatar_split_clause,[],[f5756,f5109,f1577,f9234]) ).
fof(f1577,plain,
( spl0_47
<=> c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f5756,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_47
| ~ spl0_543 ),
inference(resolution,[],[f5110,f1579]) ).
fof(f1579,plain,
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1577]) ).
fof(f9232,plain,
spl0_731,
inference(avatar_split_clause,[],[f534,f9230]) ).
fof(f9230,plain,
( spl0_731
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f534,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f9228,plain,
spl0_730,
inference(avatar_split_clause,[],[f531,f9226]) ).
fof(f9226,plain,
( spl0_730
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f531,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__0__imp__0_0) ).
fof(f9224,plain,
spl0_729,
inference(avatar_split_clause,[],[f479,f9222]) ).
fof(f9222,plain,
( spl0_729
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f479,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__inverse_0) ).
fof(f9220,plain,
spl0_728,
inference(avatar_split_clause,[],[f440,f9218]) ).
fof(f9218,plain,
( spl0_728
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f440,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ominus__left_0) ).
fof(f9216,plain,
spl0_727,
inference(avatar_split_clause,[],[f439,f9214]) ).
fof(f9214,plain,
( spl0_727
<=> ! [X25,X0,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X25,X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X4,X25,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f439,axiom,
! [X0,X4,X25] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X25,X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X4,X25,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__left_Ominus_0) ).
fof(f9212,plain,
spl0_726,
inference(avatar_split_clause,[],[f437,f9210]) ).
fof(f9210,plain,
( spl0_726
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f437,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ominus__right_0) ).
fof(f9208,plain,
spl0_725,
inference(avatar_split_clause,[],[f436,f9206]) ).
fof(f9206,plain,
( spl0_725
<=> ! [X4,X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f436,axiom,
! [X0,X1,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__minus__right_0) ).
fof(f9204,plain,
spl0_724,
inference(avatar_split_clause,[],[f288,f9202]) ).
fof(f9202,plain,
( spl0_724
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f288,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
fof(f9200,plain,
spl0_723,
inference(avatar_split_clause,[],[f287,f9198]) ).
fof(f9198,plain,
( spl0_723
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f287,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
fof(f9196,plain,
spl0_722,
inference(avatar_split_clause,[],[f286,f9194]) ).
fof(f9194,plain,
( spl0_722
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f286,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(f9192,plain,
( spl0_721
| ~ spl0_345
| ~ spl0_465 ),
inference(avatar_split_clause,[],[f4770,f4462,f3374,f9190]) ).
fof(f9190,plain,
( spl0_721
<=> ! [X0,X1] : c_Log_Opowr(X0,X1) = c_Log_Opowr(c_Log_Opowr(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f4462,plain,
( spl0_465
<=> ! [X2,X1,X4] : c_Log_Opowr(c_Log_Opowr(X4,X1),X2) = c_Log_Opowr(c_Log_Opowr(X4,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f4770,plain,
( ! [X0,X1] : c_Log_Opowr(X0,X1) = c_Log_Opowr(c_Log_Opowr(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),X1)
| ~ spl0_345
| ~ spl0_465 ),
inference(superposition,[],[f4463,f3375]) ).
fof(f4463,plain,
( ! [X2,X1,X4] : c_Log_Opowr(c_Log_Opowr(X4,X1),X2) = c_Log_Opowr(c_Log_Opowr(X4,X2),X1)
| ~ spl0_465 ),
inference(avatar_component_clause,[],[f4462]) ).
fof(f9188,plain,
spl0_720,
inference(avatar_split_clause,[],[f285,f9186]) ).
fof(f9186,plain,
( spl0_720
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f285,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(f9184,plain,
spl0_719,
inference(avatar_split_clause,[],[f261,f9182]) ).
fof(f9182,plain,
( spl0_719
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,X0),X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f261,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,X0),X2,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
fof(f9180,plain,
spl0_718,
inference(avatar_split_clause,[],[f260,f9178]) ).
fof(f9178,plain,
( spl0_718
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,X0),X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f260,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,X0),X2,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
fof(f9176,plain,
spl0_717,
inference(avatar_split_clause,[],[f258,f9174]) ).
fof(f9174,plain,
( spl0_717
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f258,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__0__imp__0_0) ).
fof(f9172,plain,
spl0_716,
inference(avatar_split_clause,[],[f240,f9170]) ).
fof(f9170,plain,
( spl0_716
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X8,X0),X8,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f240,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X8,X0),X8,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
fof(f9168,plain,
spl0_715,
inference(avatar_split_clause,[],[f200,f9166]) ).
fof(f9166,plain,
( spl0_715
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f200,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
fof(f9164,plain,
spl0_714,
inference(avatar_split_clause,[],[f199,f9162]) ).
fof(f9162,plain,
( spl0_714
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f199,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
fof(f9160,plain,
spl0_713,
inference(avatar_split_clause,[],[f164,f9158]) ).
fof(f9158,plain,
( spl0_713
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f164,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse_0) ).
fof(f9156,plain,
spl0_712,
inference(avatar_split_clause,[],[f163,f9154]) ).
fof(f9154,plain,
( spl0_712
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f163,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__inverse_0) ).
fof(f9152,plain,
spl0_711,
inference(avatar_split_clause,[],[f162,f9150]) ).
fof(f9150,plain,
( spl0_711
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f162,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__inverse_0) ).
fof(f9148,plain,
( spl0_710
| ~ spl0_242
| ~ spl0_459 ),
inference(avatar_split_clause,[],[f4731,f4438,f2596,f9145]) ).
fof(f4731,plain,
( c_Log_Opowr(v_x,c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(v_x,tc_RealDef_Oreal)
| ~ spl0_242
| ~ spl0_459 ),
inference(superposition,[],[f4439,f2598]) ).
fof(f9143,plain,
spl0_709,
inference(avatar_split_clause,[],[f160,f9141]) ).
fof(f9141,plain,
( spl0_709
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f160,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
fof(f9139,plain,
spl0_708,
inference(avatar_split_clause,[],[f159,f9137]) ).
fof(f9137,plain,
( spl0_708
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Otimes__class_Otimes(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f159,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Otimes__class_Otimes(X2,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
fof(f9135,plain,
spl0_707,
inference(avatar_split_clause,[],[f157,f9133]) ).
fof(f9133,plain,
( spl0_707
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f157,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
fof(f9131,plain,
spl0_706,
inference(avatar_split_clause,[],[f156,f9129]) ).
fof(f9129,plain,
( spl0_706
<=> ! [X4,X0,X10] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X0),X10,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f156,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X0),X10,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
fof(f9127,plain,
spl0_705,
inference(avatar_split_clause,[],[f140,f9125]) ).
fof(f9125,plain,
( spl0_705
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f140,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
fof(f9123,plain,
spl0_704,
inference(avatar_split_clause,[],[f138,f9121]) ).
fof(f9121,plain,
( spl0_704
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f138,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
fof(f9119,plain,
spl0_703,
inference(avatar_split_clause,[],[f135,f9117]) ).
fof(f9117,plain,
( spl0_703
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f135,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(f9115,plain,
spl0_702,
inference(avatar_split_clause,[],[f134,f9113]) ).
fof(f9113,plain,
( spl0_702
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f134,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(f9111,plain,
spl0_701,
inference(avatar_split_clause,[],[f123,f9109]) ).
fof(f9109,plain,
( spl0_701
<=> ! [X22,X24,X23] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X23,tc_RealDef_Oreal),X24,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X23,X24,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f123,axiom,
! [X24,X22,X23] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X22,X23,tc_RealDef_Oreal),X24,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X23,X24,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__assoc_0) ).
fof(f9107,plain,
spl0_700,
inference(avatar_split_clause,[],[f103,f9105]) ).
fof(f9105,plain,
( spl0_700
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f103,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
fof(f9103,plain,
( spl0_699
| ~ spl0_237
| ~ spl0_459 ),
inference(avatar_split_clause,[],[f4730,f4438,f2552,f9100]) ).
fof(f4730,plain,
( c_Log_Opowr(c_Transcendental_Opi,c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_237
| ~ spl0_459 ),
inference(superposition,[],[f4439,f2554]) ).
fof(f9098,plain,
spl0_698,
inference(avatar_split_clause,[],[f57,f9096]) ).
fof(f9096,plain,
( spl0_698
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__div__algebra(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X0) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f57,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__div__algebra(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X0) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__inverse_0) ).
fof(f9094,plain,
spl0_697,
inference(avatar_split_clause,[],[f50,f9092]) ).
fof(f9092,plain,
( spl0_697
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f50,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
fof(f8492,plain,
( spl0_696
| ~ spl0_125
| ~ spl0_12
| ~ spl0_520 ),
inference(avatar_split_clause,[],[f5322,f5006,f1396,f1967,f8489]) ).
fof(f8489,plain,
( spl0_696
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_Lattices_Olower__semilattice__class_Oinf(c_Transcendental_Opi,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f1396,plain,
( spl0_12
<=> c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f5322,plain,
( ~ class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| c_Transcendental_Otan(c_Transcendental_Opi) = c_Lattices_Olower__semilattice__class_Oinf(c_Transcendental_Opi,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_12
| ~ spl0_520 ),
inference(resolution,[],[f5007,f1398]) ).
fof(f1398,plain,
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f1396]) ).
fof(f8314,plain,
( spl0_695
| ~ spl0_27
| ~ spl0_352
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f3869,f3666,f3433,f1474,f8311]) ).
fof(f8311,plain,
( spl0_695
<=> c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Osin(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f1474,plain,
( spl0_27
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Osin(c_Transcendental_Otan(c_Transcendental_Opi)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f3433,plain,
( spl0_352
<=> ! [X4] : c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(X4),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f3666,plain,
( spl0_405
<=> ! [X4] : c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X4),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f3869,plain,
( c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Osin(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)))
| ~ spl0_27
| ~ spl0_352
| ~ spl0_405 ),
inference(forward_demodulation,[],[f3865,f3434]) ).
fof(f3434,plain,
( ! [X4] : c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(X4),tc_RealDef_Oreal)
| ~ spl0_352 ),
inference(avatar_component_clause,[],[f3433]) ).
fof(f3865,plain,
( c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal))
| ~ spl0_27
| ~ spl0_405 ),
inference(superposition,[],[f3667,f1476]) ).
fof(f1476,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Osin(c_Transcendental_Otan(c_Transcendental_Opi))
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f1474]) ).
fof(f3667,plain,
( ! [X4] : c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ spl0_405 ),
inference(avatar_component_clause,[],[f3666]) ).
fof(f7585,plain,
spl0_694,
inference(avatar_split_clause,[],[f1035,f7583]) ).
fof(f7583,plain,
( spl0_694
<=> ! [X4,X0,X10] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X4 = X10
| c_HOL_Ominus__class_Ominus(X4,X10,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f1035,axiom,
! [X10,X0,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X4 = X10
| c_HOL_Ominus__class_Ominus(X4,X10,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f7581,plain,
spl0_693,
inference(avatar_split_clause,[],[f1025,f7579]) ).
fof(f7579,plain,
( spl0_693
<=> ! [X4,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oplus__class_Oplus(X4,X1,X0) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f1025,axiom,
! [X0,X1,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oplus__class_Oplus(X4,X1,X0) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f7577,plain,
spl0_692,
inference(avatar_split_clause,[],[f964,f7575]) ).
fof(f7575,plain,
( spl0_692
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f964,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
fof(f7548,plain,
spl0_691,
inference(avatar_split_clause,[],[f963,f7546]) ).
fof(f7546,plain,
( spl0_691
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f963,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
fof(f7544,plain,
spl0_690,
inference(avatar_split_clause,[],[f945,f7542]) ).
fof(f945,axiom,
! [X10,X0,X14,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X4,X0)
| ~ c_lessequals(X14,X10,X0)
| c_lessequals(X14,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f7540,plain,
spl0_689,
inference(avatar_split_clause,[],[f944,f7538]) ).
fof(f7538,plain,
( spl0_689
<=> ! [X4,X0,X14,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X4,X0)
| c_HOL_Oord__class_Oless(X14,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f944,axiom,
! [X10,X0,X14,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X14,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X4,X0)
| c_HOL_Oord__class_Oless(X14,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f7536,plain,
spl0_688,
inference(avatar_split_clause,[],[f943,f7534]) ).
fof(f7534,plain,
( spl0_688
<=> ! [X4,X0,X14,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X4,X0)
| ~ c_HOL_Oord__class_Oless(X14,X10,X0)
| c_HOL_Oord__class_Oless(X14,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f943,axiom,
! [X10,X0,X14,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X4,X0)
| ~ c_HOL_Oord__class_Oless(X14,X10,X0)
| c_HOL_Oord__class_Oless(X14,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f7532,plain,
spl0_687,
inference(avatar_split_clause,[],[f941,f7530]) ).
fof(f7530,plain,
( spl0_687
<=> ! [X4,X0,X14,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X10,X0)
| ~ c_lessequals(X10,X14,X0)
| c_lessequals(X4,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f941,axiom,
! [X10,X0,X14,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X10,X0)
| ~ c_lessequals(X10,X14,X0)
| c_lessequals(X4,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f7528,plain,
spl0_686,
inference(avatar_split_clause,[],[f939,f7526]) ).
fof(f939,axiom,
! [X10,X0,X14,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X10,X14,X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| c_HOL_Oord__class_Oless(X4,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f7524,plain,
spl0_685,
inference(avatar_split_clause,[],[f938,f7522]) ).
fof(f938,axiom,
! [X10,X0,X14,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X14,X0)
| c_HOL_Oord__class_Oless(X4,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f7520,plain,
spl0_684,
inference(avatar_split_clause,[],[f911,f7518]) ).
fof(f7518,plain,
( spl0_684
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f911,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
fof(f7516,plain,
spl0_683,
inference(avatar_split_clause,[],[f902,f7514]) ).
fof(f7514,plain,
( spl0_683
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f902,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
fof(f7512,plain,
spl0_682,
inference(avatar_split_clause,[],[f901,f7510]) ).
fof(f7510,plain,
( spl0_682
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f901,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
fof(f7508,plain,
( spl0_681
| ~ spl0_185
| ~ spl0_625 ),
inference(avatar_split_clause,[],[f7357,f7163,f2266,f7506]) ).
fof(f7506,plain,
( spl0_681
<=> ! [X0,X1] :
( c_lessequals(c_RealVector_Odist__class_Odist(X0,X0,X1),v_x,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f7357,plain,
( ! [X0,X1] :
( c_lessequals(c_RealVector_Odist__class_Odist(X0,X0,X1),v_x,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) )
| ~ spl0_185
| ~ spl0_625 ),
inference(resolution,[],[f7164,f2267]) ).
fof(f7504,plain,
spl0_680,
inference(avatar_split_clause,[],[f873,f7502]) ).
fof(f7502,plain,
( spl0_680
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f873,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
fof(f7500,plain,
spl0_679,
inference(avatar_split_clause,[],[f871,f7498]) ).
fof(f7498,plain,
( spl0_679
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f871,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
fof(f7496,plain,
spl0_678,
inference(avatar_split_clause,[],[f869,f7494]) ).
fof(f7494,plain,
( spl0_678
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f869,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
fof(f7492,plain,
spl0_677,
inference(avatar_split_clause,[],[f867,f7490]) ).
fof(f7490,plain,
( spl0_677
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f867,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
fof(f7488,plain,
spl0_676,
inference(avatar_split_clause,[],[f823,f7486]) ).
fof(f7486,plain,
( spl0_676
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f823,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).
fof(f7484,plain,
spl0_675,
inference(avatar_split_clause,[],[f814,f7482]) ).
fof(f7482,plain,
( spl0_675
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f814,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
fof(f7480,plain,
spl0_674,
inference(avatar_split_clause,[],[f813,f7478]) ).
fof(f7478,plain,
( spl0_674
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f813,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
fof(f7476,plain,
spl0_673,
inference(avatar_split_clause,[],[f791,f7474]) ).
fof(f7474,plain,
( spl0_673
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f791,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).
fof(f7472,plain,
spl0_672,
inference(avatar_split_clause,[],[f784,f7470]) ).
fof(f7470,plain,
( spl0_672
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f784,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
fof(f7468,plain,
spl0_671,
inference(avatar_split_clause,[],[f783,f7466]) ).
fof(f7466,plain,
( spl0_671
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f783,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
fof(f7464,plain,
( spl0_670
| ~ spl0_189
| ~ spl0_625 ),
inference(avatar_split_clause,[],[f7356,f7163,f2282,f7462]) ).
fof(f7462,plain,
( spl0_670
<=> ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),v_x,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f7356,plain,
( ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),v_x,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_189
| ~ spl0_625 ),
inference(resolution,[],[f7164,f2283]) ).
fof(f7460,plain,
spl0_669,
inference(avatar_split_clause,[],[f764,f7458]) ).
fof(f7458,plain,
( spl0_669
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f764,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
fof(f7456,plain,
spl0_668,
inference(avatar_split_clause,[],[f763,f7454]) ).
fof(f7454,plain,
( spl0_668
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f763,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
fof(f7452,plain,
spl0_667,
inference(avatar_split_clause,[],[f761,f7450]) ).
fof(f7450,plain,
( spl0_667
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f761,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_negative__imp__inverse__negative_0) ).
fof(f7448,plain,
spl0_666,
inference(avatar_split_clause,[],[f755,f7446]) ).
fof(f7446,plain,
( spl0_666
<=> ! [X4,X0,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X10,X0)
| c_lessequals(X10,X4,X0)
| c_HOL_Oord__class_Oless(X4,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f755,axiom,
! [X10,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X10,X0)
| c_lessequals(X10,X4,X0)
| c_HOL_Oord__class_Oless(X4,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f7444,plain,
spl0_665,
inference(avatar_split_clause,[],[f720,f7442]) ).
fof(f7442,plain,
( spl0_665
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f720,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
fof(f7440,plain,
spl0_664,
inference(avatar_split_clause,[],[f719,f7438]) ).
fof(f7438,plain,
( spl0_664
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = X2
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f719,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = X2
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).
fof(f7436,plain,
spl0_663,
inference(avatar_split_clause,[],[f681,f7434]) ).
fof(f7434,plain,
( spl0_663
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = X4
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Oinverse(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f681,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = X4
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Oinverse(X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
fof(f7432,plain,
spl0_662,
inference(avatar_split_clause,[],[f630,f7430]) ).
fof(f7430,plain,
( spl0_662
<=> ! [X4,X0,X10,X25] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X10 = X25
| c_HOL_Ominus__class_Ominus(X4,X4,X0) != c_HOL_Ominus__class_Ominus(X25,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f630,axiom,
! [X10,X0,X4,X25] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X10 = X25
| c_HOL_Ominus__class_Ominus(X4,X4,X0) != c_HOL_Ominus__class_Ominus(X25,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
fof(f7428,plain,
spl0_661,
inference(avatar_split_clause,[],[f597,f7426]) ).
fof(f597,axiom,
! [X10,X0,X14,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| ~ c_HOL_Oord__class_Oless(X10,X14,X0)
| c_HOL_Oord__class_Oless(X4,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f7424,plain,
spl0_660,
inference(avatar_split_clause,[],[f596,f7422]) ).
fof(f596,axiom,
! [X10,X0,X14,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X4,X0)
| ~ c_HOL_Oord__class_Oless(X14,X10,X0)
| c_HOL_Oord__class_Oless(X14,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f7420,plain,
( spl0_659
| ~ spl0_341
| ~ spl0_625 ),
inference(avatar_split_clause,[],[f7354,f7163,f3292,f7418]) ).
fof(f7354,plain,
( ! [X0] :
( c_lessequals(X0,v_x,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_341
| ~ spl0_625 ),
inference(resolution,[],[f7164,f3293]) ).
fof(f7416,plain,
spl0_658,
inference(avatar_split_clause,[],[f539,f7414]) ).
fof(f7414,plain,
( spl0_658
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f539,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
fof(f7412,plain,
spl0_657,
inference(avatar_split_clause,[],[f491,f7410]) ).
fof(f7410,plain,
( spl0_657
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f491,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
fof(f7408,plain,
spl0_656,
inference(avatar_split_clause,[],[f490,f7406]) ).
fof(f7406,plain,
( spl0_656
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f490,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
fof(f7404,plain,
spl0_655,
inference(avatar_split_clause,[],[f473,f7402]) ).
fof(f7402,plain,
( spl0_655
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f473,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
fof(f7400,plain,
spl0_654,
inference(avatar_split_clause,[],[f472,f7398]) ).
fof(f7398,plain,
( spl0_654
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f472,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
fof(f7396,plain,
spl0_653,
inference(avatar_split_clause,[],[f467,f7394]) ).
fof(f7394,plain,
( spl0_653
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Ominus__class_Ominus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f467,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Ominus__class_Ominus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__prts_0) ).
fof(f7392,plain,
spl0_652,
inference(avatar_split_clause,[],[f446,f7390]) ).
fof(f7390,plain,
( spl0_652
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f446,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
fof(f7388,plain,
spl0_651,
inference(avatar_split_clause,[],[f445,f7386]) ).
fof(f7386,plain,
( spl0_651
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f445,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
fof(f7384,plain,
spl0_650,
inference(avatar_split_clause,[],[f399,f7382]) ).
fof(f7382,plain,
( spl0_650
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f399,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_0) ).
fof(f7380,plain,
spl0_649,
inference(avatar_split_clause,[],[f398,f7378]) ).
fof(f7378,plain,
( spl0_649
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f398,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).
fof(f7352,plain,
spl0_648,
inference(avatar_split_clause,[],[f395,f7350]) ).
fof(f7350,plain,
( spl0_648
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Osgn__class_Osgn(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f395,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Osgn__class_Osgn(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_0) ).
fof(f7348,plain,
spl0_647,
inference(avatar_split_clause,[],[f394,f7346]) ).
fof(f7346,plain,
( spl0_647
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Osgn__class_Osgn(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f394,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Osgn__class_Osgn(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_1) ).
fof(f7344,plain,
spl0_646,
inference(avatar_split_clause,[],[f348,f7342]) ).
fof(f7342,plain,
( spl0_646
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X2,X1,X0) != c_HOL_Oplus__class_Oplus(X8,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f348,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X2,X1,X0) != c_HOL_Oplus__class_Oplus(X8,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f7340,plain,
spl0_645,
inference(avatar_split_clause,[],[f347,f7338]) ).
fof(f7338,plain,
( spl0_645
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f347,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f7336,plain,
spl0_644,
inference(avatar_split_clause,[],[f346,f7334]) ).
fof(f7334,plain,
( spl0_644
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f346,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f7332,plain,
spl0_643,
inference(avatar_split_clause,[],[f326,f7330]) ).
fof(f7330,plain,
( spl0_643
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f326,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__less_1) ).
fof(f7328,plain,
spl0_642,
inference(avatar_split_clause,[],[f325,f7326]) ).
fof(f7326,plain,
( spl0_642
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f325,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__less_0) ).
fof(f7324,plain,
spl0_641,
inference(avatar_split_clause,[],[f278,f7322]) ).
fof(f7322,plain,
( spl0_641
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f278,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
fof(f7320,plain,
spl0_640,
inference(avatar_split_clause,[],[f265,f7318]) ).
fof(f7318,plain,
( spl0_640
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f265,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
fof(f7316,plain,
spl0_639,
inference(avatar_split_clause,[],[f264,f7314]) ).
fof(f7314,plain,
( spl0_639
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f264,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
fof(f7304,plain,
spl0_638,
inference(avatar_split_clause,[],[f217,f7302]) ).
fof(f7302,plain,
( spl0_638
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f217,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
fof(f7300,plain,
spl0_637,
inference(avatar_split_clause,[],[f216,f7298]) ).
fof(f7298,plain,
( spl0_637
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f216,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
fof(f7296,plain,
spl0_636,
inference(avatar_split_clause,[],[f215,f7294]) ).
fof(f7294,plain,
( spl0_636
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f215,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
fof(f7292,plain,
spl0_635,
inference(avatar_split_clause,[],[f192,f7290]) ).
fof(f7290,plain,
( spl0_635
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f192,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
fof(f7288,plain,
spl0_634,
inference(avatar_split_clause,[],[f191,f7286]) ).
fof(f7286,plain,
( spl0_634
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f191,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
fof(f7284,plain,
spl0_633,
inference(avatar_split_clause,[],[f79,f7282]) ).
fof(f7282,plain,
( spl0_633
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f79,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
fof(f7280,plain,
spl0_632,
inference(avatar_split_clause,[],[f78,f7278]) ).
fof(f7278,plain,
( spl0_632
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f78,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
fof(f7276,plain,
spl0_631,
inference(avatar_split_clause,[],[f68,f7274]) ).
fof(f7274,plain,
( spl0_631
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f68,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
fof(f7272,plain,
spl0_630,
inference(avatar_split_clause,[],[f54,f7270]) ).
fof(f7270,plain,
( spl0_630
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f54,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__sgn_1) ).
fof(f7268,plain,
spl0_629,
inference(avatar_split_clause,[],[f37,f7266]) ).
fof(f7266,plain,
( spl0_629
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f37,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
fof(f7264,plain,
( ~ spl0_140
| spl0_628
| ~ spl0_294
| ~ spl0_546
| ~ spl0_578 ),
inference(avatar_split_clause,[],[f6141,f5949,f5121,f2926,f7261,f2042]) ).
fof(f7261,plain,
( spl0_628
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f2926,plain,
( spl0_294
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Otan(c_Transcendental_Opi) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f5121,plain,
( spl0_546
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f5949,plain,
( spl0_578
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f6141,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal))
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_294
| ~ spl0_546
| ~ spl0_578 ),
inference(forward_demodulation,[],[f6140,f2928]) ).
fof(f2928,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Otan(c_Transcendental_Opi)
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f2926]) ).
fof(f6140,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal))
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_294
| ~ spl0_546
| ~ spl0_578 ),
inference(trivial_inequality_removal,[],[f6139]) ).
fof(f6139,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) != c_Transcendental_Otan(c_Transcendental_Opi)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal))
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_294
| ~ spl0_546
| ~ spl0_578 ),
inference(forward_demodulation,[],[f6137,f2928]) ).
fof(f6137,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Otan(c_Transcendental_Opi)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal))
| ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_546
| ~ spl0_578 ),
inference(superposition,[],[f5122,f5951]) ).
fof(f5951,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_578 ),
inference(avatar_component_clause,[],[f5949]) ).
fof(f5122,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X1,X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_OrderedGroup_Ogroup__add(X0) )
| ~ spl0_546 ),
inference(avatar_component_clause,[],[f5121]) ).
fof(f7259,plain,
spl0_627,
inference(avatar_split_clause,[],[f16,f7257]) ).
fof(f7257,plain,
( spl0_627
<=> ! [X4,X0] :
( ~ class_RealVector_Osgn__div__norm(X0)
| c_HOL_Osgn__class_Osgn(X4,X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f16,axiom,
! [X0,X4] :
( ~ class_RealVector_Osgn__div__norm(X0)
| c_HOL_Osgn__class_Osgn(X4,X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__div__norm_0) ).
fof(f7255,plain,
spl0_626,
inference(avatar_split_clause,[],[f14,f7253]) ).
fof(f14,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| X1 = X2
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
fof(f7165,plain,
( spl0_625
| ~ spl0_295
| ~ spl0_543 ),
inference(avatar_split_clause,[],[f5762,f5109,f2937,f7163]) ).
fof(f5762,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,v_x,tc_RealDef_Oreal) )
| ~ spl0_295
| ~ spl0_543 ),
inference(resolution,[],[f5110,f2939]) ).
fof(f6878,plain,
( ~ spl0_124
| spl0_624
| ~ spl0_124
| ~ spl0_295
| ~ spl0_491
| ~ spl0_531 ),
inference(avatar_split_clause,[],[f5601,f5061,f4570,f2937,f1962,f6875,f1962]) ).
fof(f6875,plain,
( spl0_624
<=> v_x = c_Lattices_Oupper__semilattice__class_Osup(v_x,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f4570,plain,
( spl0_491
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(X10,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f5601,plain,
( v_x = c_Lattices_Oupper__semilattice__class_Osup(v_x,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Lattices_Oupper__semilattice(tc_RealDef_Oreal)
| ~ spl0_124
| ~ spl0_295
| ~ spl0_491
| ~ spl0_531 ),
inference(forward_demodulation,[],[f5590,f4901]) ).
fof(f4901,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_RealDef_Oreal)
| ~ spl0_124
| ~ spl0_491 ),
inference(resolution,[],[f4571,f1964]) ).
fof(f1964,plain,
( class_Lattices_Oupper__semilattice(tc_RealDef_Oreal)
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1962]) ).
fof(f4571,plain,
( ! [X10,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(X10,X4,X0) )
| ~ spl0_491 ),
inference(avatar_component_clause,[],[f4570]) ).
fof(f5590,plain,
( ~ class_Lattices_Oupper__semilattice(tc_RealDef_Oreal)
| v_x = c_Lattices_Oupper__semilattice__class_Osup(c_Transcendental_Otan(c_Transcendental_Opi),v_x,tc_RealDef_Oreal)
| ~ spl0_295
| ~ spl0_531 ),
inference(resolution,[],[f5062,f2939]) ).
fof(f6149,plain,
spl0_623,
inference(avatar_split_clause,[],[f1019,f6147]) ).
fof(f6147,plain,
( spl0_623
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f1019,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
fof(f6145,plain,
spl0_622,
inference(avatar_split_clause,[],[f1010,f6143]) ).
fof(f6143,plain,
( spl0_622
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X9,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f1010,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X9,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
fof(f6125,plain,
spl0_621,
inference(avatar_split_clause,[],[f1002,f6123]) ).
fof(f6123,plain,
( spl0_621
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f1002,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
fof(f6121,plain,
spl0_620,
inference(avatar_split_clause,[],[f981,f6119]) ).
fof(f6119,plain,
( spl0_620
<=> ! [X6,X41,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X41,X6,X0)
| c_HOL_Oabs__class_Oabs(X6,X0) != c_HOL_Oabs__class_Oabs(X41,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f981,axiom,
! [X41,X0,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X41,X6,X0)
| c_HOL_Oabs__class_Oabs(X6,X0) != c_HOL_Oabs__class_Oabs(X41,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).
fof(f6117,plain,
spl0_619,
inference(avatar_split_clause,[],[f979,f6115]) ).
fof(f6115,plain,
( spl0_619
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Osgn__class_Osgn(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f979,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Osgn__class_Osgn(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__1__pos_0) ).
fof(f6113,plain,
spl0_618,
inference(avatar_split_clause,[],[f978,f6111]) ).
fof(f6111,plain,
( spl0_618
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f978,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__pos_0) ).
fof(f6109,plain,
spl0_617,
inference(avatar_split_clause,[],[f974,f6107]) ).
fof(f6107,plain,
( spl0_617
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f974,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
fof(f6105,plain,
spl0_616,
inference(avatar_split_clause,[],[f973,f6103]) ).
fof(f6103,plain,
( spl0_616
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f973,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
fof(f6101,plain,
spl0_615,
inference(avatar_split_clause,[],[f970,f6099]) ).
fof(f6099,plain,
( spl0_615
<=> ! [X4,X0,X10] :
( ~ class_RealVector_Odist__norm(X0)
| c_RealVector_Odist__class_Odist(X4,X10,X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f970,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Odist__norm(X0)
| c_RealVector_Odist__class_Odist(X4,X10,X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__norm_0) ).
fof(f6097,plain,
spl0_614,
inference(avatar_split_clause,[],[f960,f6094]) ).
fof(f6094,plain,
( spl0_614
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f960,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__is__one_2) ).
fof(f6092,plain,
spl0_613,
inference(avatar_split_clause,[],[f899,f6090]) ).
fof(f6090,plain,
( spl0_613
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f899,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
fof(f6088,plain,
spl0_612,
inference(avatar_split_clause,[],[f877,f6086]) ).
fof(f6086,plain,
( spl0_612
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f877,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__right_1) ).
fof(f6084,plain,
( spl0_611
| ~ spl0_185
| ~ spl0_557 ),
inference(avatar_split_clause,[],[f5897,f5850,f2266,f6082]) ).
fof(f6082,plain,
( spl0_611
<=> ! [X0,X1] :
( c_lessequals(c_RealVector_Odist__class_Odist(X0,X0,X1),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f5897,plain,
( ! [X0,X1] :
( c_lessequals(c_RealVector_Odist__class_Odist(X0,X0,X1),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) )
| ~ spl0_185
| ~ spl0_557 ),
inference(resolution,[],[f5851,f2267]) ).
fof(f6080,plain,
spl0_610,
inference(avatar_split_clause,[],[f864,f6078]) ).
fof(f6078,plain,
( spl0_610
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X1,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f864,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X1,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
fof(f6076,plain,
spl0_609,
inference(avatar_split_clause,[],[f841,f6074]) ).
fof(f6074,plain,
( spl0_609
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f841,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
fof(f6072,plain,
spl0_608,
inference(avatar_split_clause,[],[f773,f6070]) ).
fof(f6070,plain,
( spl0_608
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f773,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
fof(f6068,plain,
spl0_607,
inference(avatar_split_clause,[],[f772,f6066]) ).
fof(f6066,plain,
( spl0_607
<=> ! [X0,X14,X10] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X14,X0),c_HOL_Oplus__class_Oplus(X10,X14,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f772,axiom,
! [X10,X0,X14] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X14,X0),c_HOL_Oplus__class_Oplus(X10,X14,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
fof(f6064,plain,
spl0_606,
inference(avatar_split_clause,[],[f619,f6062]) ).
fof(f6062,plain,
( spl0_606
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f619,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self_0) ).
fof(f6060,plain,
spl0_605,
inference(avatar_split_clause,[],[f607,f6058]) ).
fof(f6058,plain,
( spl0_605
<=> ! [X4,X0,X15] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_OscaleR__class_OscaleR(X15,X4,X0) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X15,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f607,axiom,
! [X0,X4,X15] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_OscaleR__class_OscaleR(X15,X4,X0) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X15,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__conv__of__real_0) ).
fof(f6056,plain,
spl0_604,
inference(avatar_split_clause,[],[f571,f6054]) ).
fof(f6054,plain,
( spl0_604
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) != c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f571,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) != c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__zero__iff__zero__pprt_1) ).
fof(f6052,plain,
spl0_603,
inference(avatar_split_clause,[],[f570,f6050]) ).
fof(f6050,plain,
( spl0_603
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f570,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__zero__iff__zero__pprt_0) ).
fof(f6048,plain,
spl0_602,
inference(avatar_split_clause,[],[f567,f6046]) ).
fof(f6046,plain,
( spl0_602
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f567,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
fof(f6044,plain,
spl0_601,
inference(avatar_split_clause,[],[f558,f6042]) ).
fof(f6042,plain,
( spl0_601
<=> ! [X0,X15] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Osgn__class_Osgn(c_RealVector_Oof__real(X15,X0),X0) = c_RealVector_Oof__real(c_HOL_Osgn__class_Osgn(X15,tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f558,axiom,
! [X0,X15] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Osgn__class_Osgn(c_RealVector_Oof__real(X15,X0),X0) = c_RealVector_Oof__real(c_HOL_Osgn__class_Osgn(X15,tc_RealDef_Oreal),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__of__real_0) ).
fof(f6040,plain,
( spl0_600
| ~ spl0_189
| ~ spl0_557 ),
inference(avatar_split_clause,[],[f5896,f5850,f2282,f6038]) ).
fof(f6038,plain,
( spl0_600
<=> ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f5896,plain,
( ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_189
| ~ spl0_557 ),
inference(resolution,[],[f5851,f2283]) ).
fof(f6036,plain,
spl0_599,
inference(avatar_split_clause,[],[f556,f6034]) ).
fof(f6034,plain,
( spl0_599
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f556,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
fof(f6032,plain,
spl0_598,
inference(avatar_split_clause,[],[f555,f6030]) ).
fof(f6030,plain,
( spl0_598
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f555,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
fof(f6028,plain,
spl0_597,
inference(avatar_split_clause,[],[f554,f6026]) ).
fof(f6026,plain,
( spl0_597
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f554,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
fof(f6024,plain,
spl0_596,
inference(avatar_split_clause,[],[f553,f6022]) ).
fof(f6022,plain,
( spl0_596
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f553,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
fof(f6020,plain,
spl0_595,
inference(avatar_split_clause,[],[f552,f6018]) ).
fof(f6018,plain,
( spl0_595
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f552,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
fof(f6016,plain,
spl0_594,
inference(avatar_split_clause,[],[f551,f6014]) ).
fof(f6014,plain,
( spl0_594
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f551,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
fof(f6012,plain,
spl0_593,
inference(avatar_split_clause,[],[f550,f6010]) ).
fof(f6010,plain,
( spl0_593
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f550,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
fof(f6008,plain,
spl0_592,
inference(avatar_split_clause,[],[f549,f6006]) ).
fof(f6006,plain,
( spl0_592
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f549,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
fof(f6004,plain,
spl0_591,
inference(avatar_split_clause,[],[f540,f6002]) ).
fof(f6002,plain,
( spl0_591
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f540,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__self_0) ).
fof(f6000,plain,
spl0_590,
inference(avatar_split_clause,[],[f510,f5998]) ).
fof(f5998,plain,
( spl0_590
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f510,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nprt__neg_0) ).
fof(f5996,plain,
( spl0_589
| ~ spl0_341
| ~ spl0_557 ),
inference(avatar_split_clause,[],[f5894,f5850,f3292,f5994]) ).
fof(f5894,plain,
( ! [X0] :
( c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_341
| ~ spl0_557 ),
inference(resolution,[],[f5851,f3293]) ).
fof(f5992,plain,
spl0_588,
inference(avatar_split_clause,[],[f366,f5990]) ).
fof(f5990,plain,
( spl0_588
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Divides_Odiv__class_Omod(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f366,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Divides_Odiv__class_Omod(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
fof(f5988,plain,
spl0_587,
inference(avatar_split_clause,[],[f365,f5986]) ).
fof(f5986,plain,
( spl0_587
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f365,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
fof(f5984,plain,
spl0_586,
inference(avatar_split_clause,[],[f331,f5982]) ).
fof(f5982,plain,
( spl0_586
<=> ! [X4,X0,X14,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X4,X10,X0)
| ~ c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f331,axiom,
! [X10,X0,X14,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X4,X10,X0)
| ~ c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X10,X14,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
fof(f5980,plain,
spl0_585,
inference(avatar_split_clause,[],[f330,f5978]) ).
fof(f5978,plain,
( spl0_585
<=> ! [X4,X0,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X2,X4,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f330,axiom,
! [X2,X0,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X2,X4,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).
fof(f5976,plain,
spl0_584,
inference(avatar_split_clause,[],[f329,f5974]) ).
fof(f5974,plain,
( spl0_584
<=> ! [X2,X4,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X4,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f329,axiom,
! [X2,X0,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X1,X4,X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).
fof(f5972,plain,
spl0_583,
inference(avatar_split_clause,[],[f328,f5970]) ).
fof(f5970,plain,
( spl0_583
<=> ! [X4,X0,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X4,X2,X0)
| ~ c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f328,axiom,
! [X2,X0,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X4,X2,X0)
| ~ c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).
fof(f5968,plain,
spl0_582,
inference(avatar_split_clause,[],[f316,f5966]) ).
fof(f5966,plain,
( spl0_582
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f316,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus_0) ).
fof(f5964,plain,
spl0_581,
inference(avatar_split_clause,[],[f315,f5962]) ).
fof(f5962,plain,
( spl0_581
<=> ! [X4,X0,X10] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X4,X10,X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f315,axiom,
! [X10,X0,X4] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X4,X10,X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
fof(f5960,plain,
spl0_580,
inference(avatar_split_clause,[],[f314,f5958]) ).
fof(f5958,plain,
( spl0_580
<=> ! [X4,X0,X10] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X4,X10,X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f314,axiom,
! [X10,X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X4,X10,X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__def_0) ).
fof(f5956,plain,
spl0_579,
inference(avatar_split_clause,[],[f251,f5954]) ).
fof(f5954,plain,
( spl0_579
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f251,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__iff__zero__nprt_0) ).
fof(f5952,plain,
( spl0_578
| ~ spl0_8
| ~ spl0_140
| ~ spl0_380
| ~ spl0_405
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f4072,f3976,f3666,f3563,f2042,f1376,f5949]) ).
fof(f3976,plain,
( spl0_435
<=> c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(v_x,tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f4072,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_8
| ~ spl0_140
| ~ spl0_380
| ~ spl0_405
| ~ spl0_435 ),
inference(forward_demodulation,[],[f4071,f1378]) ).
fof(f4071,plain,
( c_Transcendental_Osin(v_x) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_140
| ~ spl0_380
| ~ spl0_405
| ~ spl0_435 ),
inference(forward_demodulation,[],[f4067,f3794]) ).
fof(f4067,plain,
( c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v_x,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_405
| ~ spl0_435 ),
inference(superposition,[],[f3667,f3978]) ).
fof(f3978,plain,
( c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(v_x,tc_RealDef_Oreal))
| ~ spl0_435 ),
inference(avatar_component_clause,[],[f3976]) ).
fof(f5947,plain,
spl0_577,
inference(avatar_split_clause,[],[f250,f5945]) ).
fof(f5945,plain,
( spl0_577
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f250,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__iff__zero__nprt_1) ).
fof(f5943,plain,
spl0_576,
inference(avatar_split_clause,[],[f248,f5941]) ).
fof(f5941,plain,
( spl0_576
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f248,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
fof(f5939,plain,
spl0_575,
inference(avatar_split_clause,[],[f229,f5937]) ).
fof(f5937,plain,
( spl0_575
<=> ! [X4,X0,X10] :
( ~ class_Orderings_Oorder(X0)
| X4 = X10
| ~ c_lessequals(X10,X4,X0)
| ~ c_lessequals(X4,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f229,axiom,
! [X10,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| X4 = X10
| ~ c_lessequals(X10,X4,X0)
| ~ c_lessequals(X4,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
fof(f5935,plain,
spl0_574,
inference(avatar_split_clause,[],[f227,f5933]) ).
fof(f5933,plain,
( spl0_574
<=> ! [X4,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| X4 = X10
| c_HOL_Oord__class_Oless(X10,X4,X0)
| c_HOL_Oord__class_Oless(X4,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f227,axiom,
! [X10,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| X4 = X10
| c_HOL_Oord__class_Oless(X10,X4,X0)
| c_HOL_Oord__class_Oless(X4,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
fof(f5931,plain,
spl0_573,
inference(avatar_split_clause,[],[f225,f5929]) ).
fof(f5929,plain,
( spl0_573
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X4 = X10
| c_HOL_Oord__class_Oless(X4,X10,X0)
| c_HOL_Oord__class_Oless(X10,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f225,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X4 = X10
| c_HOL_Oord__class_Oless(X4,X10,X0)
| c_HOL_Oord__class_Oless(X10,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f5927,plain,
spl0_572,
inference(avatar_split_clause,[],[f222,f5925]) ).
fof(f5925,plain,
( spl0_572
<=> ! [X2,X4,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,X4,X0)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f222,axiom,
! [X2,X0,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,X4,X0)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI1_0) ).
fof(f5923,plain,
spl0_571,
inference(avatar_split_clause,[],[f221,f5921]) ).
fof(f5921,plain,
( spl0_571
<=> ! [X4,X0,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f221,axiom,
! [X2,X0,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X2,X4,X0)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI2_0) ).
fof(f5919,plain,
spl0_570,
inference(avatar_split_clause,[],[f201,f5917]) ).
fof(f5917,plain,
( spl0_570
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f201,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__minus_0) ).
fof(f5915,plain,
spl0_569,
inference(avatar_split_clause,[],[f186,f5913]) ).
fof(f5913,plain,
( spl0_569
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f186,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pprt__neg_0) ).
fof(f5911,plain,
spl0_568,
inference(avatar_split_clause,[],[f179,f5909]) ).
fof(f5909,plain,
( spl0_568
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f179,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__minus_0) ).
fof(f5892,plain,
spl0_567,
inference(avatar_split_clause,[],[f137,f5890]) ).
fof(f5890,plain,
( spl0_567
<=> ! [X4,X0,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X4,X2,X0)
| c_HOL_Oord__class_Oless(X4,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f137,axiom,
! [X2,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X4,X2,X0)
| c_HOL_Oord__class_Oless(X4,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI2_0) ).
fof(f5888,plain,
spl0_566,
inference(avatar_split_clause,[],[f136,f5886]) ).
fof(f5886,plain,
( spl0_566
<=> ! [X2,X4,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X4,X1,X0)
| c_HOL_Oord__class_Oless(X4,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f136,axiom,
! [X2,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X4,X1,X0)
| c_HOL_Oord__class_Oless(X4,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI1_0) ).
fof(f5884,plain,
spl0_565,
inference(avatar_split_clause,[],[f113,f5882]) ).
fof(f5882,plain,
( spl0_565
<=> ! [X4,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f113,axiom,
! [X0,X4] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
fof(f5880,plain,
spl0_564,
inference(avatar_split_clause,[],[f99,f5878]) ).
fof(f5878,plain,
( spl0_564
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f99,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
fof(f5876,plain,
spl0_563,
inference(avatar_split_clause,[],[f96,f5874]) ).
fof(f5874,plain,
( spl0_563
<=> ! [X4,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| X4 = X10
| ~ c_lessequals(X4,X10,X0)
| c_HOL_Oord__class_Oless(X4,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f96,axiom,
! [X10,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| X4 = X10
| ~ c_lessequals(X4,X10,X0)
| c_HOL_Oord__class_Oless(X4,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
fof(f5872,plain,
spl0_562,
inference(avatar_split_clause,[],[f67,f5870]) ).
fof(f5870,plain,
( spl0_562
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f67,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
fof(f5868,plain,
spl0_561,
inference(avatar_split_clause,[],[f61,f5866]) ).
fof(f5866,plain,
( spl0_561
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f61,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
fof(f5864,plain,
spl0_560,
inference(avatar_split_clause,[],[f60,f5862]) ).
fof(f5862,plain,
( spl0_560
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f60,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
fof(f5860,plain,
spl0_559,
inference(avatar_split_clause,[],[f59,f5858]) ).
fof(f5858,plain,
( spl0_559
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X8,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f59,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X8,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
fof(f5856,plain,
spl0_558,
inference(avatar_split_clause,[],[f58,f5854]) ).
fof(f5854,plain,
( spl0_558
<=> ! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X8,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f58,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X8,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
fof(f5852,plain,
( spl0_557
| ~ spl0_12
| ~ spl0_543 ),
inference(avatar_split_clause,[],[f5761,f5109,f1396,f5850]) ).
fof(f5761,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_12
| ~ spl0_543 ),
inference(resolution,[],[f5110,f1398]) ).
fof(f5848,plain,
spl0_556,
inference(avatar_split_clause,[],[f30,f5846]) ).
fof(f5846,plain,
( spl0_556
<=> ! [X2,X4,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,X4,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f30,axiom,
! [X2,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X1,X4,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
fof(f5844,plain,
spl0_555,
inference(avatar_split_clause,[],[f29,f5842]) ).
fof(f5842,plain,
( spl0_555
<=> ! [X4,X0,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X2,X4,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f29,axiom,
! [X2,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X2,X4,X0)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
fof(f5840,plain,
spl0_554,
inference(avatar_split_clause,[],[f28,f5838]) ).
fof(f5838,plain,
( spl0_554
<=> ! [X2,X4,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X4,X1,X0)
| c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f28,axiom,
! [X2,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X4,X1,X0)
| c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
fof(f5836,plain,
spl0_553,
inference(avatar_split_clause,[],[f27,f5834]) ).
fof(f5834,plain,
( spl0_553
<=> ! [X4,X0,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X4,X2,X0)
| c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f27,axiom,
! [X2,X0,X1,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X4,X2,X0)
| c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
fof(f5668,plain,
( ~ spl0_124
| spl0_552
| ~ spl0_12
| ~ spl0_124
| ~ spl0_491
| ~ spl0_531 ),
inference(avatar_split_clause,[],[f5600,f5061,f4570,f1962,f1396,f5665,f1962]) ).
fof(f5665,plain,
( spl0_552
<=> c_Transcendental_Opi = c_Lattices_Oupper__semilattice__class_Osup(c_Transcendental_Opi,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f5600,plain,
( c_Transcendental_Opi = c_Lattices_Oupper__semilattice__class_Osup(c_Transcendental_Opi,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Lattices_Oupper__semilattice(tc_RealDef_Oreal)
| ~ spl0_12
| ~ spl0_124
| ~ spl0_491
| ~ spl0_531 ),
inference(forward_demodulation,[],[f5589,f4901]) ).
fof(f5589,plain,
( ~ class_Lattices_Oupper__semilattice(tc_RealDef_Oreal)
| c_Transcendental_Opi = c_Lattices_Oupper__semilattice__class_Osup(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_12
| ~ spl0_531 ),
inference(resolution,[],[f5062,f1398]) ).
fof(f5227,plain,
( spl0_551
| ~ spl0_36
| ~ spl0_116
| ~ spl0_352
| ~ spl0_378
| ~ spl0_459 ),
inference(avatar_split_clause,[],[f4741,f4438,f3555,f3433,f1922,f1522,f5225]) ).
fof(f5225,plain,
( spl0_551
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Log_Opowr(X0,c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f1522,plain,
( spl0_36
<=> ! [X4] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Log_Opowr(X4,c_Transcendental_Otan(c_Transcendental_Opi)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f3555,plain,
( spl0_378
<=> ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f4741,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Log_Opowr(X0,c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)))
| ~ spl0_36
| ~ spl0_116
| ~ spl0_352
| ~ spl0_378
| ~ spl0_459 ),
inference(forward_demodulation,[],[f4740,f3787]) ).
fof(f3787,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_116
| ~ spl0_378 ),
inference(resolution,[],[f3556,f1924]) ).
fof(f1924,plain,
( class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal)
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1922]) ).
fof(f3556,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_378 ),
inference(avatar_component_clause,[],[f3555]) ).
fof(f4740,plain,
( ! [X0] : c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Log_Opowr(X0,c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)))
| ~ spl0_36
| ~ spl0_352
| ~ spl0_459 ),
inference(forward_demodulation,[],[f4727,f3434]) ).
fof(f4727,plain,
( ! [X0] : c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Log_Opowr(X0,c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal))
| ~ spl0_36
| ~ spl0_459 ),
inference(superposition,[],[f4439,f1523]) ).
fof(f1523,plain,
( ! [X4] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Log_Opowr(X4,c_Transcendental_Otan(c_Transcendental_Opi))
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1522]) ).
fof(f5139,plain,
spl0_550,
inference(avatar_split_clause,[],[f1041,f5137]) ).
fof(f5137,plain,
( spl0_550
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f1041,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__zero__iff_0) ).
fof(f5135,plain,
spl0_549,
inference(avatar_split_clause,[],[f1040,f5133]) ).
fof(f5133,plain,
( spl0_549
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f1040,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).
fof(f5131,plain,
spl0_548,
inference(avatar_split_clause,[],[f1034,f5129]) ).
fof(f5129,plain,
( spl0_548
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f1034,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f5127,plain,
spl0_547,
inference(avatar_split_clause,[],[f1033,f5125]) ).
fof(f5125,plain,
( spl0_547
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f1033,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f5123,plain,
spl0_546,
inference(avatar_split_clause,[],[f1030,f5121]) ).
fof(f1030,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
fof(f5119,plain,
spl0_545,
inference(avatar_split_clause,[],[f948,f5117]) ).
fof(f5117,plain,
( spl0_545
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f948,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
fof(f5115,plain,
spl0_544,
inference(avatar_split_clause,[],[f947,f5113]) ).
fof(f5113,plain,
( spl0_544
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f947,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
fof(f5111,plain,
spl0_543,
inference(avatar_split_clause,[],[f936,f5109]) ).
fof(f936,axiom,
! [X40,X39,X6] :
( ~ c_lessequals(X39,X40,tc_RealDef_Oreal)
| ~ c_lessequals(X40,X6,tc_RealDef_Oreal)
| c_lessequals(X39,X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f5107,plain,
spl0_542,
inference(avatar_split_clause,[],[f912,f5105]) ).
fof(f5105,plain,
( spl0_542
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f912,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_1) ).
fof(f5103,plain,
spl0_541,
inference(avatar_split_clause,[],[f904,f5101]) ).
fof(f5101,plain,
( spl0_541
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0) != X1
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f904,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0) != X1
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__iff__nprt__id_1) ).
fof(f5099,plain,
( ~ spl0_150
| spl0_540
| ~ spl0_41
| ~ spl0_432 ),
inference(avatar_split_clause,[],[f4290,f3964,f1544,f5097,f2092]) ).
fof(f4290,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Log_Opowr(X0,X1),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_41
| ~ spl0_432 ),
inference(resolution,[],[f3965,f1545]) ).
fof(f5095,plain,
spl0_539,
inference(avatar_split_clause,[],[f903,f5093]) ).
fof(f5093,plain,
( spl0_539
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f903,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__iff__nprt__id_0) ).
fof(f5091,plain,
spl0_538,
inference(avatar_split_clause,[],[f881,f5089]) ).
fof(f5089,plain,
( spl0_538
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f881,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
fof(f5087,plain,
spl0_537,
inference(avatar_split_clause,[],[f878,f5085]) ).
fof(f5085,plain,
( spl0_537
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f878,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
fof(f5083,plain,
spl0_536,
inference(avatar_split_clause,[],[f875,f5081]) ).
fof(f5081,plain,
( spl0_536
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f875,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
fof(f5079,plain,
spl0_535,
inference(avatar_split_clause,[],[f809,f5077]) ).
fof(f5077,plain,
( spl0_535
<=> ! [X4,X32] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X32,X32,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f809,axiom,
! [X4,X32] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X32,X32,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__minus__mult__self__le_0) ).
fof(f5075,plain,
spl0_534,
inference(avatar_split_clause,[],[f790,f5073]) ).
fof(f5073,plain,
( spl0_534
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f790,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
fof(f5071,plain,
spl0_533,
inference(avatar_split_clause,[],[f771,f5069]) ).
fof(f5069,plain,
( spl0_533
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X10,X4,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f771,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X10,X4,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
fof(f5067,plain,
spl0_532,
inference(avatar_split_clause,[],[f770,f5065]) ).
fof(f5065,plain,
( spl0_532
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X4,X10,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) != X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f770,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X4,X10,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) != X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
fof(f5063,plain,
spl0_531,
inference(avatar_split_clause,[],[f769,f5061]) ).
fof(f769,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_lessequals(X4,X10,X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
fof(f5059,plain,
spl0_530,
inference(avatar_split_clause,[],[f750,f5057]) ).
fof(f5057,plain,
( spl0_530
<=> ! [X6,X0,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X30,X6,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X30,c_HOL_Oabs__class_Oabs(X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f750,axiom,
! [X0,X6,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X30,X6,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X30,c_HOL_Oabs__class_Oabs(X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
fof(f5044,plain,
spl0_529,
inference(avatar_split_clause,[],[f749,f5042]) ).
fof(f5042,plain,
( spl0_529
<=> ! [X6,X0,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X30,X6,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X30,c_HOL_Oabs__class_Oabs(X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f749,axiom,
! [X0,X6,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X30,X6,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X30,c_HOL_Oabs__class_Oabs(X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
fof(f5040,plain,
spl0_528,
inference(avatar_split_clause,[],[f748,f5038]) ).
fof(f5038,plain,
( spl0_528
<=> ! [X6,X0,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X30,X6,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X30,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f748,axiom,
! [X0,X6,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X30,X6,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X30,X0),X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
fof(f5036,plain,
spl0_527,
inference(avatar_split_clause,[],[f747,f5034]) ).
fof(f5034,plain,
( spl0_527
<=> ! [X6,X0,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X30,X6,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X30,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f747,axiom,
! [X0,X6,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X30,X6,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X30,X0),X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
fof(f5032,plain,
spl0_526,
inference(avatar_split_clause,[],[f738,f5030]) ).
fof(f5030,plain,
( spl0_526
<=> ! [X2,X1,X4] : c_Log_Opowr(c_Log_Opowr(X4,X1),X2) = c_Log_Opowr(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f738,axiom,
! [X2,X1,X4] : c_Log_Opowr(c_Log_Opowr(X4,X1),X2) = c_Log_Opowr(X4,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__powr_0) ).
fof(f5028,plain,
spl0_525,
inference(avatar_split_clause,[],[f723,f5026]) ).
fof(f5026,plain,
( spl0_525
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f723,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
fof(f5024,plain,
spl0_524,
inference(avatar_split_clause,[],[f691,f5022]) ).
fof(f5022,plain,
( spl0_524
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f691,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
fof(f5020,plain,
spl0_523,
inference(avatar_split_clause,[],[f675,f5018]) ).
fof(f675,axiom,
! [X10,X4] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__mult_0) ).
fof(f5016,plain,
spl0_522,
inference(avatar_split_clause,[],[f655,f5014]) ).
fof(f5014,plain,
( spl0_522
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X4,X10,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f655,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X4,X10,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
fof(f5012,plain,
spl0_521,
inference(avatar_split_clause,[],[f654,f5010]) ).
fof(f5010,plain,
( spl0_521
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X4,X10,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f654,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(X4,X10,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
fof(f5008,plain,
spl0_520,
inference(avatar_split_clause,[],[f653,f5006]) ).
fof(f653,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_lessequals(X10,X4,X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
fof(f5004,plain,
( ~ spl0_150
| spl0_519
| ~ spl0_41
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f4115,f3912,f1544,f5002,f2092]) ).
fof(f4115,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Log_Opowr(X0,X1),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_41
| ~ spl0_419 ),
inference(resolution,[],[f3913,f1545]) ).
fof(f5000,plain,
spl0_518,
inference(avatar_split_clause,[],[f517,f4998]) ).
fof(f4998,plain,
( spl0_518
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f517,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__abs_0) ).
fof(f4996,plain,
spl0_517,
inference(avatar_split_clause,[],[f512,f4994]) ).
fof(f4994,plain,
( spl0_517
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0) != X1
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f512,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0) != X1
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__zero__iff__pprt__id_1) ).
fof(f4992,plain,
spl0_516,
inference(avatar_split_clause,[],[f511,f4990]) ).
fof(f4990,plain,
( spl0_516
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f511,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__zero__iff__pprt__id_0) ).
fof(f4988,plain,
spl0_515,
inference(avatar_split_clause,[],[f448,f4986]) ).
fof(f4986,plain,
( spl0_515
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f448,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
fof(f4984,plain,
spl0_514,
inference(avatar_split_clause,[],[f442,f4982]) ).
fof(f4982,plain,
( spl0_514
<=> ! [X4,X0,X10] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| X4 = X10
| c_RealVector_Oof__real(X4,X0) != c_RealVector_Oof__real(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f442,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| X4 = X10
| c_RealVector_Oof__real(X4,X0) != c_RealVector_Oof__real(X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__iff_0) ).
fof(f4980,plain,
spl0_513,
inference(avatar_split_clause,[],[f414,f4978]) ).
fof(f4978,plain,
( spl0_513
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X4,X0),c_HOL_Oabs__class_Oabs(X4,X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f414,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X4,X0),c_HOL_Oabs__class_Oabs(X4,X0),X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__sgn__abs_0) ).
fof(f4976,plain,
spl0_512,
inference(avatar_split_clause,[],[f324,f4974]) ).
fof(f4974,plain,
( spl0_512
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X10,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X4,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f324,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X10,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X4,X0),X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
fof(f4972,plain,
spl0_511,
inference(avatar_split_clause,[],[f323,f4970]) ).
fof(f4970,plain,
( spl0_511
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X10,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X4,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f323,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X10,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X4,X0),X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
fof(f4968,plain,
spl0_510,
inference(avatar_split_clause,[],[f322,f4966]) ).
fof(f4966,plain,
( spl0_510
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X10,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ouminus__class_Ouminus(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f322,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X10,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ouminus__class_Ouminus(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
fof(f4964,plain,
spl0_509,
inference(avatar_split_clause,[],[f321,f4962]) ).
fof(f4962,plain,
( spl0_509
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X10,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ouminus__class_Ouminus(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f321,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X10,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ouminus__class_Ouminus(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
fof(f4954,plain,
spl0_508,
inference(avatar_split_clause,[],[f303,f4952]) ).
fof(f4952,plain,
( spl0_508
<=> ! [X6,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(X6,X0) = c_HOL_Otimes__class_Otimes(X6,c_HOL_Osgn__class_Osgn(X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f303,axiom,
! [X0,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(X6,X0) = c_HOL_Otimes__class_Otimes(X6,c_HOL_Osgn__class_Osgn(X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__sgn_0) ).
fof(f4950,plain,
spl0_507,
inference(avatar_split_clause,[],[f253,f4948]) ).
fof(f4948,plain,
( spl0_507
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f253,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__lattice_0) ).
fof(f4946,plain,
spl0_506,
inference(avatar_split_clause,[],[f237,f4944]) ).
fof(f4944,plain,
( spl0_506
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f237,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f4942,plain,
spl0_505,
inference(avatar_split_clause,[],[f224,f4940]) ).
fof(f4940,plain,
( spl0_505
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f224,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
fof(f4938,plain,
spl0_504,
inference(avatar_split_clause,[],[f154,f4936]) ).
fof(f4936,plain,
( spl0_504
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f154,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f4934,plain,
spl0_503,
inference(avatar_split_clause,[],[f42,f4932]) ).
fof(f4932,plain,
( spl0_503
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f42,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_prts_0) ).
fof(f4840,plain,
( ~ spl0_150
| ~ spl0_502
| ~ spl0_58
| ~ spl0_432 ),
inference(avatar_split_clause,[],[f4289,f3964,f1632,f4837,f2092]) ).
fof(f4837,plain,
( spl0_502
<=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f1632,plain,
( spl0_58
<=> c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f4289,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl0_58
| ~ spl0_432 ),
inference(resolution,[],[f3965,f1634]) ).
fof(f1634,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f1632]) ).
fof(f4614,plain,
( ~ spl0_150
| ~ spl0_501
| ~ spl0_58
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f4114,f3912,f1632,f4611,f2092]) ).
fof(f4611,plain,
( spl0_501
<=> c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f4114,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl0_58
| ~ spl0_419 ),
inference(resolution,[],[f3913,f1634]) ).
fof(f4609,plain,
( spl0_499
| ~ spl0_500 ),
inference(avatar_split_clause,[],[f1072,f4606,f4602]) ).
fof(f4602,plain,
( spl0_499
<=> c_OrderedGroup_Olordered__ab__group__add__class_Opprt(v_x,t_a) = c_Lattices_Oupper__semilattice__class_Osup(v_x,c_HOL_Ozero__class_Ozero(t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f4606,plain,
( spl0_500
<=> class_OrderedGroup_Olordered__ab__group__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f1072,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(t_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(v_x,t_a) = c_Lattices_Oupper__semilattice__class_Osup(v_x,c_HOL_Ozero__class_Ozero(t_a),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pprt__def__raw_0) ).
fof(f4600,plain,
spl0_498,
inference(avatar_split_clause,[],[f1046,f4598]) ).
fof(f4598,plain,
( spl0_498
<=> ! [X4,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f1046,axiom,
! [X0,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f4596,plain,
spl0_497,
inference(avatar_split_clause,[],[f1028,f4594]) ).
fof(f4594,plain,
( spl0_497
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f1028,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f4592,plain,
spl0_496,
inference(avatar_split_clause,[],[f1024,f4590]) ).
fof(f4590,plain,
( spl0_496
<=> ! [X4,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f1024,axiom,
! [X0,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f4588,plain,
spl0_495,
inference(avatar_split_clause,[],[f1005,f4586]) ).
fof(f4586,plain,
( spl0_495
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f1005,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f4584,plain,
spl0_494,
inference(avatar_split_clause,[],[f1003,f4582]) ).
fof(f4582,plain,
( spl0_494
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f1003,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
fof(f4580,plain,
spl0_493,
inference(avatar_split_clause,[],[f853,f4578]) ).
fof(f4578,plain,
( spl0_493
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f853,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f4576,plain,
spl0_492,
inference(avatar_split_clause,[],[f802,f4574]) ).
fof(f4574,plain,
( spl0_492
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(X10,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f802,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(X10,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
fof(f4572,plain,
spl0_491,
inference(avatar_split_clause,[],[f801,f4570]) ).
fof(f801,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0) = c_Lattices_Oupper__semilattice__class_Osup(X10,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
fof(f4568,plain,
( spl0_490
| ~ spl0_312
| ~ spl0_435 ),
inference(avatar_split_clause,[],[f4068,f3976,f3051,f4565]) ).
fof(f4565,plain,
( spl0_490
<=> c_lessequals(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f3051,plain,
( spl0_312
<=> ! [X4] : c_lessequals(c_Transcendental_Osin(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f4068,plain,
( c_lessequals(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_312
| ~ spl0_435 ),
inference(superposition,[],[f3052,f3978]) ).
fof(f3052,plain,
( ! [X4] : c_lessequals(c_Transcendental_Osin(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_312 ),
inference(avatar_component_clause,[],[f3051]) ).
fof(f4563,plain,
spl0_489,
inference(avatar_split_clause,[],[f775,f4561]) ).
fof(f4561,plain,
( spl0_489
<=> ! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f775,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
fof(f4559,plain,
spl0_488,
inference(avatar_split_clause,[],[f756,f4557]) ).
fof(f4557,plain,
( spl0_488
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f756,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
fof(f4555,plain,
spl0_487,
inference(avatar_split_clause,[],[f743,f4553]) ).
fof(f4553,plain,
( spl0_487
<=> ! [X4] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f743,axiom,
! [X4] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__1__iff_0) ).
fof(f4551,plain,
spl0_486,
inference(avatar_split_clause,[],[f742,f4549]) ).
fof(f4549,plain,
( spl0_486
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f742,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__1__iff_1) ).
fof(f4547,plain,
spl0_485,
inference(avatar_split_clause,[],[f731,f4545]) ).
fof(f4545,plain,
( spl0_485
<=> ! [X10] :
( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f731,axiom,
! [X10] :
( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__1__iff_0) ).
fof(f4543,plain,
spl0_484,
inference(avatar_split_clause,[],[f730,f4541]) ).
fof(f4541,plain,
( spl0_484
<=> ! [X10] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f730,axiom,
! [X10] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__1__iff_1) ).
fof(f4539,plain,
spl0_483,
inference(avatar_split_clause,[],[f665,f4537]) ).
fof(f4537,plain,
( spl0_483
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f665,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).
fof(f4535,plain,
spl0_482,
inference(avatar_split_clause,[],[f664,f4533]) ).
fof(f4533,plain,
( spl0_482
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f664,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
fof(f4531,plain,
spl0_481,
inference(avatar_split_clause,[],[f663,f4529]) ).
fof(f4529,plain,
( spl0_481
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f663,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
fof(f4527,plain,
spl0_480,
inference(avatar_split_clause,[],[f660,f4525]) ).
fof(f4525,plain,
( spl0_480
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) = c_Lattices_Olower__semilattice__class_Oinf(X10,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f660,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) = c_Lattices_Olower__semilattice__class_Oinf(X10,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f4521,plain,
spl0_479,
inference(avatar_split_clause,[],[f659,f4519]) ).
fof(f659,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0) = c_Lattices_Olower__semilattice__class_Oinf(X10,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f4517,plain,
spl0_478,
inference(avatar_split_clause,[],[f657,f4515]) ).
fof(f4515,plain,
( spl0_478
<=> ! [X10] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f657,axiom,
! [X10] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__1__iff_1) ).
fof(f4513,plain,
spl0_477,
inference(avatar_split_clause,[],[f656,f4511]) ).
fof(f4511,plain,
( spl0_477
<=> ! [X10] :
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f656,axiom,
! [X10] :
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__1__iff_0) ).
fof(f4509,plain,
spl0_476,
inference(avatar_split_clause,[],[f579,f4507]) ).
fof(f4507,plain,
( spl0_476
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f579,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f4505,plain,
spl0_475,
inference(avatar_split_clause,[],[f577,f4503]) ).
fof(f4503,plain,
( spl0_475
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X8,X0) = c_HOL_Oplus__class_Oplus(X8,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f577,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X8,X0) = c_HOL_Oplus__class_Oplus(X8,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f4501,plain,
spl0_474,
inference(avatar_split_clause,[],[f568,f4499]) ).
fof(f4499,plain,
( spl0_474
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X4,X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f568,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X4,X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
fof(f4497,plain,
spl0_473,
inference(avatar_split_clause,[],[f562,f4495]) ).
fof(f4495,plain,
( spl0_473
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f562,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
fof(f4493,plain,
spl0_472,
inference(avatar_split_clause,[],[f521,f4491]) ).
fof(f4491,plain,
( spl0_472
<=> ! [X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oone__class_Oone(X0) = c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f521,axiom,
! [X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oone__class_Oone(X0) = c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__zero_0) ).
fof(f4489,plain,
spl0_471,
inference(avatar_split_clause,[],[f487,f4487]) ).
fof(f4487,plain,
( spl0_471
<=> ! [X4,X0,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X4,X10,X0) = c_HOL_Otimes__class_Otimes(X10,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f487,axiom,
! [X10,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X4,X10,X0) = c_HOL_Otimes__class_Otimes(X10,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
fof(f4485,plain,
spl0_470,
inference(avatar_split_clause,[],[f481,f4483]) ).
fof(f4483,plain,
( spl0_470
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f481,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
fof(f4481,plain,
( ~ spl0_150
| ~ spl0_469
| ~ spl0_13
| ~ spl0_432 ),
inference(avatar_split_clause,[],[f4294,f3964,f1401,f4478,f2092]) ).
fof(f4478,plain,
( spl0_469
<=> c_HOL_Oord__class_Oless(v_x,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f4294,plain,
( ~ c_HOL_Oord__class_Oless(v_x,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl0_13
| ~ spl0_432 ),
inference(resolution,[],[f3965,f1403]) ).
fof(f4476,plain,
spl0_468,
inference(avatar_split_clause,[],[f480,f4474]) ).
fof(f4474,plain,
( spl0_468
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f480,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X2,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f4472,plain,
spl0_467,
inference(avatar_split_clause,[],[f450,f4470]) ).
fof(f4470,plain,
( spl0_467
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f450,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
fof(f4468,plain,
spl0_466,
inference(avatar_split_clause,[],[f441,f4466]) ).
fof(f4466,plain,
( spl0_466
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f441,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
fof(f4464,plain,
spl0_465,
inference(avatar_split_clause,[],[f432,f4462]) ).
fof(f432,axiom,
! [X2,X1,X4] : c_Log_Opowr(c_Log_Opowr(X4,X1),X2) = c_Log_Opowr(c_Log_Opowr(X4,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__powr__swap_0) ).
fof(f4460,plain,
spl0_464,
inference(avatar_split_clause,[],[f385,f4458]) ).
fof(f4458,plain,
( spl0_464
<=> ! [X4,X0,X10] :
( ~ class_RealVector_Ometric__space(X0)
| c_RealVector_Odist__class_Odist(X4,X10,X0) = c_RealVector_Odist__class_Odist(X10,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f385,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Ometric__space(X0)
| c_RealVector_Odist__class_Odist(X4,X10,X0) = c_RealVector_Odist__class_Odist(X10,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__commute_0) ).
fof(f4456,plain,
spl0_463,
inference(avatar_split_clause,[],[f344,f4454]) ).
fof(f4454,plain,
( spl0_463
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f344,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
fof(f4452,plain,
spl0_462,
inference(avatar_split_clause,[],[f304,f4450]) ).
fof(f4450,plain,
( spl0_462
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f304,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
fof(f4448,plain,
spl0_461,
inference(avatar_split_clause,[],[f298,f4446]) ).
fof(f4446,plain,
( spl0_461
<=> ! [X4] :
( c_lessequals(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f298,axiom,
! [X4] :
( c_lessequals(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__1__iff_0) ).
fof(f4444,plain,
spl0_460,
inference(avatar_split_clause,[],[f297,f4442]) ).
fof(f4442,plain,
( spl0_460
<=> ! [X4] :
( ~ c_lessequals(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f297,axiom,
! [X4] :
( ~ c_lessequals(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__1__iff_1) ).
fof(f4440,plain,
spl0_459,
inference(avatar_split_clause,[],[f289,f4438]) ).
fof(f289,axiom,
! [X1,X4] : c_Log_Opowr(X4,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_Log_Opowr(X4,X1),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__minus_0) ).
fof(f4432,plain,
spl0_458,
inference(avatar_split_clause,[],[f233,f4430]) ).
fof(f4430,plain,
( spl0_458
<=> ! [X29,X14] :
( X14 = X29
| ~ c_lessequals(X14,X29,tc_RealDef_Oreal)
| ~ c_lessequals(X29,X14,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f233,axiom,
! [X29,X14] :
( X14 = X29
| ~ c_lessequals(X14,X29,tc_RealDef_Oreal)
| ~ c_lessequals(X29,X14,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f4428,plain,
spl0_457,
inference(avatar_split_clause,[],[f223,f4426]) ).
fof(f4426,plain,
( spl0_457
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f223,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
fof(f4424,plain,
spl0_456,
inference(avatar_split_clause,[],[f169,f4422]) ).
fof(f4422,plain,
( spl0_456
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(X1,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f169,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(X1,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).
fof(f4420,plain,
spl0_455,
inference(avatar_split_clause,[],[f114,f4418]) ).
fof(f4418,plain,
( spl0_455
<=> ! [X0,X15] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(X15,X0) = c_RealVector_OscaleR__class_OscaleR(X15,c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f114,axiom,
! [X0,X15] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(X15,X0) = c_RealVector_OscaleR__class_OscaleR(X15,c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__def_0) ).
fof(f4416,plain,
spl0_454,
inference(avatar_split_clause,[],[f93,f4414]) ).
fof(f4414,plain,
( spl0_454
<=> ! [X4,X10] :
( X4 = X10
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f93,axiom,
! [X10,X4] :
( X4 = X10
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_2) ).
fof(f4403,plain,
( ~ spl0_150
| ~ spl0_453
| ~ spl0_13
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f4119,f3912,f1401,f4400,f2092]) ).
fof(f4400,plain,
( spl0_453
<=> c_lessequals(v_x,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f4119,plain,
( ~ c_lessequals(v_x,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl0_13
| ~ spl0_419 ),
inference(resolution,[],[f3913,f1403]) ).
fof(f4212,plain,
( ~ spl0_150
| ~ spl0_452
| ~ spl0_14
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f4118,f3912,f1406,f4209,f2092]) ).
fof(f4209,plain,
( spl0_452
<=> c_lessequals(c_Transcendental_Opi,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f4118,plain,
( ~ c_lessequals(c_Transcendental_Opi,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl0_14
| ~ spl0_419 ),
inference(resolution,[],[f3913,f1408]) ).
fof(f4044,plain,
spl0_451,
inference(avatar_split_clause,[],[f1250,f4042]) ).
fof(f4042,plain,
( spl0_451
<=> ! [X4] :
( c_Transcendental_Osin(X4) = c_Transcendental_Otan(c_Transcendental_Opi)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f1250,plain,
! [X4] :
( c_Transcendental_Osin(X4) = c_Transcendental_Otan(c_Transcendental_Opi)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(X4) ),
inference(forward_demodulation,[],[f1075,f908]) ).
fof(f908,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Otan(c_Transcendental_Opi),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__pi_0) ).
fof(f1075,axiom,
! [X4] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(X4)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__one__sin__zero_0) ).
fof(f4040,plain,
spl0_450,
inference(avatar_split_clause,[],[f1042,f4038]) ).
fof(f4038,plain,
( spl0_450
<=> ! [X4,X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Transcendental_Oexp(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f1042,axiom,
! [X0,X4] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Transcendental_Oexp(X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__not__eq__zero_0) ).
fof(f4036,plain,
spl0_449,
inference(avatar_split_clause,[],[f1039,f4034]) ).
fof(f4034,plain,
( spl0_449
<=> ! [X0,X10] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f1039,axiom,
! [X10,X0] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
fof(f4032,plain,
spl0_448,
inference(avatar_split_clause,[],[f1036,f4030]) ).
fof(f4030,plain,
( spl0_448
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f1036,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
fof(f4028,plain,
spl0_447,
inference(avatar_split_clause,[],[f1032,f4026]) ).
fof(f4026,plain,
( spl0_447
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f1032,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_2) ).
fof(f4024,plain,
( spl0_446
| ~ spl0_11
| ~ spl0_352
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f3868,f3666,f3433,f1391,f4021]) ).
fof(f4021,plain,
( spl0_446
<=> c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f1391,plain,
( spl0_11
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Osin(c_Transcendental_Opi) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f3868,plain,
( c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal))
| ~ spl0_11
| ~ spl0_352
| ~ spl0_405 ),
inference(forward_demodulation,[],[f3864,f3434]) ).
fof(f3864,plain,
( c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal))
| ~ spl0_11
| ~ spl0_405 ),
inference(superposition,[],[f3667,f1393]) ).
fof(f1393,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Osin(c_Transcendental_Opi)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f1391]) ).
fof(f4019,plain,
spl0_445,
inference(avatar_split_clause,[],[f1031,f4017]) ).
fof(f4017,plain,
( spl0_445
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f1031,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ozero__right_0) ).
fof(f4015,plain,
spl0_444,
inference(avatar_split_clause,[],[f1027,f4013]) ).
fof(f4013,plain,
( spl0_444
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f1027,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).
fof(f4011,plain,
spl0_443,
inference(avatar_split_clause,[],[f1018,f4009]) ).
fof(f4009,plain,
( spl0_443
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f1018,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__0_0) ).
fof(f4007,plain,
spl0_442,
inference(avatar_split_clause,[],[f1017,f4005]) ).
fof(f4005,plain,
( spl0_442
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f1017,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__by__0_0) ).
fof(f4003,plain,
spl0_441,
inference(avatar_split_clause,[],[f997,f4001]) ).
fof(f4001,plain,
( spl0_441
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f997,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f3999,plain,
spl0_440,
inference(avatar_split_clause,[],[f996,f3997]) ).
fof(f3997,plain,
( spl0_440
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f996,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f3995,plain,
spl0_439,
inference(avatar_split_clause,[],[f994,f3993]) ).
fof(f3993,plain,
( spl0_439
<=> ! [X2,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f994,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
fof(f3991,plain,
spl0_438,
inference(avatar_split_clause,[],[f992,f3989]) ).
fof(f3989,plain,
( spl0_438
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f992,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
fof(f3987,plain,
spl0_437,
inference(avatar_split_clause,[],[f990,f3985]) ).
fof(f3985,plain,
( spl0_437
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f990,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f3983,plain,
spl0_436,
inference(avatar_split_clause,[],[f989,f3981]) ).
fof(f3981,plain,
( spl0_436
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f989,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f3979,plain,
( spl0_435
| ~ spl0_8
| ~ spl0_352
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f3867,f3666,f3433,f1376,f3976]) ).
fof(f3867,plain,
( c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(v_x,tc_RealDef_Oreal))
| ~ spl0_8
| ~ spl0_352
| ~ spl0_405 ),
inference(forward_demodulation,[],[f3863,f3434]) ).
fof(f3863,plain,
( c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(v_x,tc_RealDef_Oreal))
| ~ spl0_8
| ~ spl0_405 ),
inference(superposition,[],[f3667,f1378]) ).
fof(f3974,plain,
spl0_434,
inference(avatar_split_clause,[],[f988,f3972]) ).
fof(f3972,plain,
( spl0_434
<=> ! [X4,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f988,axiom,
! [X10,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X10,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f3970,plain,
spl0_433,
inference(avatar_split_clause,[],[f986,f3968]) ).
fof(f3968,plain,
( spl0_433
<=> ! [X4,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X10,X0)
| c_lessequals(X10,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f986,axiom,
! [X10,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X10,X0)
| c_lessequals(X10,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f3966,plain,
spl0_432,
inference(avatar_split_clause,[],[f984,f3964]) ).
fof(f984,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f3962,plain,
spl0_431,
inference(avatar_split_clause,[],[f922,f3960]) ).
fof(f3960,plain,
( spl0_431
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f922,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
fof(f3958,plain,
spl0_430,
inference(avatar_split_clause,[],[f889,f3956]) ).
fof(f3956,plain,
( spl0_430
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f889,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f3954,plain,
spl0_429,
inference(avatar_split_clause,[],[f888,f3952]) ).
fof(f3952,plain,
( spl0_429
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f888,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f3950,plain,
spl0_428,
inference(avatar_split_clause,[],[f887,f3948]) ).
fof(f3948,plain,
( spl0_428
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f887,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f3946,plain,
spl0_427,
inference(avatar_split_clause,[],[f817,f3944]) ).
fof(f3944,plain,
( spl0_427
<=> ! [X4,X10] :
( ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f817,axiom,
! [X10,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_1) ).
fof(f3942,plain,
spl0_426,
inference(avatar_split_clause,[],[f816,f3940]) ).
fof(f3940,plain,
( spl0_426
<=> ! [X4,X10] :
( c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f816,axiom,
! [X10,X4] :
( c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_0) ).
fof(f3938,plain,
spl0_425,
inference(avatar_split_clause,[],[f768,f3936]) ).
fof(f3936,plain,
( spl0_425
<=> ! [X4,X0,X10] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| c_lessequals(X4,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f768,axiom,
! [X10,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| c_lessequals(X4,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f3934,plain,
spl0_424,
inference(avatar_split_clause,[],[f766,f3932]) ).
fof(f3932,plain,
( spl0_424
<=> ! [X4,X0,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| c_lessequals(X4,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f766,axiom,
! [X10,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0)
| c_lessequals(X4,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f3930,plain,
spl0_423,
inference(avatar_split_clause,[],[f744,f3928]) ).
fof(f3928,plain,
( spl0_423
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f744,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
fof(f3926,plain,
spl0_422,
inference(avatar_split_clause,[],[f710,f3924]) ).
fof(f3924,plain,
( spl0_422
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f710,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
fof(f3922,plain,
spl0_421,
inference(avatar_split_clause,[],[f615,f3920]) ).
fof(f615,axiom,
! [X10,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X10,X4,X0)
| c_HOL_Oord__class_Oless(X4,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
fof(f3918,plain,
spl0_420,
inference(avatar_split_clause,[],[f614,f3916]) ).
fof(f3916,plain,
( spl0_420
<=> ! [X4,X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X10,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f614,axiom,
! [X10,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X10,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
fof(f3914,plain,
spl0_419,
inference(avatar_split_clause,[],[f610,f3912]) ).
fof(f610,axiom,
! [X10,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X10,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f3910,plain,
spl0_418,
inference(avatar_split_clause,[],[f546,f3908]) ).
fof(f546,axiom,
! [X10,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(X4),c_Transcendental_Oarctan(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arctan__monotone_0) ).
fof(f3906,plain,
spl0_417,
inference(avatar_split_clause,[],[f520,f3904]) ).
fof(f3904,plain,
( spl0_417
<=> ! [X4,X10] :
( c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f520,axiom,
! [X10,X4] :
( c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_0) ).
fof(f3902,plain,
spl0_416,
inference(avatar_split_clause,[],[f519,f3900]) ).
fof(f3900,plain,
( spl0_416
<=> ! [X4,X10] :
( ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f519,axiom,
! [X10,X4] :
( ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_1) ).
fof(f3898,plain,
spl0_415,
inference(avatar_split_clause,[],[f499,f3896]) ).
fof(f3896,plain,
( spl0_415
<=> ! [X9,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f499,axiom,
! [X0,X9] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f3894,plain,
( ~ spl0_414
| ~ spl0_22
| ~ spl0_407 ),
inference(avatar_split_clause,[],[f3848,f3790,f1451,f3891]) ).
fof(f3891,plain,
( spl0_414
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Ocos(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f1451,plain,
( spl0_22
<=> ! [X4] : c_Transcendental_Ocos(c_Transcendental_Oarctan(X4)) != c_Transcendental_Otan(c_Transcendental_Opi) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f3790,plain,
( spl0_407
<=> c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Oarctan(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f3848,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) != c_Transcendental_Ocos(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)))
| ~ spl0_22
| ~ spl0_407 ),
inference(superposition,[],[f1452,f3792]) ).
fof(f3792,plain,
( c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Oarctan(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)))
| ~ spl0_407 ),
inference(avatar_component_clause,[],[f3790]) ).
fof(f1452,plain,
( ! [X4] : c_Transcendental_Ocos(c_Transcendental_Oarctan(X4)) != c_Transcendental_Otan(c_Transcendental_Opi)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1451]) ).
fof(f3889,plain,
spl0_413,
inference(avatar_split_clause,[],[f418,f3887]) ).
fof(f418,axiom,
! [X10,X4] :
( ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Oarctan(X4),c_Transcendental_Oarctan(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arctan__monotone_H_0) ).
fof(f3885,plain,
spl0_412,
inference(avatar_split_clause,[],[f360,f3883]) ).
fof(f3883,plain,
( spl0_412
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f360,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
fof(f3881,plain,
spl0_411,
inference(avatar_split_clause,[],[f350,f3879]) ).
fof(f3879,plain,
( spl0_411
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f350,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f3877,plain,
spl0_410,
inference(avatar_split_clause,[],[f196,f3875]) ).
fof(f3875,plain,
( spl0_410
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f196,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f3873,plain,
spl0_409,
inference(avatar_split_clause,[],[f107,f3871]) ).
fof(f3871,plain,
( spl0_409
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f107,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
fof(f3824,plain,
( spl0_408
| ~ spl0_28
| ~ spl0_352
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f3784,f3539,f3433,f1479,f3821]) ).
fof(f3821,plain,
( spl0_408
<=> c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) = c_NthRoot_Osqrt(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f1479,plain,
( spl0_28
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_NthRoot_Osqrt(c_Transcendental_Otan(c_Transcendental_Opi)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f3539,plain,
( spl0_374
<=> ! [X4] : c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f3784,plain,
( c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) = c_NthRoot_Osqrt(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)))
| ~ spl0_28
| ~ spl0_352
| ~ spl0_374 ),
inference(forward_demodulation,[],[f3781,f3434]) ).
fof(f3781,plain,
( c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal))
| ~ spl0_28
| ~ spl0_374 ),
inference(superposition,[],[f3540,f1481]) ).
fof(f1481,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_NthRoot_Osqrt(c_Transcendental_Otan(c_Transcendental_Opi))
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f1479]) ).
fof(f3540,plain,
( ! [X4] : c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(X4),tc_RealDef_Oreal)
| ~ spl0_374 ),
inference(avatar_component_clause,[],[f3539]) ).
fof(f3793,plain,
( spl0_407
| ~ spl0_26
| ~ spl0_352
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f3718,f3531,f3433,f1469,f3790]) ).
fof(f3531,plain,
( spl0_372
<=> ! [X4] : c_Transcendental_Oarctan(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Oarctan(X4),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f3718,plain,
( c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Oarctan(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)))
| ~ spl0_26
| ~ spl0_352
| ~ spl0_372 ),
inference(forward_demodulation,[],[f3716,f3434]) ).
fof(f3716,plain,
( c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) = c_Transcendental_Oarctan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal))
| ~ spl0_26
| ~ spl0_372 ),
inference(superposition,[],[f3532,f1471]) ).
fof(f3532,plain,
( ! [X4] : c_Transcendental_Oarctan(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Oarctan(X4),tc_RealDef_Oreal)
| ~ spl0_372 ),
inference(avatar_component_clause,[],[f3531]) ).
fof(f3688,plain,
( spl0_406
| ~ spl0_25
| ~ spl0_352 ),
inference(avatar_split_clause,[],[f3676,f3433,f1464,f3685]) ).
fof(f3685,plain,
( spl0_406
<=> c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Otan(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f1464,plain,
( spl0_25
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Otan(c_Transcendental_Otan(c_Transcendental_Opi)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f3676,plain,
( c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Otan(c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal)))
| ~ spl0_25
| ~ spl0_352 ),
inference(forward_demodulation,[],[f3673,f3434]) ).
fof(f3673,plain,
( c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) = c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal))
| ~ spl0_25
| ~ spl0_352 ),
inference(superposition,[],[f3434,f1466]) ).
fof(f1466,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Otan(c_Transcendental_Otan(c_Transcendental_Opi))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f1464]) ).
fof(f3668,plain,
spl0_405,
inference(avatar_split_clause,[],[f1077,f3666]) ).
fof(f1077,axiom,
! [X4] : c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X4),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__minus_0) ).
fof(f3664,plain,
spl0_404,
inference(avatar_split_clause,[],[f1050,f3662]) ).
fof(f3662,plain,
( spl0_404
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f1050,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f3660,plain,
spl0_403,
inference(avatar_split_clause,[],[f1049,f3658]) ).
fof(f3658,plain,
( spl0_403
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f1049,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f3656,plain,
spl0_402,
inference(avatar_split_clause,[],[f1048,f3654]) ).
fof(f3654,plain,
( spl0_402
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f1048,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f3652,plain,
spl0_401,
inference(avatar_split_clause,[],[f1045,f3650]) ).
fof(f3650,plain,
( spl0_401
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f1045,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f3648,plain,
spl0_400,
inference(avatar_split_clause,[],[f1044,f3646]) ).
fof(f3646,plain,
( spl0_400
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f1044,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f3644,plain,
spl0_399,
inference(avatar_split_clause,[],[f1043,f3642]) ).
fof(f3642,plain,
( spl0_399
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f1043,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f3640,plain,
spl0_398,
inference(avatar_split_clause,[],[f1029,f3638]) ).
fof(f3638,plain,
( spl0_398
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f1029,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
fof(f3636,plain,
spl0_397,
inference(avatar_split_clause,[],[f1026,f3634]) ).
fof(f3634,plain,
( spl0_397
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f1026,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pprt__0_0) ).
fof(f3629,plain,
spl0_396,
inference(avatar_split_clause,[],[f1023,f3627]) ).
fof(f3627,plain,
( spl0_396
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f1023,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
fof(f3625,plain,
spl0_395,
inference(avatar_split_clause,[],[f1022,f3623]) ).
fof(f3623,plain,
( spl0_395
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f1022,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f3621,plain,
spl0_394,
inference(avatar_split_clause,[],[f1020,f3619]) ).
fof(f3619,plain,
( spl0_394
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f1020,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f3617,plain,
spl0_393,
inference(avatar_split_clause,[],[f1009,f3615]) ).
fof(f3615,plain,
( spl0_393
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f1009,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nprt__0_0) ).
fof(f3613,plain,
spl0_392,
inference(avatar_split_clause,[],[f1006,f3611]) ).
fof(f3611,plain,
( spl0_392
<=> ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f1006,axiom,
! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
fof(f3609,plain,
spl0_391,
inference(avatar_split_clause,[],[f1000,f3607]) ).
fof(f3607,plain,
( spl0_391
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f1000,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
fof(f3605,plain,
spl0_390,
inference(avatar_split_clause,[],[f999,f3603]) ).
fof(f3603,plain,
( spl0_390
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f999,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).
fof(f3601,plain,
spl0_389,
inference(avatar_split_clause,[],[f980,f3599]) ).
fof(f3599,plain,
( spl0_389
<=> ! [X4] : c_NthRoot_Osqrt(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f980,axiom,
! [X4] : c_NthRoot_Osqrt(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_NthRoot_Osqrt(X4),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__inverse_0) ).
fof(f3597,plain,
spl0_388,
inference(avatar_split_clause,[],[f975,f3595]) ).
fof(f3595,plain,
( spl0_388
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f975,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
fof(f3593,plain,
spl0_387,
inference(avatar_split_clause,[],[f886,f3591]) ).
fof(f3591,plain,
( spl0_387
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f886,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__zero_0) ).
fof(f3589,plain,
( spl0_386
| ~ spl0_211
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f3343,f3292,f2403,f3587]) ).
fof(f3587,plain,
( spl0_386
<=> ! [X0] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f2403,plain,
( spl0_211
<=> ! [X4] :
( c_lessequals(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f3343,plain,
( ! [X0] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_211
| ~ spl0_341 ),
inference(resolution,[],[f3293,f2404]) ).
fof(f2404,plain,
( ! [X4] :
( ~ c_lessequals(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f2403]) ).
fof(f3585,plain,
spl0_385,
inference(avatar_split_clause,[],[f885,f3583]) ).
fof(f3583,plain,
( spl0_385
<=> ! [X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f885,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn0_0) ).
fof(f3581,plain,
spl0_384,
inference(avatar_split_clause,[],[f884,f3579]) ).
fof(f3579,plain,
( spl0_384
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f884,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).
fof(f3577,plain,
spl0_383,
inference(avatar_split_clause,[],[f883,f3575]) ).
fof(f3575,plain,
( spl0_383
<=> ! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f883,axiom,
! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
fof(f3573,plain,
spl0_382,
inference(avatar_split_clause,[],[f879,f3571]) ).
fof(f3571,plain,
( spl0_382
<=> ! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f879,axiom,
! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
fof(f3569,plain,
spl0_381,
inference(avatar_split_clause,[],[f863,f3567]) ).
fof(f3567,plain,
( spl0_381
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f863,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__by__1_0) ).
fof(f3565,plain,
spl0_380,
inference(avatar_split_clause,[],[f859,f3563]) ).
fof(f859,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
fof(f3561,plain,
spl0_379,
inference(avatar_split_clause,[],[f785,f3559]) ).
fof(f3559,plain,
( spl0_379
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f785,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
fof(f3557,plain,
spl0_378,
inference(avatar_split_clause,[],[f777,f3555]) ).
fof(f777,axiom,
! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).
fof(f3553,plain,
spl0_377,
inference(avatar_split_clause,[],[f694,f3551]) ).
fof(f3551,plain,
( spl0_377
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f694,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nprt__le__zero_0) ).
fof(f3549,plain,
spl0_376,
inference(avatar_split_clause,[],[f674,f3547]) ).
fof(f3547,plain,
( spl0_376
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f674,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__one_0) ).
fof(f3545,plain,
( spl0_375
| ~ spl0_210
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f3327,f3280,f2397,f3543]) ).
fof(f3543,plain,
( spl0_375
<=> ! [X0] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f3327,plain,
( ! [X0] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_210
| ~ spl0_338 ),
inference(resolution,[],[f3281,f2398]) ).
fof(f3541,plain,
spl0_374,
inference(avatar_split_clause,[],[f569,f3539]) ).
fof(f569,axiom,
! [X4] : c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(X4),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__minus_0) ).
fof(f3537,plain,
spl0_373,
inference(avatar_split_clause,[],[f488,f3535]) ).
fof(f488,axiom,
! [X29,X14] : c_HOL_Otimes__class_Otimes(X14,X29,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X29,X14,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
fof(f3533,plain,
spl0_372,
inference(avatar_split_clause,[],[f476,f3531]) ).
fof(f476,axiom,
! [X4] : c_Transcendental_Oarctan(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Oarctan(X4),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arctan__minus_0) ).
fof(f3529,plain,
spl0_371,
inference(avatar_split_clause,[],[f466,f3527]) ).
fof(f3527,plain,
( spl0_371
<=> ! [X6,X2,X0] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f466,axiom,
! [X2,X0,X6] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvdI_0) ).
fof(f3525,plain,
spl0_370,
inference(avatar_split_clause,[],[f465,f3523]) ).
fof(f465,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
fof(f3521,plain,
spl0_369,
inference(avatar_split_clause,[],[f464,f3519]) ).
fof(f464,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
fof(f3517,plain,
spl0_368,
inference(avatar_split_clause,[],[f462,f3515]) ).
fof(f3515,plain,
( spl0_368
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f462,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(f3513,plain,
spl0_367,
inference(avatar_split_clause,[],[f460,f3511]) ).
fof(f3511,plain,
( spl0_367
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f460,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X4,X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
fof(f3509,plain,
spl0_366,
inference(avatar_split_clause,[],[f459,f3507]) ).
fof(f3507,plain,
( spl0_366
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f459,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
fof(f3505,plain,
spl0_365,
inference(avatar_split_clause,[],[f458,f3503]) ).
fof(f3503,plain,
( spl0_365
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f458,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
fof(f3501,plain,
( spl0_364
| ~ spl0_207
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f3317,f3280,f2385,f3499]) ).
fof(f3317,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_207
| ~ spl0_338 ),
inference(resolution,[],[f3281,f2386]) ).
fof(f3497,plain,
spl0_363,
inference(avatar_split_clause,[],[f457,f3495]) ).
fof(f3495,plain,
( spl0_363
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f457,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
fof(f3493,plain,
spl0_362,
inference(avatar_split_clause,[],[f413,f3491]) ).
fof(f3491,plain,
( spl0_362
<=> ! [X4] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X4
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f413,axiom,
! [X4] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X4
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__1__iff_0) ).
fof(f3489,plain,
spl0_361,
inference(avatar_split_clause,[],[f376,f3487]) ).
fof(f3487,plain,
( spl0_361
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f376,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__one_0) ).
fof(f3485,plain,
spl0_360,
inference(avatar_split_clause,[],[f373,f3483]) ).
fof(f3483,plain,
( spl0_360
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f373,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
fof(f3481,plain,
spl0_359,
inference(avatar_split_clause,[],[f372,f3479]) ).
fof(f3479,plain,
( spl0_359
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f372,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
fof(f3477,plain,
spl0_358,
inference(avatar_split_clause,[],[f370,f3475]) ).
fof(f3475,plain,
( spl0_358
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f370,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X10,c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
fof(f3473,plain,
spl0_357,
inference(avatar_split_clause,[],[f369,f3471]) ).
fof(f3471,plain,
( spl0_357
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f369,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
fof(f3469,plain,
spl0_356,
inference(avatar_split_clause,[],[f341,f3467]) ).
fof(f3467,plain,
( spl0_356
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f341,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).
fof(f3465,plain,
spl0_355,
inference(avatar_split_clause,[],[f296,f3463]) ).
fof(f3463,plain,
( spl0_355
<=> ! [X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f296,axiom,
! [X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__1_0) ).
fof(f3461,plain,
spl0_354,
inference(avatar_split_clause,[],[f295,f3459]) ).
fof(f3459,plain,
( spl0_354
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f295,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__pprt_0) ).
fof(f3439,plain,
spl0_353,
inference(avatar_split_clause,[],[f151,f3437]) ).
fof(f3437,plain,
( spl0_353
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f151,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__one_0) ).
fof(f3435,plain,
spl0_352,
inference(avatar_split_clause,[],[f133,f3433]) ).
fof(f133,axiom,
! [X4] : c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(X4),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__minus_0) ).
fof(f3431,plain,
spl0_351,
inference(avatar_split_clause,[],[f88,f3429]) ).
fof(f88,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
fof(f3427,plain,
spl0_350,
inference(avatar_split_clause,[],[f87,f3425]) ).
fof(f87,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
fof(f3423,plain,
spl0_349,
inference(avatar_split_clause,[],[f86,f3421]) ).
fof(f3421,plain,
( spl0_349
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f86,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
fof(f3419,plain,
spl0_348,
inference(avatar_split_clause,[],[f85,f3417]) ).
fof(f3417,plain,
( spl0_348
<=> ! [X4,X0,X10] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f85,axiom,
! [X10,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X10,X0),X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).
fof(f3415,plain,
spl0_347,
inference(avatar_split_clause,[],[f38,f3413]) ).
fof(f3413,plain,
( spl0_347
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f38,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__vector_Oscale__one_0) ).
fof(f3380,plain,
( spl0_346
| ~ spl0_8
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f3368,f3364,f1376,f3378]) ).
fof(f3378,plain,
( spl0_346
<=> ! [X38,X4,X10,X32] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),X32,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f3364,plain,
( spl0_343
<=> ! [X38,X4,X10,X32] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),X32,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f3368,plain,
( ! [X38,X10,X4,X32] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),X32,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_343 ),
inference(forward_demodulation,[],[f3367,f1378]) ).
fof(f3367,plain,
( ! [X38,X10,X4,X32] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),X32,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_343 ),
inference(forward_demodulation,[],[f3365,f1378]) ).
fof(f3365,plain,
( ! [X38,X10,X4,X32] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),X32,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_343 ),
inference(avatar_component_clause,[],[f3364]) ).
fof(f3376,plain,
( spl0_345
| ~ spl0_41
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2438,f2393,f1544,f3374]) ).
fof(f2438,plain,
( ! [X0,X1] : c_Log_Opowr(X0,X1) = c_Log_Opowr(c_Log_Opowr(X0,X1),c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_41
| ~ spl0_209 ),
inference(resolution,[],[f2394,f1545]) ).
fof(f3372,plain,
( spl0_344
| ~ spl0_8
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f3362,f3358,f1376,f3370]) ).
fof(f3370,plain,
( spl0_344
<=> ! [X38,X4,X10,X32] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X32,c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f3358,plain,
( spl0_342
<=> ! [X38,X4,X10,X32] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X32,c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f3362,plain,
( ! [X38,X10,X4,X32] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X32,c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_342 ),
inference(forward_demodulation,[],[f3361,f1378]) ).
fof(f3361,plain,
( ! [X38,X10,X4,X32] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X32,c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_342 ),
inference(forward_demodulation,[],[f3359,f1378]) ).
fof(f3359,plain,
( ! [X38,X10,X4,X32] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X32,c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_342 ),
inference(avatar_component_clause,[],[f3358]) ).
fof(f3366,plain,
spl0_343,
inference(avatar_split_clause,[],[f1332,f3364]) ).
fof(f1332,plain,
! [X38,X10,X4,X32] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),X32,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1331,f1092]) ).
fof(f1092,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(v_x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1331,plain,
! [X38,X10,X4,X32] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),X32,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f589,f1092]) ).
fof(f589,axiom,
! [X38,X10,X4,X32] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),X32,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__inverse__cancel_0) ).
fof(f3360,plain,
spl0_342,
inference(avatar_split_clause,[],[f1330,f3358]) ).
fof(f1330,plain,
! [X38,X10,X4,X32] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X32,c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1329,f1092]) ).
fof(f1329,plain,
! [X38,X10,X4,X32] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X32,c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f690,f1092]) ).
fof(f690,axiom,
! [X38,X10,X4,X32] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X38,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X38,X10,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X32,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X10,c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X32,c_HOL_Oinverse__class_Oinverse(X38,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__inverse__cancel2_0) ).
fof(f3294,plain,
spl0_341,
inference(avatar_split_clause,[],[f987,f3292]) ).
fof(f987,axiom,
! [X29,X14] :
( c_lessequals(X14,X29,tc_RealDef_Oreal)
| c_lessequals(X29,X14,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
fof(f3290,plain,
spl0_340,
inference(avatar_split_clause,[],[f921,f3288]) ).
fof(f3288,plain,
( spl0_340
<=> ! [X4,X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f921,axiom,
! [X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X4,X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f3286,plain,
spl0_339,
inference(avatar_split_clause,[],[f786,f3284]) ).
fof(f3284,plain,
( spl0_339
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f786,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f3282,plain,
spl0_338,
inference(avatar_split_clause,[],[f767,f3280]) ).
fof(f767,axiom,
! [X10,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_lessequals(X4,X10,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_0) ).
fof(f3278,plain,
spl0_337,
inference(avatar_split_clause,[],[f758,f3276]) ).
fof(f3276,plain,
( spl0_337
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f758,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f3274,plain,
spl0_336,
inference(avatar_split_clause,[],[f736,f3272]) ).
fof(f3272,plain,
( spl0_336
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f736,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f3270,plain,
spl0_335,
inference(avatar_split_clause,[],[f722,f3268]) ).
fof(f3268,plain,
( spl0_335
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f722,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f3263,plain,
spl0_334,
inference(avatar_split_clause,[],[f711,f3261]) ).
fof(f3261,plain,
( spl0_334
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f711,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
fof(f3259,plain,
spl0_333,
inference(avatar_split_clause,[],[f595,f3257]) ).
fof(f3257,plain,
( spl0_333
<=> ! [X4,X0] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f595,axiom,
! [X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X4,X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
fof(f3255,plain,
spl0_332,
inference(avatar_split_clause,[],[f55,f3253]) ).
fof(f3253,plain,
( spl0_332
<=> ! [X4,X10] :
( X4 = X10
| c_NthRoot_Osqrt(X4) != c_NthRoot_Osqrt(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f55,axiom,
! [X10,X4] :
( X4 = X10
| c_NthRoot_Osqrt(X4) != c_NthRoot_Osqrt(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__iff_0) ).
fof(f3201,plain,
spl0_331,
inference(avatar_split_clause,[],[f1001,f3199]) ).
fof(f3199,plain,
( spl0_331
<=> ! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f1001,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f3197,plain,
( spl0_330
| ~ spl0_41
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2429,f2389,f1544,f3195]) ).
fof(f2429,plain,
( ! [X0,X1] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_Log_Opowr(X0,X1),tc_RealDef_Oreal)
| ~ spl0_41
| ~ spl0_208 ),
inference(resolution,[],[f2390,f1545]) ).
fof(f3193,plain,
spl0_329,
inference(avatar_split_clause,[],[f998,f3191]) ).
fof(f3191,plain,
( spl0_329
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f998,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
fof(f3189,plain,
spl0_328,
inference(avatar_split_clause,[],[f951,f3187]) ).
fof(f3187,plain,
( spl0_328
<=> ! [X1] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Log_Opowr(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f951,axiom,
! [X1] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Log_Opowr(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__one__eq__one_0) ).
fof(f3185,plain,
spl0_327,
inference(avatar_split_clause,[],[f782,f3183]) ).
fof(f3183,plain,
( spl0_327
<=> ! [X4] : c_Transcendental_Ocos(X4) = c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f782,axiom,
! [X4] : c_Transcendental_Ocos(X4) = c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__minus_0) ).
fof(f3181,plain,
spl0_326,
inference(avatar_split_clause,[],[f461,f3179]) ).
fof(f461,axiom,
! [X14] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X14,tc_RealDef_Oreal) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__1_0) ).
fof(f3177,plain,
spl0_325,
inference(avatar_split_clause,[],[f89,f3175]) ).
fof(f3175,plain,
( spl0_325
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f89,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__dvd_0) ).
fof(f3155,plain,
( spl0_324
| ~ spl0_8
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f3147,f3144,f1376,f3153]) ).
fof(f3153,plain,
( spl0_324
<=> ! [X4,X0,X1] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X1
| ~ class_RealVector_Oreal__div__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oinverse__class_Oinverse(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f3144,plain,
( spl0_322
<=> ! [X4,X0,X1] :
( c_Transcendental_Osin(v_x) = X1
| ~ class_RealVector_Oreal__div__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oinverse__class_Oinverse(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f3147,plain,
( ! [X0,X1,X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X1
| ~ class_RealVector_Oreal__div__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oinverse__class_Oinverse(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) )
| ~ spl0_8
| ~ spl0_322 ),
inference(forward_demodulation,[],[f3145,f1378]) ).
fof(f3145,plain,
( ! [X0,X1,X4] :
( c_Transcendental_Osin(v_x) = X1
| ~ class_RealVector_Oreal__div__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oinverse__class_Oinverse(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) )
| ~ spl0_322 ),
inference(avatar_component_clause,[],[f3144]) ).
fof(f3151,plain,
( spl0_323
| ~ spl0_8
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3138,f3134,f1376,f3149]) ).
fof(f3149,plain,
( spl0_323
<=> ! [X4,X1,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| c_Log_Opowr(c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),X1) = c_HOL_Otimes__class_Otimes(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f3134,plain,
( spl0_320
<=> ! [X4,X1,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_Log_Opowr(c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),X1) = c_HOL_Otimes__class_Otimes(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f3138,plain,
( ! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| c_Log_Opowr(c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),X1) = c_HOL_Otimes__class_Otimes(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_320 ),
inference(forward_demodulation,[],[f3137,f1378]) ).
fof(f3137,plain,
( ! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_Log_Opowr(c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),X1) = c_HOL_Otimes__class_Otimes(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_320 ),
inference(forward_demodulation,[],[f3135,f1378]) ).
fof(f3135,plain,
( ! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_Log_Opowr(c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),X1) = c_HOL_Otimes__class_Otimes(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) )
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f3134]) ).
fof(f3146,plain,
spl0_322,
inference(avatar_split_clause,[],[f1314,f3144]) ).
fof(f1314,plain,
! [X0,X1,X4] :
( c_Transcendental_Osin(v_x) = X1
| ~ class_RealVector_Oreal__div__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oinverse__class_Oinverse(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
inference(forward_demodulation,[],[f266,f1092]) ).
fof(f266,axiom,
! [X0,X1,X4] :
( ~ class_RealVector_Oreal__div__algebra(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oinverse__class_Oinverse(c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__scaleR__distrib_0) ).
fof(f3142,plain,
( spl0_321
| ~ spl0_139
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f2295,f2270,f2037,f3140]) ).
fof(f3140,plain,
( spl0_321
<=> ! [X0] : c_Transcendental_Otan(c_Transcendental_Opi) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f2037,plain,
( spl0_139
<=> class_RealVector_Oreal__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f2270,plain,
( spl0_186
<=> ! [X4,X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Otan(c_Transcendental_Opi),X4,X0)
| ~ class_RealVector_Oreal__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f2295,plain,
( ! [X0] : c_Transcendental_Otan(c_Transcendental_Opi) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal)
| ~ spl0_139
| ~ spl0_186 ),
inference(forward_demodulation,[],[f2294,f908]) ).
fof(f2294,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Otan(c_Transcendental_Opi),X0,tc_RealDef_Oreal)
| ~ spl0_139
| ~ spl0_186 ),
inference(resolution,[],[f2271,f2039]) ).
fof(f2039,plain,
( class_RealVector_Oreal__vector(tc_RealDef_Oreal)
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f2037]) ).
fof(f2271,plain,
( ! [X0,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Otan(c_Transcendental_Opi),X4,X0) )
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f2270]) ).
fof(f3136,plain,
spl0_320,
inference(avatar_split_clause,[],[f1310,f3134]) ).
fof(f1310,plain,
! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_Log_Opowr(c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),X1) = c_HOL_Otimes__class_Otimes(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1309,f1092]) ).
fof(f1309,plain,
! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_Log_Opowr(c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),X1) = c_HOL_Otimes__class_Otimes(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f543,f1092]) ).
fof(f543,axiom,
! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_Log_Opowr(c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),X1) = c_HOL_Otimes__class_Otimes(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__mult_0) ).
fof(f3082,plain,
spl0_319,
inference(avatar_split_clause,[],[f935,f3080]) ).
fof(f3080,plain,
( spl0_319
<=> ! [X4,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f935,axiom,
! [X0,X4] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f3078,plain,
spl0_318,
inference(avatar_split_clause,[],[f934,f3076]) ).
fof(f3076,plain,
( spl0_318
<=> ! [X4,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f934,axiom,
! [X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f3074,plain,
spl0_317,
inference(avatar_split_clause,[],[f898,f3071]) ).
fof(f3071,plain,
( spl0_317
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f898,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__one_0) ).
fof(f3069,plain,
spl0_316,
inference(avatar_split_clause,[],[f754,f3067]) ).
fof(f3067,plain,
( spl0_316
<=> ! [X4,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f754,axiom,
! [X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f3065,plain,
spl0_315,
inference(avatar_split_clause,[],[f752,f3063]) ).
fof(f3063,plain,
( spl0_315
<=> ! [X4,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f752,axiom,
! [X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f3061,plain,
spl0_314,
inference(avatar_split_clause,[],[f751,f3059]) ).
fof(f3059,plain,
( spl0_314
<=> ! [X4,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f751,axiom,
! [X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f3057,plain,
spl0_313,
inference(avatar_split_clause,[],[f218,f3055]) ).
fof(f3055,plain,
( spl0_313
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f218,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
fof(f3053,plain,
spl0_312,
inference(avatar_split_clause,[],[f146,f3051]) ).
fof(f146,axiom,
! [X4] : c_lessequals(c_Transcendental_Osin(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__le__one_0) ).
fof(f3049,plain,
spl0_311,
inference(avatar_split_clause,[],[f69,f3047]) ).
fof(f3047,plain,
( spl0_311
<=> ! [X4] : c_lessequals(c_Transcendental_Ocos(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f69,axiom,
! [X4] : c_lessequals(c_Transcendental_Ocos(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__le__one_0) ).
fof(f3041,plain,
( spl0_310
| ~ spl0_58
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2428,f2389,f1632,f3038]) ).
fof(f3038,plain,
( spl0_310
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f2428,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_58
| ~ spl0_208 ),
inference(resolution,[],[f2390,f1634]) ).
fof(f3036,plain,
( spl0_309
| ~ spl0_8
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f3032,f3029,f1376,f3034]) ).
fof(f3034,plain,
( spl0_309
<=> ! [X4,X0,X15] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X15,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__div__algebra(X0)
| ~ c_lessequals(X15,c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(X4,X0),X0),c_HOL_Oinverse__class_Oinverse(X15,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f3029,plain,
( spl0_308
<=> ! [X4,X0,X15] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X15,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__div__algebra(X0)
| ~ c_lessequals(X15,c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(X4,X0),X0),c_HOL_Oinverse__class_Oinverse(X15,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f3032,plain,
( ! [X0,X4,X15] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X15,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__div__algebra(X0)
| ~ c_lessequals(X15,c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(X4,X0),X0),c_HOL_Oinverse__class_Oinverse(X15,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_308 ),
inference(forward_demodulation,[],[f3030,f1378]) ).
fof(f3030,plain,
( ! [X0,X4,X15] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X15,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__div__algebra(X0)
| ~ c_lessequals(X15,c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(X4,X0),X0),c_HOL_Oinverse__class_Oinverse(X15,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_308 ),
inference(avatar_component_clause,[],[f3029]) ).
fof(f3031,plain,
spl0_308,
inference(avatar_split_clause,[],[f1315,f3029]) ).
fof(f1315,plain,
! [X0,X4,X15] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X15,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__div__algebra(X0)
| ~ c_lessequals(X15,c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(X4,X0),X0),c_HOL_Oinverse__class_Oinverse(X15,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f741,f1092]) ).
fof(f741,axiom,
! [X0,X4,X15] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X15,tc_RealDef_Oreal)
| ~ c_lessequals(X15,c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(X4,X0),X0),c_HOL_Oinverse__class_Oinverse(X15,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Bseq__inverse__lemma_0) ).
fof(f3001,plain,
( spl0_307
| ~ spl0_8
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f2985,f2981,f1376,f2999]) ).
fof(f2999,plain,
( spl0_307
<=> ! [X4,X1,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f2981,plain,
( spl0_303
<=> ! [X4,X1,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f2985,plain,
( ! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_303 ),
inference(forward_demodulation,[],[f2984,f1378]) ).
fof(f2984,plain,
( ! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_303 ),
inference(forward_demodulation,[],[f2982,f1378]) ).
fof(f2982,plain,
( ! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) )
| ~ spl0_303 ),
inference(avatar_component_clause,[],[f2981]) ).
fof(f2997,plain,
( spl0_306
| ~ spl0_8
| ~ spl0_302 ),
inference(avatar_split_clause,[],[f2979,f2975,f1376,f2995]) ).
fof(f2995,plain,
( spl0_306
<=> ! [X4,X1,X10] :
( ~ c_HOL_Oord__class_Oless(X1,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X10,X1),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f2975,plain,
( spl0_302
<=> ! [X4,X1,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X10,X1),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f2979,plain,
( ! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X1,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X10,X1),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_302 ),
inference(forward_demodulation,[],[f2978,f1378]) ).
fof(f2978,plain,
( ! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X10,X1),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_302 ),
inference(forward_demodulation,[],[f2976,f1378]) ).
fof(f2976,plain,
( ! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X10,X1),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) )
| ~ spl0_302 ),
inference(avatar_component_clause,[],[f2975]) ).
fof(f2993,plain,
( spl0_305
| ~ spl0_8
| ~ spl0_301 ),
inference(avatar_split_clause,[],[f2973,f2969,f1376,f2991]) ).
fof(f2991,plain,
( spl0_305
<=> ! [X4,X1,X10] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f2969,plain,
( spl0_301
<=> ! [X4,X1,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Osin(v_x),X1,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f2973,plain,
( ! [X10,X1,X4] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_301 ),
inference(forward_demodulation,[],[f2972,f1378]) ).
fof(f2972,plain,
( ! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Osin(v_x),X1,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_301 ),
inference(forward_demodulation,[],[f2970,f1378]) ).
fof(f2970,plain,
( ! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Osin(v_x),X1,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) )
| ~ spl0_301 ),
inference(avatar_component_clause,[],[f2969]) ).
fof(f2989,plain,
( spl0_304
| ~ spl0_8
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f2967,f2964,f1376,f2987]) ).
fof(f2987,plain,
( spl0_304
<=> ! [X4,X0,X10,X8] :
( ~ c_lessequals(X8,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X4,X0),c_HOL_Otimes__class_Otimes(X8,c_RealVector_Onorm__class_Onorm(X10,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f2964,plain,
( spl0_300
<=> ! [X4,X0,X10,X8] :
( ~ c_lessequals(X8,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X4,X0),c_HOL_Otimes__class_Otimes(X8,c_RealVector_Onorm__class_Onorm(X10,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f2967,plain,
( ! [X10,X0,X8,X4] :
( ~ c_lessequals(X8,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X4,X0),c_HOL_Otimes__class_Otimes(X8,c_RealVector_Onorm__class_Onorm(X10,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_300 ),
inference(forward_demodulation,[],[f2965,f1378]) ).
fof(f2965,plain,
( ! [X10,X0,X8,X4] :
( ~ c_lessequals(X8,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X4,X0),c_HOL_Otimes__class_Otimes(X8,c_RealVector_Onorm__class_Onorm(X10,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_300 ),
inference(avatar_component_clause,[],[f2964]) ).
fof(f2983,plain,
spl0_303,
inference(avatar_split_clause,[],[f1328,f2981]) ).
fof(f1328,plain,
! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1327,f1092]) ).
fof(f1327,plain,
! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f683,f1092]) ).
fof(f683,axiom,
! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__less__mono2_0) ).
fof(f2977,plain,
spl0_302,
inference(avatar_split_clause,[],[f1326,f2975]) ).
fof(f1326,plain,
! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X10,X1),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1325,f1092]) ).
fof(f1325,plain,
! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X1,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X10,X1),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f684,f1092]) ).
fof(f684,axiom,
! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Log_Opowr(X10,X1),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__less__mono2__neg_0) ).
fof(f2971,plain,
spl0_301,
inference(avatar_split_clause,[],[f1322,f2969]) ).
fof(f1322,plain,
! [X10,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Osin(v_x),X1,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1321,f1092]) ).
fof(f1321,plain,
! [X10,X1,X4] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),X1,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f396,f1092]) ).
fof(f396,axiom,
! [X10,X1,X4] :
( ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_Log_Opowr(X4,X1),c_Log_Opowr(X10,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__mono2_0) ).
fof(f2966,plain,
spl0_300,
inference(avatar_split_clause,[],[f1318,f2964]) ).
fof(f1318,plain,
! [X10,X0,X8,X4] :
( ~ c_lessequals(X8,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X4,X0),c_HOL_Otimes__class_Otimes(X8,c_RealVector_Onorm__class_Onorm(X10,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f953,f1092]) ).
fof(f953,axiom,
! [X10,X0,X8,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X4,X0),c_HOL_Otimes__class_Otimes(X8,c_RealVector_Onorm__class_Onorm(X10,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ratiotest__lemma_0) ).
fof(f2958,plain,
( spl0_299
| ~ spl0_8
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f2950,f2947,f1376,f2956]) ).
fof(f2956,plain,
( spl0_299
<=> ! [X4,X10] :
( ~ c_lessequals(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X10),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f2947,plain,
( spl0_297
<=> ! [X4,X10] :
( ~ c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X10),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f2950,plain,
( ! [X10,X4] :
( ~ c_lessequals(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X10),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_297 ),
inference(forward_demodulation,[],[f2948,f1378]) ).
fof(f2948,plain,
( ! [X10,X4] :
( ~ c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X10),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) )
| ~ spl0_297 ),
inference(avatar_component_clause,[],[f2947]) ).
fof(f2954,plain,
( spl0_298
| ~ spl0_8
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f2945,f2942,f1376,f2952]) ).
fof(f2952,plain,
( spl0_298
<=> ! [X4,X10] :
( ~ c_lessequals(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_lessequals(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X10),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f2942,plain,
( spl0_296
<=> ! [X4,X10] :
( ~ c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_lessequals(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X10),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f2945,plain,
( ! [X10,X4] :
( ~ c_lessequals(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_lessequals(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X10),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_296 ),
inference(forward_demodulation,[],[f2943,f1378]) ).
fof(f2943,plain,
( ! [X10,X4] :
( ~ c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_lessequals(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X10),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) )
| ~ spl0_296 ),
inference(avatar_component_clause,[],[f2942]) ).
fof(f2949,plain,
spl0_297,
inference(avatar_split_clause,[],[f1324,f2947]) ).
fof(f1324,plain,
! [X10,X4] :
( ~ c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X10),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f361,f1092]) ).
fof(f361,axiom,
! [X10,X4] :
( ~ c_HOL_Oord__class_Oless(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X10),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__monotone__minus__pi__0_0) ).
fof(f2944,plain,
spl0_296,
inference(avatar_split_clause,[],[f1320,f2942]) ).
fof(f1320,plain,
! [X10,X4] :
( ~ c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_lessequals(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X10),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f238,f1092]) ).
fof(f238,axiom,
! [X10,X4] :
( ~ c_lessequals(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X10),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__monotone__minus__pi__0_H_0) ).
fof(f2940,plain,
( spl0_295
| ~ spl0_40
| ~ spl0_242 ),
inference(avatar_split_clause,[],[f2811,f2596,f1540,f2937]) ).
fof(f2811,plain,
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),v_x,tc_RealDef_Oreal)
| ~ spl0_40
| ~ spl0_242 ),
inference(superposition,[],[f1541,f2598]) ).
fof(f2929,plain,
spl0_294,
inference(avatar_split_clause,[],[f908,f2926]) ).
fof(f2924,plain,
spl0_293,
inference(avatar_split_clause,[],[f852,f2922]) ).
fof(f2922,plain,
( spl0_293
<=> ! [X4,X0] : c_Fun_Oid(X4,X0) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f852,axiom,
! [X0,X4] : c_Fun_Oid(X4,X0) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__apply_0) ).
fof(f2920,plain,
spl0_292,
inference(avatar_split_clause,[],[f468,f2918]) ).
fof(f2918,plain,
( spl0_292
<=> ! [X10] : c_Transcendental_Otan(c_Transcendental_Oarctan(X10)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f468,axiom,
! [X10] : c_Transcendental_Otan(c_Transcendental_Oarctan(X10)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arctan_2) ).
fof(f2884,plain,
( spl0_291
| ~ spl0_8
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f2843,f2840,f1376,f2882]) ).
fof(f2882,plain,
( spl0_291
<=> ! [X4,X10] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X10,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f2840,plain,
( spl0_281
<=> ! [X4,X10] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X10,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f2843,plain,
( ! [X10,X4] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X10,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X10),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_281 ),
inference(forward_demodulation,[],[f2841,f1378]) ).
fof(f2841,plain,
( ! [X10,X4] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X10,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X10),tc_RealDef_Oreal) )
| ~ spl0_281 ),
inference(avatar_component_clause,[],[f2840]) ).
fof(f2880,plain,
( spl0_290
| ~ spl0_8
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f2838,f2835,f1376,f2878]) ).
fof(f2878,plain,
( spl0_290
<=> ! [X4,X10] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| ~ c_lessequals(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f2835,plain,
( spl0_280
<=> ! [X4,X10] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_lessequals(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f2838,plain,
( ! [X10,X4] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| ~ c_lessequals(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X10),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_280 ),
inference(forward_demodulation,[],[f2836,f1378]) ).
fof(f2836,plain,
( ! [X10,X4] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_lessequals(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X10),tc_RealDef_Oreal) )
| ~ spl0_280 ),
inference(avatar_component_clause,[],[f2835]) ).
fof(f2876,plain,
( spl0_289
| ~ spl0_8
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f2833,f2830,f1376,f2874]) ).
fof(f2874,plain,
( spl0_289
<=> ! [X4,X14,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X14,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f2830,plain,
( spl0_279
<=> ! [X4,X14,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f2833,plain,
( ! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X14,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_279 ),
inference(forward_demodulation,[],[f2831,f1378]) ).
fof(f2831,plain,
( ! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f2830]) ).
fof(f2872,plain,
( spl0_288
| ~ spl0_8
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f2828,f2825,f1376,f2870]) ).
fof(f2870,plain,
( spl0_288
<=> ! [X4,X14,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X14,tc_RealDef_Oreal)
| c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f2825,plain,
( spl0_278
<=> ! [X4,X14,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f2828,plain,
( ! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X14,tc_RealDef_Oreal)
| c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_278 ),
inference(forward_demodulation,[],[f2826,f1378]) ).
fof(f2826,plain,
( ! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f2825]) ).
fof(f2868,plain,
( spl0_287
| ~ spl0_8
| ~ spl0_277 ),
inference(avatar_split_clause,[],[f2823,f2820,f1376,f2866]) ).
fof(f2866,plain,
( spl0_287
<=> ! [X4,X14,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X14,tc_RealDef_Oreal)
| c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f2820,plain,
( spl0_277
<=> ! [X4,X14,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f2823,plain,
( ! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X14,tc_RealDef_Oreal)
| c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_277 ),
inference(forward_demodulation,[],[f2821,f1378]) ).
fof(f2821,plain,
( ! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_277 ),
inference(avatar_component_clause,[],[f2820]) ).
fof(f2864,plain,
( ~ spl0_286
| ~ spl0_23
| ~ spl0_242 ),
inference(avatar_split_clause,[],[f2812,f2596,f1455,f2861]) ).
fof(f2861,plain,
( spl0_286
<=> c_Transcendental_Otan(c_Transcendental_Opi) = v_x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f2812,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) != v_x
| ~ spl0_23
| ~ spl0_242 ),
inference(superposition,[],[f1456,f2598]) ).
fof(f2859,plain,
( spl0_285
| ~ spl0_8
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f2818,f2815,f1376,f2857]) ).
fof(f2857,plain,
( spl0_285
<=> ! [X4,X14,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X14,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f2815,plain,
( spl0_276
<=> ! [X4,X14,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f2818,plain,
( ! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X14,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_276 ),
inference(forward_demodulation,[],[f2816,f1378]) ).
fof(f2816,plain,
( ! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_276 ),
inference(avatar_component_clause,[],[f2815]) ).
fof(f2855,plain,
( spl0_284
| ~ spl0_8
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2807,f2804,f1376,f2853]) ).
fof(f2853,plain,
( spl0_284
<=> ! [X4,X14,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X14,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f2804,plain,
( spl0_275
<=> ! [X4,X14,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2807,plain,
( ! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X14,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_275 ),
inference(forward_demodulation,[],[f2805,f1378]) ).
fof(f2805,plain,
( ! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_275 ),
inference(avatar_component_clause,[],[f2804]) ).
fof(f2851,plain,
( spl0_283
| ~ spl0_8
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2802,f2799,f1376,f2849]) ).
fof(f2849,plain,
( spl0_283
<=> ! [X4,X14,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X14,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f2799,plain,
( spl0_274
<=> ! [X4,X14,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2802,plain,
( ! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X14,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_274 ),
inference(forward_demodulation,[],[f2800,f1378]) ).
fof(f2800,plain,
( ! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f2799]) ).
fof(f2847,plain,
( spl0_282
| ~ spl0_8
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2797,f2794,f1376,f2845]) ).
fof(f2845,plain,
( spl0_282
<=> ! [X4,X14,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X14,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2794,plain,
( spl0_273
<=> ! [X4,X14,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2797,plain,
( ! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X14,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_273 ),
inference(forward_demodulation,[],[f2795,f1378]) ).
fof(f2795,plain,
( ! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f2794]) ).
fof(f2842,plain,
spl0_281,
inference(avatar_split_clause,[],[f1323,f2840]) ).
fof(f1323,plain,
! [X10,X4] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X10,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X10),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f364,f1092]) ).
fof(f364,axiom,
! [X10,X4] :
( ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__monotone__0__pi_0) ).
fof(f2837,plain,
spl0_280,
inference(avatar_split_clause,[],[f1319,f2835]) ).
fof(f1319,plain,
! [X10,X4] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_lessequals(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X10),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f249,f1092]) ).
fof(f249,axiom,
! [X10,X4] :
( ~ c_lessequals(X10,X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__monotone__0__pi_H_0) ).
fof(f2832,plain,
spl0_279,
inference(avatar_split_clause,[],[f1303,f2830]) ).
fof(f1303,plain,
! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f839,f1092]) ).
fof(f839,axiom,
! [X10,X14,X4] :
( c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__iff1_0) ).
fof(f2827,plain,
spl0_278,
inference(avatar_split_clause,[],[f1302,f2825]) ).
fof(f1302,plain,
! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f642,f1092]) ).
fof(f642,axiom,
! [X10,X14,X4] :
( c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_0) ).
fof(f2822,plain,
spl0_277,
inference(avatar_split_clause,[],[f1301,f2820]) ).
fof(f1301,plain,
! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f644,f1092]) ).
fof(f644,axiom,
! [X10,X14,X4] :
( c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_0) ).
fof(f2817,plain,
spl0_276,
inference(avatar_split_clause,[],[f1294,f2815]) ).
fof(f1294,plain,
! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f837,f1092]) ).
fof(f837,axiom,
! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__mono2_0) ).
fof(f2806,plain,
spl0_275,
inference(avatar_split_clause,[],[f1293,f2804]) ).
fof(f1293,plain,
! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f838,f1092]) ).
fof(f838,axiom,
! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__iff1_1) ).
fof(f2801,plain,
spl0_274,
inference(avatar_split_clause,[],[f1290,f2799]) ).
fof(f1290,plain,
! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f641,f1092]) ).
fof(f641,axiom,
! [X10,X14,X4] :
( ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X14,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X14,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_1) ).
fof(f2796,plain,
spl0_273,
inference(avatar_split_clause,[],[f1289,f2794]) ).
fof(f1289,plain,
! [X10,X14,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X14,tc_RealDef_Oreal)
| ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f643,f1092]) ).
fof(f643,axiom,
! [X10,X14,X4] :
( ~ c_lessequals(X4,X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X14,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X14,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_1) ).
fof(f2786,plain,
( spl0_272
| ~ spl0_8
| ~ spl0_270 ),
inference(avatar_split_clause,[],[f2778,f2775,f1376,f2784]) ).
fof(f2784,plain,
( spl0_272
<=> ! [X4,X0,X10,X1] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X1
| ~ class_RealVector_Oreal__vector(X0)
| X4 = X10
| c_RealVector_OscaleR__class_OscaleR(X1,X4,X0) != c_RealVector_OscaleR__class_OscaleR(X1,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f2775,plain,
( spl0_270
<=> ! [X4,X0,X10,X1] :
( c_Transcendental_Osin(v_x) = X1
| ~ class_RealVector_Oreal__vector(X0)
| X4 = X10
| c_RealVector_OscaleR__class_OscaleR(X1,X4,X0) != c_RealVector_OscaleR__class_OscaleR(X1,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f2778,plain,
( ! [X10,X0,X1,X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X1
| ~ class_RealVector_Oreal__vector(X0)
| X4 = X10
| c_RealVector_OscaleR__class_OscaleR(X1,X4,X0) != c_RealVector_OscaleR__class_OscaleR(X1,X10,X0) )
| ~ spl0_8
| ~ spl0_270 ),
inference(forward_demodulation,[],[f2776,f1378]) ).
fof(f2776,plain,
( ! [X10,X0,X1,X4] :
( c_Transcendental_Osin(v_x) = X1
| ~ class_RealVector_Oreal__vector(X0)
| X4 = X10
| c_RealVector_OscaleR__class_OscaleR(X1,X4,X0) != c_RealVector_OscaleR__class_OscaleR(X1,X10,X0) )
| ~ spl0_270 ),
inference(avatar_component_clause,[],[f2775]) ).
fof(f2782,plain,
( spl0_271
| ~ spl0_8
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f2773,f2768,f1376,f2780]) ).
fof(f2780,plain,
( spl0_271
<=> ! [X4,X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f2768,plain,
( spl0_269
<=> ! [X4,X10] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f2773,plain,
( ! [X10,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_269 ),
inference(forward_demodulation,[],[f2772,f1378]) ).
fof(f2772,plain,
( ! [X10,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_269 ),
inference(forward_demodulation,[],[f2771,f1378]) ).
fof(f2771,plain,
( ! [X10,X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_269 ),
inference(forward_demodulation,[],[f2769,f1378]) ).
fof(f2769,plain,
( ! [X10,X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal) )
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f2768]) ).
fof(f2777,plain,
spl0_270,
inference(avatar_split_clause,[],[f1316,f2775]) ).
fof(f1316,plain,
! [X10,X0,X1,X4] :
( c_Transcendental_Osin(v_x) = X1
| ~ class_RealVector_Oreal__vector(X0)
| X4 = X10
| c_RealVector_OscaleR__class_OscaleR(X1,X4,X0) != c_RealVector_OscaleR__class_OscaleR(X1,X10,X0) ),
inference(forward_demodulation,[],[f1056,f1092]) ).
fof(f1056,axiom,
! [X10,X0,X1,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| X4 = X10
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_RealVector_OscaleR__class_OscaleR(X1,X4,X0) != c_RealVector_OscaleR__class_OscaleR(X1,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__left_0) ).
fof(f2770,plain,
spl0_269,
inference(avatar_split_clause,[],[f1308,f2768]) ).
fof(f1308,plain,
! [X10,X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1307,f1092]) ).
fof(f1307,plain,
! [X10,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1306,f1092]) ).
fof(f1306,plain,
! [X10,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f284,f1092]) ).
fof(f284,axiom,
! [X10,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__order_0) ).
fof(f2755,plain,
( spl0_268
| ~ spl0_8
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2735,f2732,f1376,f2753]) ).
fof(f2753,plain,
( spl0_268
<=> ! [X4,X0,X1] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X1
| ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_RealVector_OscaleR__class_OscaleR(X1,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f2732,plain,
( spl0_263
<=> ! [X4,X0,X1] :
( c_Transcendental_Osin(v_x) = X1
| ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_RealVector_OscaleR__class_OscaleR(X1,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2735,plain,
( ! [X0,X1,X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X1
| ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_RealVector_OscaleR__class_OscaleR(X1,X4,X0) )
| ~ spl0_8
| ~ spl0_263 ),
inference(forward_demodulation,[],[f2733,f1378]) ).
fof(f2733,plain,
( ! [X0,X1,X4] :
( c_Transcendental_Osin(v_x) = X1
| ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_RealVector_OscaleR__class_OscaleR(X1,X4,X0) )
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f2732]) ).
fof(f2751,plain,
( spl0_267
| ~ spl0_8
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2725,f2722,f1376,f2749]) ).
fof(f2749,plain,
( spl0_267
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f2722,plain,
( spl0_261
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f2725,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_261 ),
inference(forward_demodulation,[],[f2723,f1378]) ).
fof(f2723,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_261 ),
inference(avatar_component_clause,[],[f2722]) ).
fof(f2747,plain,
( spl0_266
| ~ spl0_8
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f2720,f2717,f1376,f2745]) ).
fof(f2745,plain,
( spl0_266
<=> ! [X4,X1] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X1,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f2717,plain,
( spl0_260
<=> ! [X4,X1] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),X1,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f2720,plain,
( ! [X1,X4] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X1,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_260 ),
inference(forward_demodulation,[],[f2718,f1378]) ).
fof(f2718,plain,
( ! [X1,X4] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),X1,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) )
| ~ spl0_260 ),
inference(avatar_component_clause,[],[f2717]) ).
fof(f2743,plain,
( spl0_265
| ~ spl0_8
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2715,f2711,f1376,f2741]) ).
fof(f2741,plain,
( spl0_265
<=> ! [X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X4
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f2711,plain,
( spl0_259
<=> ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_Transcendental_Osin(v_x) = X4
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2715,plain,
( ! [X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X4
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_259 ),
inference(forward_demodulation,[],[f2714,f1378]) ).
fof(f2714,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_Transcendental_Osin(v_x) = X4
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_259 ),
inference(forward_demodulation,[],[f2712,f1378]) ).
fof(f2712,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_Transcendental_Osin(v_x) = X4
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) )
| ~ spl0_259 ),
inference(avatar_component_clause,[],[f2711]) ).
fof(f2739,plain,
( spl0_264
| ~ spl0_8
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f2709,f2706,f1376,f2737]) ).
fof(f2737,plain,
( spl0_264
<=> ! [X4,X0] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X4
| ~ class_RealVector_Oreal__div__algebra(X0)
| c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X0) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2706,plain,
( spl0_258
<=> ! [X4,X0] :
( c_Transcendental_Osin(v_x) = X4
| ~ class_RealVector_Oreal__div__algebra(X0)
| c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X0) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f2709,plain,
( ! [X0,X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X4
| ~ class_RealVector_Oreal__div__algebra(X0)
| c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X0) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(X4,X0),X0) )
| ~ spl0_8
| ~ spl0_258 ),
inference(forward_demodulation,[],[f2707,f1378]) ).
fof(f2707,plain,
( ! [X0,X4] :
( c_Transcendental_Osin(v_x) = X4
| ~ class_RealVector_Oreal__div__algebra(X0)
| c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X0) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(X4,X0),X0) )
| ~ spl0_258 ),
inference(avatar_component_clause,[],[f2706]) ).
fof(f2734,plain,
spl0_263,
inference(avatar_split_clause,[],[f1317,f2732]) ).
fof(f1317,plain,
! [X0,X1,X4] :
( c_Transcendental_Osin(v_x) = X1
| ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_RealVector_OscaleR__class_OscaleR(X1,X4,X0) ),
inference(forward_demodulation,[],[f1080,f1092]) ).
fof(f1080,axiom,
! [X0,X1,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_RealVector_OscaleR__class_OscaleR(X1,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_0) ).
fof(f2730,plain,
( ~ spl0_262
| ~ spl0_23
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f2691,f2552,f1455,f2727]) ).
fof(f2727,plain,
( spl0_262
<=> c_Transcendental_Opi = c_Transcendental_Otan(c_Transcendental_Opi) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f2691,plain,
( c_Transcendental_Opi != c_Transcendental_Otan(c_Transcendental_Opi)
| ~ spl0_23
| ~ spl0_237 ),
inference(superposition,[],[f1456,f2554]) ).
fof(f2724,plain,
spl0_261,
inference(avatar_split_clause,[],[f1305,f2722]) ).
fof(f1305,plain,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f774,f1092]) ).
fof(f774,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__inverse__gt__one_0) ).
fof(f2719,plain,
spl0_260,
inference(avatar_split_clause,[],[f1304,f2717]) ).
fof(f1304,plain,
! [X1,X4] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),X1,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f43,f1092]) ).
fof(f43,axiom,
! [X1,X4] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ge__one__powr__ge__zero_0) ).
fof(f2713,plain,
spl0_259,
inference(avatar_split_clause,[],[f1300,f2711]) ).
fof(f1300,plain,
! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_Transcendental_Osin(v_x) = X4
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1299,f1092]) ).
fof(f1299,plain,
! [X4] :
( c_Transcendental_Osin(v_x) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f507,f1092]) ).
fof(f507,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sgn__def_2) ).
fof(f2708,plain,
spl0_258,
inference(avatar_split_clause,[],[f1276,f2706]) ).
fof(f1276,plain,
! [X0,X4] :
( c_Transcendental_Osin(v_x) = X4
| ~ class_RealVector_Oreal__div__algebra(X0)
| c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X0) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(X4,X0),X0) ),
inference(forward_demodulation,[],[f780,f1092]) ).
fof(f780,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__div__algebra(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X0) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__of__real__inverse_0) ).
fof(f2702,plain,
spl0_257,
inference(avatar_split_clause,[],[f1090,f2699]) ).
fof(f1090,axiom,
c_HOL_Oord__class_Oless(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f2697,plain,
~ spl0_256,
inference(avatar_split_clause,[],[f1064,f2694]) ).
fof(f2694,plain,
( spl0_256
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Opi ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f1064,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Opi,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__neq__zero_0) ).
fof(f2687,plain,
spl0_255,
inference(avatar_split_clause,[],[f937,f2685]) ).
fof(f2685,plain,
( spl0_255
<=> ! [X29] : c_lessequals(X29,X29,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f937,axiom,
! [X29] : c_lessequals(X29,X29,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
fof(f2683,plain,
spl0_254,
inference(avatar_split_clause,[],[f753,f2681]) ).
fof(f753,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_1) ).
fof(f2658,plain,
( spl0_253
| ~ spl0_8
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2646,f2641,f1376,f2656]) ).
fof(f2656,plain,
( spl0_253
<=> ! [X4,X9] :
( c_HOL_Oord__class_Oless(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_NthRoot_Oroot(X9,X4) = c_Transcendental_Otan(c_Transcendental_Opi) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f2641,plain,
( spl0_250
<=> ! [X4,X9] :
( c_NthRoot_Oroot(X9,X4) = c_Transcendental_Osin(v_x)
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2646,plain,
( ! [X9,X4] :
( c_HOL_Oord__class_Oless(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_NthRoot_Oroot(X9,X4) = c_Transcendental_Otan(c_Transcendental_Opi) )
| ~ spl0_8
| ~ spl0_250 ),
inference(forward_demodulation,[],[f2645,f1378]) ).
fof(f2645,plain,
( ! [X9,X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_NthRoot_Oroot(X9,X4) = c_Transcendental_Otan(c_Transcendental_Opi)
| c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_250 ),
inference(forward_demodulation,[],[f2644,f1378]) ).
fof(f2644,plain,
( ! [X9,X4] :
( c_NthRoot_Oroot(X9,X4) = c_Transcendental_Otan(c_Transcendental_Opi)
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_250 ),
inference(forward_demodulation,[],[f2642,f1378]) ).
fof(f2642,plain,
( ! [X9,X4] :
( c_NthRoot_Oroot(X9,X4) = c_Transcendental_Osin(v_x)
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) )
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2641]) ).
fof(f2654,plain,
( spl0_252
| ~ spl0_8
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f2639,f2636,f1376,f2652]) ).
fof(f2652,plain,
( spl0_252
<=> ! [X2,X1,X8] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X8
| X1 = X2
| c_HOL_Otimes__class_Otimes(X8,X1,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X8,X2,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f2636,plain,
( spl0_249
<=> ! [X2,X1,X8] :
( c_Transcendental_Osin(v_x) = X8
| X1 = X2
| c_HOL_Otimes__class_Otimes(X8,X1,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X8,X2,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f2639,plain,
( ! [X2,X1,X8] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X8
| X1 = X2
| c_HOL_Otimes__class_Otimes(X8,X1,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X8,X2,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_249 ),
inference(forward_demodulation,[],[f2637,f1378]) ).
fof(f2637,plain,
( ! [X2,X1,X8] :
( c_Transcendental_Osin(v_x) = X8
| X1 = X2
| c_HOL_Otimes__class_Otimes(X8,X1,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X8,X2,tc_RealDef_Oreal) )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2636]) ).
fof(f2650,plain,
( spl0_251
| ~ spl0_8
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2634,f2631,f1376,f2648]) ).
fof(f2631,plain,
( spl0_248
<=> ! [X2,X1,X8] :
( c_Transcendental_Osin(v_x) = X8
| X1 = X2
| c_HOL_Otimes__class_Otimes(X1,X8,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X2,X8,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f2634,plain,
( ! [X2,X1,X8] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X8
| X1 = X2
| c_HOL_Otimes__class_Otimes(X1,X8,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X2,X8,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_248 ),
inference(forward_demodulation,[],[f2632,f1378]) ).
fof(f2632,plain,
( ! [X2,X1,X8] :
( c_Transcendental_Osin(v_x) = X8
| X1 = X2
| c_HOL_Otimes__class_Otimes(X1,X8,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X2,X8,tc_RealDef_Oreal) )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2631]) ).
fof(f2643,plain,
spl0_250,
inference(avatar_split_clause,[],[f1313,f2641]) ).
fof(f1313,plain,
! [X9,X4] :
( c_NthRoot_Oroot(X9,X4) = c_Transcendental_Osin(v_x)
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1312,f1092]) ).
fof(f1312,plain,
! [X9,X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Oroot(X9,X4) ),
inference(forward_demodulation,[],[f1311,f1092]) ).
fof(f1311,plain,
! [X9,X4] :
( c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Oroot(X9,X4) ),
inference(forward_demodulation,[],[f188,f1092]) ).
fof(f188,axiom,
! [X9,X4] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Oroot(X9,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NthRoot_Oroot__def_2) ).
fof(f2638,plain,
spl0_249,
inference(avatar_split_clause,[],[f1286,f2636]) ).
fof(f1286,plain,
! [X2,X1,X8] :
( c_Transcendental_Osin(v_x) = X8
| X1 = X2
| c_HOL_Otimes__class_Otimes(X8,X1,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X8,X2,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1061,f1092]) ).
fof(f1061,axiom,
! [X2,X1,X8] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X8
| c_HOL_Otimes__class_Otimes(X8,X1,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X8,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__left__cancel_0) ).
fof(f2633,plain,
spl0_248,
inference(avatar_split_clause,[],[f1285,f2631]) ).
fof(f1285,plain,
! [X2,X1,X8] :
( c_Transcendental_Osin(v_x) = X8
| X1 = X2
| c_HOL_Otimes__class_Otimes(X1,X8,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X2,X8,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1060,f1092]) ).
fof(f1060,axiom,
! [X2,X1,X8] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X8
| c_HOL_Otimes__class_Otimes(X1,X8,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X2,X8,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__right__cancel_0) ).
fof(f2621,plain,
( spl0_247
| ~ spl0_8
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2605,f2601,f1376,f2619]) ).
fof(f2619,plain,
( spl0_247
<=> ! [X4] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f2601,plain,
( spl0_243
<=> ! [X4] :
( c_lessequals(c_Transcendental_Osin(v_x),c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2605,plain,
( ! [X4] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_243 ),
inference(forward_demodulation,[],[f2604,f1378]) ).
fof(f2604,plain,
( ! [X4] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_243 ),
inference(forward_demodulation,[],[f2602,f1378]) ).
fof(f2602,plain,
( ! [X4] :
( c_lessequals(c_Transcendental_Osin(v_x),c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2601]) ).
fof(f2617,plain,
( spl0_246
| ~ spl0_8
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2594,f2590,f1376,f2615]) ).
fof(f2590,plain,
( spl0_241
<=> ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Opi,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f2594,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_241 ),
inference(forward_demodulation,[],[f2593,f1378]) ).
fof(f2593,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_241 ),
inference(forward_demodulation,[],[f2591,f1378]) ).
fof(f2591,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f2590]) ).
fof(f2613,plain,
( spl0_245
| ~ spl0_8
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2588,f2585,f1376,f2611]) ).
fof(f2585,plain,
( spl0_240
<=> ! [X4,X10] :
( c_Transcendental_Osin(v_x) = X10
| c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f2588,plain,
( ! [X10,X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X10
| c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_240 ),
inference(forward_demodulation,[],[f2586,f1378]) ).
fof(f2586,plain,
( ! [X10,X4] :
( c_Transcendental_Osin(v_x) = X10
| c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_240 ),
inference(avatar_component_clause,[],[f2585]) ).
fof(f2609,plain,
( spl0_244
| ~ spl0_8
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2583,f2580,f1376,f2607]) ).
fof(f2580,plain,
( spl0_239
<=> ! [X4,X10] :
( c_Transcendental_Osin(v_x) = X4
| c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f2583,plain,
( ! [X10,X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X4
| c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_239 ),
inference(forward_demodulation,[],[f2581,f1378]) ).
fof(f2581,plain,
( ! [X10,X4] :
( c_Transcendental_Osin(v_x) = X4
| c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_239 ),
inference(avatar_component_clause,[],[f2580]) ).
fof(f2603,plain,
spl0_243,
inference(avatar_split_clause,[],[f1292,f2601]) ).
fof(f1292,plain,
! [X4] :
( c_lessequals(c_Transcendental_Osin(v_x),c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1291,f1092]) ).
fof(f1291,plain,
! [X4] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(X4),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1076,f1092]) ).
fof(f1076,axiom,
! [X4] :
( ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__ge__zero_0) ).
fof(f2599,plain,
( spl0_242
| ~ spl0_13
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2440,f2393,f1401,f2596]) ).
fof(f2440,plain,
( v_x = c_Log_Opowr(v_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_13
| ~ spl0_209 ),
inference(resolution,[],[f2394,f1403]) ).
fof(f2592,plain,
spl0_241,
inference(avatar_split_clause,[],[f1288,f2590]) ).
fof(f1288,plain,
! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Opi,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1287,f1092]) ).
fof(f1287,plain,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(X4),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1074,f1092]) ).
fof(f1074,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__gt__zero__pi_0) ).
fof(f2587,plain,
spl0_240,
inference(avatar_split_clause,[],[f1249,f2585]) ).
fof(f1249,plain,
! [X10,X4] :
( c_Transcendental_Osin(v_x) = X10
| c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f311,f1092]) ).
fof(f311,axiom,
! [X10,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X10
| c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_1) ).
fof(f2582,plain,
spl0_239,
inference(avatar_split_clause,[],[f1248,f2580]) ).
fof(f1248,plain,
! [X10,X4] :
( c_Transcendental_Osin(v_x) = X4
| c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f310,f1092]) ).
fof(f310,axiom,
! [X10,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_0) ).
fof(f2559,plain,
( spl0_238
| ~ spl0_8
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2530,f2527,f1376,f2557]) ).
fof(f2527,plain,
( spl0_231
<=> ! [X4,X0] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f2530,plain,
( ! [X0,X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 )
| ~ spl0_8
| ~ spl0_231 ),
inference(forward_demodulation,[],[f2528,f1378]) ).
fof(f2528,plain,
( ! [X0,X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 )
| ~ spl0_231 ),
inference(avatar_component_clause,[],[f2527]) ).
fof(f2555,plain,
( spl0_237
| ~ spl0_14
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2439,f2393,f1406,f2552]) ).
fof(f2439,plain,
( c_Transcendental_Opi = c_Log_Opowr(c_Transcendental_Opi,c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_14
| ~ spl0_209 ),
inference(resolution,[],[f2394,f1408]) ).
fof(f2550,plain,
( spl0_236
| ~ spl0_8
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2525,f2522,f1376,f2548]) ).
fof(f2548,plain,
( spl0_236
<=> ! [X4,X0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X4,X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f2522,plain,
( spl0_230
<=> ! [X4,X0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X4,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f2525,plain,
( ! [X0,X4] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X4,X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 )
| ~ spl0_8
| ~ spl0_230 ),
inference(forward_demodulation,[],[f2523,f1378]) ).
fof(f2523,plain,
( ! [X0,X4] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X4,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 )
| ~ spl0_230 ),
inference(avatar_component_clause,[],[f2522]) ).
fof(f2546,plain,
( spl0_235
| ~ spl0_8
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2520,f2517,f1376,f2544]) ).
fof(f2517,plain,
( spl0_229
<=> ! [X4,X0,X10] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_RealVector_Odist__class_Odist(X4,X10,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2520,plain,
( ! [X10,X0,X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Odist__class_Odist(X4,X10,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 )
| ~ spl0_8
| ~ spl0_229 ),
inference(forward_demodulation,[],[f2518,f1378]) ).
fof(f2518,plain,
( ! [X10,X0,X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_RealVector_Odist__class_Odist(X4,X10,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 )
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f2517]) ).
fof(f2542,plain,
( spl0_234
| ~ spl0_8
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2515,f2512,f1376,f2540]) ).
fof(f2540,plain,
( spl0_234
<=> ! [X4,X0,X10] :
( ~ c_lessequals(c_RealVector_Odist__class_Odist(X4,X10,X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f2512,plain,
( spl0_228
<=> ! [X4,X0,X10] :
( ~ c_lessequals(c_RealVector_Odist__class_Odist(X4,X10,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f2515,plain,
( ! [X10,X0,X4] :
( ~ c_lessequals(c_RealVector_Odist__class_Odist(X4,X10,X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 )
| ~ spl0_8
| ~ spl0_228 ),
inference(forward_demodulation,[],[f2513,f1378]) ).
fof(f2513,plain,
( ! [X10,X0,X4] :
( ~ c_lessequals(c_RealVector_Odist__class_Odist(X4,X10,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f2512]) ).
fof(f2538,plain,
( spl0_233
| ~ spl0_8
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f2510,f2507,f1376,f2536]) ).
fof(f2507,plain,
( spl0_227
<=> ! [X4] :
( c_Transcendental_Osin(v_x) = X4
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f2510,plain,
( ! [X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X4
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X4,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_227 ),
inference(forward_demodulation,[],[f2508,f1378]) ).
fof(f2508,plain,
( ! [X4] :
( c_Transcendental_Osin(v_x) = X4
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X4,tc_RealDef_Oreal) )
| ~ spl0_227 ),
inference(avatar_component_clause,[],[f2507]) ).
fof(f2534,plain,
( spl0_232
| ~ spl0_8
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2505,f2502,f1376,f2532]) ).
fof(f2532,plain,
( spl0_232
<=> ! [X4,X0,X10] :
( c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Otan(c_Transcendental_Opi),X4,X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Otan(c_Transcendental_Opi),X10,X0)
| ~ class_RealVector_Oreal__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f2502,plain,
( spl0_226
<=> ! [X4,X0,X10] :
( c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Osin(v_x),X4,X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Osin(v_x),X10,X0)
| ~ class_RealVector_Oreal__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f2505,plain,
( ! [X10,X0,X4] :
( c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Otan(c_Transcendental_Opi),X4,X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Otan(c_Transcendental_Opi),X10,X0)
| ~ class_RealVector_Oreal__vector(X0) )
| ~ spl0_8
| ~ spl0_226 ),
inference(forward_demodulation,[],[f2503,f1378]) ).
fof(f2503,plain,
( ! [X10,X0,X4] :
( c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Osin(v_x),X4,X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Osin(v_x),X10,X0)
| ~ class_RealVector_Oreal__vector(X0) )
| ~ spl0_226 ),
inference(avatar_component_clause,[],[f2502]) ).
fof(f2529,plain,
spl0_231,
inference(avatar_split_clause,[],[f1284,f2527]) ).
fof(f1284,plain,
! [X0,X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 ),
inference(forward_demodulation,[],[f1052,f1092]) ).
fof(f1052,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__norm__iff_1) ).
fof(f2524,plain,
spl0_230,
inference(avatar_split_clause,[],[f1283,f2522]) ).
fof(f1283,plain,
! [X0,X4] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X4,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 ),
inference(forward_demodulation,[],[f1055,f1092]) ).
fof(f1055,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X4,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_0) ).
fof(f2519,plain,
spl0_229,
inference(avatar_split_clause,[],[f1279,f2517]) ).
fof(f1279,plain,
! [X10,X0,X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_RealVector_Odist__class_Odist(X4,X10,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 ),
inference(forward_demodulation,[],[f77,f1092]) ).
fof(f77,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Ometric__space(X0)
| X4 = X10
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X4,X10,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__dist__iff_1) ).
fof(f2514,plain,
spl0_228,
inference(avatar_split_clause,[],[f1278,f2512]) ).
fof(f1278,plain,
! [X10,X0,X4] :
( ~ c_lessequals(c_RealVector_Odist__class_Odist(X4,X10,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 ),
inference(forward_demodulation,[],[f822,f1092]) ).
fof(f822,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Ometric__space(X0)
| X4 = X10
| ~ c_lessequals(c_RealVector_Odist__class_Odist(X4,X10,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__le__zero__iff_0) ).
fof(f2509,plain,
spl0_227,
inference(avatar_split_clause,[],[f1247,f2507]) ).
fof(f1247,plain,
! [X4] :
( c_Transcendental_Osin(v_x) = X4
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f161,f1092]) ).
fof(f161,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__inverse__left_0) ).
fof(f2504,plain,
spl0_226,
inference(avatar_split_clause,[],[f1235,f2502]) ).
fof(f1235,plain,
! [X10,X0,X4] :
( c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Osin(v_x),X4,X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Osin(v_x),X10,X0)
| ~ class_RealVector_Oreal__vector(X0) ),
inference(forward_demodulation,[],[f1057,f1092]) ).
fof(f1057,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__left_1) ).
fof(f2493,plain,
( spl0_225
| ~ spl0_8
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2477,f2474,f1376,f2491]) ).
fof(f2491,plain,
( spl0_225
<=> ! [X4,X0] :
( c_RealVector_Onorm__class_Onorm(X4,X0) != c_Transcendental_Otan(c_Transcendental_Opi)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f2474,plain,
( spl0_221
<=> ! [X4,X0] :
( c_RealVector_Onorm__class_Onorm(X4,X0) != c_Transcendental_Osin(v_x)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f2477,plain,
( ! [X0,X4] :
( c_RealVector_Onorm__class_Onorm(X4,X0) != c_Transcendental_Otan(c_Transcendental_Opi)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 )
| ~ spl0_8
| ~ spl0_221 ),
inference(forward_demodulation,[],[f2475,f1378]) ).
fof(f2475,plain,
( ! [X0,X4] :
( c_RealVector_Onorm__class_Onorm(X4,X0) != c_Transcendental_Osin(v_x)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 )
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f2474]) ).
fof(f2489,plain,
( spl0_224
| ~ spl0_8
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2467,f2464,f1376,f2487]) ).
fof(f2487,plain,
( spl0_224
<=> ! [X4,X0] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X4
| ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(X4,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f2464,plain,
( spl0_219
<=> ! [X4,X0] :
( c_Transcendental_Osin(v_x) = X4
| ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(X4,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f2467,plain,
( ! [X0,X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X4
| ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(X4,X0) != c_HOL_Ozero__class_Ozero(X0) )
| ~ spl0_8
| ~ spl0_219 ),
inference(forward_demodulation,[],[f2465,f1378]) ).
fof(f2465,plain,
( ! [X0,X4] :
( c_Transcendental_Osin(v_x) = X4
| ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(X4,X0) != c_HOL_Ozero__class_Ozero(X0) )
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f2464]) ).
fof(f2485,plain,
( spl0_223
| ~ spl0_8
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2462,f2459,f1376,f2483]) ).
fof(f2483,plain,
( spl0_223
<=> ! [X4,X0,X10] :
( c_RealVector_Odist__class_Odist(X4,X10,X0) != c_Transcendental_Otan(c_Transcendental_Opi)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2459,plain,
( spl0_218
<=> ! [X4,X0,X10] :
( c_RealVector_Odist__class_Odist(X4,X10,X0) != c_Transcendental_Osin(v_x)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2462,plain,
( ! [X10,X0,X4] :
( c_RealVector_Odist__class_Odist(X4,X10,X0) != c_Transcendental_Otan(c_Transcendental_Opi)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 )
| ~ spl0_8
| ~ spl0_218 ),
inference(forward_demodulation,[],[f2460,f1378]) ).
fof(f2460,plain,
( ! [X10,X0,X4] :
( c_RealVector_Odist__class_Odist(X4,X10,X0) != c_Transcendental_Osin(v_x)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f2459]) ).
fof(f2481,plain,
( spl0_222
| ~ spl0_8
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2457,f2453,f1376,f2479]) ).
fof(f2453,plain,
( spl0_217
<=> ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Osin(v_x) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f2457,plain,
( ! [X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X4
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_217 ),
inference(forward_demodulation,[],[f2456,f1378]) ).
fof(f2456,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Osin(v_x) = X4 )
| ~ spl0_8
| ~ spl0_217 ),
inference(forward_demodulation,[],[f2454,f1378]) ).
fof(f2454,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Osin(v_x) = X4 )
| ~ spl0_217 ),
inference(avatar_component_clause,[],[f2453]) ).
fof(f2476,plain,
spl0_221,
inference(avatar_split_clause,[],[f1282,f2474]) ).
fof(f1282,plain,
! [X0,X4] :
( c_RealVector_Onorm__class_Onorm(X4,X0) != c_Transcendental_Osin(v_x)
| ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4 ),
inference(forward_demodulation,[],[f1084,f1092]) ).
fof(f1084,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_RealVector_Onorm__class_Onorm(X4,X0) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
fof(f2472,plain,
( spl0_220
| ~ spl0_13
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2431,f2389,f1401,f2469]) ).
fof(f2469,plain,
( spl0_220
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(v_x,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f2431,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(v_x,tc_RealDef_Oreal)
| ~ spl0_13
| ~ spl0_208 ),
inference(resolution,[],[f2390,f1403]) ).
fof(f2466,plain,
spl0_219,
inference(avatar_split_clause,[],[f1281,f2464]) ).
fof(f1281,plain,
! [X0,X4] :
( c_Transcendental_Osin(v_x) = X4
| ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(X4,X0) != c_HOL_Ozero__class_Ozero(X0) ),
inference(forward_demodulation,[],[f1081,f1092]) ).
fof(f1081,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_RealVector_Oof__real(X4,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).
fof(f2461,plain,
spl0_218,
inference(avatar_split_clause,[],[f1277,f2459]) ).
fof(f1277,plain,
! [X10,X0,X4] :
( c_RealVector_Odist__class_Odist(X4,X10,X0) != c_Transcendental_Osin(v_x)
| ~ class_RealVector_Ometric__space(X0)
| X4 = X10 ),
inference(forward_demodulation,[],[f1071,f1092]) ).
fof(f1071,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Ometric__space(X0)
| X4 = X10
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Odist__class_Odist(X4,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__eq__0__iff_0) ).
fof(f2455,plain,
spl0_217,
inference(avatar_split_clause,[],[f1246,f2453]) ).
fof(f1246,plain,
! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_Transcendental_Osin(v_x) = X4 ),
inference(forward_demodulation,[],[f1245,f1092]) ).
fof(f1245,plain,
! [X4] :
( c_Transcendental_Osin(v_x) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f961,f1092]) ).
fof(f961,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_0) ).
fof(f2436,plain,
( spl0_216
| ~ spl0_14
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f2430,f2389,f1406,f2433]) ).
fof(f2433,plain,
( spl0_216
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f2430,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_14
| ~ spl0_208 ),
inference(resolution,[],[f2390,f1408]) ).
fof(f2421,plain,
( spl0_215
| ~ spl0_8
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2371,f2367,f1376,f2419]) ).
fof(f2367,plain,
( spl0_203
<=> ! [X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2371,plain,
( ! [X10] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_203 ),
inference(forward_demodulation,[],[f2370,f1378]) ).
fof(f2370,plain,
( ! [X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_203 ),
inference(forward_demodulation,[],[f2368,f1378]) ).
fof(f2368,plain,
( ! [X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f2367]) ).
fof(f2417,plain,
( spl0_214
| ~ spl0_8
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2365,f2362,f1376,f2415]) ).
fof(f2415,plain,
( spl0_214
<=> ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_Log_Opowr(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f2362,plain,
( spl0_202
<=> ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_Log_Opowr(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f2365,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_Log_Opowr(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) != X4 )
| ~ spl0_8
| ~ spl0_202 ),
inference(forward_demodulation,[],[f2363,f1378]) ).
fof(f2363,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_Log_Opowr(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) != X4 )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f2362]) ).
fof(f2413,plain,
( spl0_213
| ~ spl0_8
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2360,f2356,f1376,f2411]) ).
fof(f2356,plain,
( spl0_201
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f2360,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_201 ),
inference(forward_demodulation,[],[f2359,f1378]) ).
fof(f2359,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_201 ),
inference(forward_demodulation,[],[f2357,f1378]) ).
fof(f2357,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f2356]) ).
fof(f2409,plain,
( spl0_212
| ~ spl0_8
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2354,f2350,f1376,f2407]) ).
fof(f2350,plain,
( spl0_200
<=> ! [X10] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f2354,plain,
( ! [X10] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_200 ),
inference(forward_demodulation,[],[f2353,f1378]) ).
fof(f2353,plain,
( ! [X10] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_200 ),
inference(forward_demodulation,[],[f2351,f1378]) ).
fof(f2351,plain,
( ! [X10] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal) )
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f2350]) ).
fof(f2405,plain,
( spl0_211
| ~ spl0_8
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2348,f2344,f1376,f2403]) ).
fof(f2344,plain,
( spl0_199
<=> ! [X4] :
( ~ c_lessequals(c_NthRoot_Osqrt(X4),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f2348,plain,
( ! [X4] :
( c_lessequals(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_199 ),
inference(forward_demodulation,[],[f2347,f1378]) ).
fof(f2347,plain,
( ! [X4] :
( ~ c_lessequals(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_199 ),
inference(forward_demodulation,[],[f2345,f1378]) ).
fof(f2345,plain,
( ! [X4] :
( ~ c_lessequals(c_NthRoot_Osqrt(X4),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f2344]) ).
fof(f2399,plain,
( spl0_210
| ~ spl0_8
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2342,f2338,f1376,f2397]) ).
fof(f2338,plain,
( spl0_198
<=> ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2342,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_198 ),
inference(forward_demodulation,[],[f2341,f1378]) ).
fof(f2341,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_198 ),
inference(forward_demodulation,[],[f2339,f1378]) ).
fof(f2339,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f2338]) ).
fof(f2395,plain,
( spl0_209
| ~ spl0_8
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2336,f2333,f1376,f2393]) ).
fof(f2333,plain,
( spl0_197
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_Log_Opowr(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f2336,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_Log_Opowr(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X4 )
| ~ spl0_8
| ~ spl0_197 ),
inference(forward_demodulation,[],[f2334,f1378]) ).
fof(f2334,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_Log_Opowr(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X4 )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f2333]) ).
fof(f2391,plain,
( spl0_208
| ~ spl0_8
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2331,f2328,f1376,f2389]) ).
fof(f2328,plain,
( spl0_196
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f2331,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_196 ),
inference(forward_demodulation,[],[f2329,f1378]) ).
fof(f2329,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) )
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f2328]) ).
fof(f2387,plain,
( spl0_207
| ~ spl0_8
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2326,f2322,f1376,f2385]) ).
fof(f2322,plain,
( spl0_195
<=> ! [X4] :
( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f2326,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_195 ),
inference(forward_demodulation,[],[f2325,f1378]) ).
fof(f2325,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_195 ),
inference(forward_demodulation,[],[f2323,f1378]) ).
fof(f2323,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f2322]) ).
fof(f2383,plain,
( spl0_206
| ~ spl0_8
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f2320,f2316,f1376,f2381]) ).
fof(f2381,plain,
( spl0_206
<=> ! [X10] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f2316,plain,
( spl0_194
<=> ! [X10] :
( c_lessequals(c_Transcendental_Osin(v_x),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f2320,plain,
( ! [X10] :
( ~ c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),X10,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_194 ),
inference(forward_demodulation,[],[f2319,f1378]) ).
fof(f2319,plain,
( ! [X10] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_194 ),
inference(forward_demodulation,[],[f2317,f1378]) ).
fof(f2317,plain,
( ! [X10] :
( c_lessequals(c_Transcendental_Osin(v_x),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal) )
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f2316]) ).
fof(f2379,plain,
( spl0_205
| ~ spl0_8
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2314,f2310,f1376,f2377]) ).
fof(f2310,plain,
( spl0_193
<=> ! [X4] :
( c_lessequals(c_NthRoot_Osqrt(X4),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f2314,plain,
( ! [X4] :
( ~ c_lessequals(X4,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_193 ),
inference(forward_demodulation,[],[f2313,f1378]) ).
fof(f2313,plain,
( ! [X4] :
( c_lessequals(c_NthRoot_Osqrt(X4),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_193 ),
inference(forward_demodulation,[],[f2311,f1378]) ).
fof(f2311,plain,
( ! [X4] :
( c_lessequals(c_NthRoot_Osqrt(X4),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) )
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f2310]) ).
fof(f2375,plain,
( spl0_204
| ~ spl0_8
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2308,f2305,f1376,f2373]) ).
fof(f2373,plain,
( spl0_204
<=> ! [X0] :
( c_Transcendental_Otan(c_Transcendental_Opi) = c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f2305,plain,
( spl0_192
<=> ! [X0] :
( c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0),X0) = c_Transcendental_Osin(v_x)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f2308,plain,
( ! [X0] :
( c_Transcendental_Otan(c_Transcendental_Opi) = c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_8
| ~ spl0_192 ),
inference(forward_demodulation,[],[f2306,f1378]) ).
fof(f2306,plain,
( ! [X0] :
( c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0),X0) = c_Transcendental_Osin(v_x)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f2305]) ).
fof(f2369,plain,
spl0_203,
inference(avatar_split_clause,[],[f1275,f2367]) ).
fof(f1275,plain,
! [X10] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1274,f1092]) ).
fof(f1274,plain,
! [X10] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f383,f1092]) ).
fof(f383,axiom,
! [X10] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__0__iff_0) ).
fof(f2364,plain,
spl0_202,
inference(avatar_split_clause,[],[f1273,f2362]) ).
fof(f1273,plain,
! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_Log_Opowr(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) != X4 ),
inference(forward_demodulation,[],[f545,f1092]) ).
fof(f545,axiom,
! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_Log_Opowr(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__one__gt__zero__iff_0) ).
fof(f2358,plain,
spl0_201,
inference(avatar_split_clause,[],[f1272,f2356]) ).
fof(f1272,plain,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1271,f1092]) ).
fof(f1271,plain,
! [X4] :
( c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f482,f1092]) ).
fof(f482,axiom,
! [X4] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_0) ).
fof(f2352,plain,
spl0_200,
inference(avatar_split_clause,[],[f1270,f2350]) ).
fof(f1270,plain,
! [X10] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1269,f1092]) ).
fof(f1269,plain,
! [X10] :
( c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f63,f1092]) ).
fof(f63,axiom,
! [X10] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__0__iff_0) ).
fof(f2346,plain,
spl0_199,
inference(avatar_split_clause,[],[f1268,f2344]) ).
fof(f1268,plain,
! [X4] :
( ~ c_lessequals(c_NthRoot_Osqrt(X4),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1267,f1092]) ).
fof(f1267,plain,
! [X4] :
( c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f679,f1092]) ).
fof(f679,axiom,
! [X4] :
( c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_0) ).
fof(f2340,plain,
spl0_198,
inference(avatar_split_clause,[],[f1264,f2338]) ).
fof(f1264,plain,
! [X4] :
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1263,f1092]) ).
fof(f1263,plain,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f384,f1092]) ).
fof(f384,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__zero_0) ).
fof(f2335,plain,
spl0_197,
inference(avatar_split_clause,[],[f1262,f2333]) ).
fof(f1262,plain,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_Log_Opowr(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X4 ),
inference(forward_demodulation,[],[f544,f1092]) ).
fof(f544,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_Log_Opowr(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__one__gt__zero__iff_1) ).
fof(f2330,plain,
spl0_196,
inference(avatar_split_clause,[],[f1261,f2328]) ).
fof(f1261,plain,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f977,f1092]) ).
fof(f977,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sgn__pos_0) ).
fof(f2324,plain,
spl0_195,
inference(avatar_split_clause,[],[f1260,f2322]) ).
fof(f1260,plain,
! [X4] :
( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1259,f1092]) ).
fof(f1259,plain,
! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f483,f1092]) ).
fof(f483,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_1) ).
fof(f2318,plain,
spl0_194,
inference(avatar_split_clause,[],[f1256,f2316]) ).
fof(f1256,plain,
! [X10] :
( c_lessequals(c_Transcendental_Osin(v_x),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1255,f1092]) ).
fof(f1255,plain,
! [X10] :
( ~ c_lessequals(c_Transcendental_Osin(v_x),X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f64,f1092]) ).
fof(f64,axiom,
! [X10] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X10,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X10),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__0__iff_1) ).
fof(f2312,plain,
spl0_193,
inference(avatar_split_clause,[],[f1254,f2310]) ).
fof(f1254,plain,
! [X4] :
( c_lessequals(c_NthRoot_Osqrt(X4),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1253,f1092]) ).
fof(f1253,plain,
! [X4] :
( ~ c_lessequals(X4,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f680,f1092]) ).
fof(f680,axiom,
! [X4] :
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_1) ).
fof(f2307,plain,
spl0_192,
inference(avatar_split_clause,[],[f1242,f2305]) ).
fof(f1242,plain,
! [X0] :
( c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0),X0) = c_Transcendental_Osin(v_x)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(forward_demodulation,[],[f1051,f1092]) ).
fof(f1051,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__sgn_0) ).
fof(f2293,plain,
( spl0_191
| ~ spl0_8
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f2247,f2243,f1376,f2291]) ).
fof(f2291,plain,
( spl0_191
<=> ! [X4] :
( c_NthRoot_Osqrt(X4) != c_Transcendental_Otan(c_Transcendental_Opi)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f2243,plain,
( spl0_180
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X4) != c_Transcendental_Osin(v_x) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f2247,plain,
( ! [X4] :
( c_NthRoot_Osqrt(X4) != c_Transcendental_Otan(c_Transcendental_Opi)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal) )
| ~ spl0_8
| ~ spl0_180 ),
inference(forward_demodulation,[],[f2246,f1378]) ).
fof(f2246,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),X4,tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X4) != c_Transcendental_Osin(v_x) )
| ~ spl0_8
| ~ spl0_180 ),
inference(forward_demodulation,[],[f2244,f1378]) ).
fof(f2244,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X4) != c_Transcendental_Osin(v_x) )
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f2243]) ).
fof(f2289,plain,
( spl0_190
| ~ spl0_110
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2185,f2170,f1892,f2286]) ).
fof(f2286,plain,
( spl0_190
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_RealVector_Onorm__class_Onorm(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1892,plain,
( spl0_110
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f2170,plain,
( spl0_166
<=> ! [X0] :
( c_Transcendental_Otan(c_Transcendental_Opi) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f2185,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_RealVector_Onorm__class_Onorm(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_110
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2184,f908]) ).
fof(f2184,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_110
| ~ spl0_166 ),
inference(resolution,[],[f2171,f1894]) ).
fof(f1894,plain,
( class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1892]) ).
fof(f2171,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Transcendental_Otan(c_Transcendental_Opi) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f2170]) ).
fof(f2284,plain,
( spl0_189
| ~ spl0_8
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f2236,f2233,f1376,f2282]) ).
fof(f2233,plain,
( spl0_178
<=> ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f2236,plain,
( ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_8
| ~ spl0_178 ),
inference(forward_demodulation,[],[f2234,f1378]) ).
fof(f2234,plain,
( ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f2233]) ).
fof(f2280,plain,
( spl0_188
| ~ spl0_8
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f2231,f2228,f1376,f2278]) ).
fof(f2278,plain,
( spl0_188
<=> ! [X2,X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Otan(c_Transcendental_Opi),X2,X0)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f2228,plain,
( spl0_177
<=> ! [X2,X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Osin(v_x),X2,X0)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f2231,plain,
( ! [X2,X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Otan(c_Transcendental_Opi),X2,X0)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_8
| ~ spl0_177 ),
inference(forward_demodulation,[],[f2229,f1378]) ).
fof(f2229,plain,
( ! [X2,X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Osin(v_x),X2,X0)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f2228]) ).
fof(f2276,plain,
( spl0_187
| ~ spl0_8
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f2226,f2223,f1376,f2274]) ).
fof(f2223,plain,
( spl0_176
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f2226,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_8
| ~ spl0_176 ),
inference(forward_demodulation,[],[f2224,f1378]) ).
fof(f2224,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f2223]) ).
fof(f2272,plain,
( spl0_186
| ~ spl0_8
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f2221,f2218,f1376,f2270]) ).
fof(f2218,plain,
( spl0_175
<=> ! [X4,X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Osin(v_x),X4,X0)
| ~ class_RealVector_Oreal__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f2221,plain,
( ! [X0,X4] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Otan(c_Transcendental_Opi),X4,X0)
| ~ class_RealVector_Oreal__vector(X0) )
| ~ spl0_8
| ~ spl0_175 ),
inference(forward_demodulation,[],[f2219,f1378]) ).
fof(f2219,plain,
( ! [X0,X4] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Osin(v_x),X4,X0)
| ~ class_RealVector_Oreal__vector(X0) )
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f2218]) ).
fof(f2268,plain,
( spl0_185
| ~ spl0_8
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f2216,f2213,f1376,f2266]) ).
fof(f2213,plain,
( spl0_174
<=> ! [X4,X0] :
( c_lessequals(c_RealVector_Odist__class_Odist(X4,X4,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f2216,plain,
( ! [X0,X4] :
( c_lessequals(c_RealVector_Odist__class_Odist(X4,X4,X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) )
| ~ spl0_8
| ~ spl0_174 ),
inference(forward_demodulation,[],[f2214,f1378]) ).
fof(f2214,plain,
( ! [X0,X4] :
( c_lessequals(c_RealVector_Odist__class_Odist(X4,X4,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) )
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f2213]) ).
fof(f2264,plain,
( spl0_184
| ~ spl0_8
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2211,f2208,f1376,f2262]) ).
fof(f2208,plain,
( spl0_173
<=> ! [X4,X0,X10] :
( c_lessequals(c_Transcendental_Osin(v_x),c_RealVector_Odist__class_Odist(X4,X10,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f2211,plain,
( ! [X10,X0,X4] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Odist__class_Odist(X4,X10,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) )
| ~ spl0_8
| ~ spl0_173 ),
inference(forward_demodulation,[],[f2209,f1378]) ).
fof(f2209,plain,
( ! [X10,X0,X4] :
( c_lessequals(c_Transcendental_Osin(v_x),c_RealVector_Odist__class_Odist(X4,X10,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f2208]) ).
fof(f2260,plain,
( spl0_183
| ~ spl0_8
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f2206,f2203,f1376,f2258]) ).
fof(f2258,plain,
( spl0_183
<=> ! [X4,X0,X10] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(X4,X10,X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f2203,plain,
( spl0_172
<=> ! [X4,X0,X10] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(X4,X10,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f2206,plain,
( ! [X10,X0,X4] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(X4,X10,X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) )
| ~ spl0_8
| ~ spl0_172 ),
inference(forward_demodulation,[],[f2204,f1378]) ).
fof(f2204,plain,
( ! [X10,X0,X4] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(X4,X10,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) )
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f2203]) ).
fof(f2256,plain,
( spl0_182
| ~ spl0_8
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f2201,f2198,f1376,f2254]) ).
fof(f2198,plain,
( spl0_171
<=> ! [X4,X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_RealVector_Odist__class_Odist(X4,X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f2201,plain,
( ! [X0,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Odist__class_Odist(X4,X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) )
| ~ spl0_8
| ~ spl0_171 ),
inference(forward_demodulation,[],[f2199,f1378]) ).
fof(f2199,plain,
( ! [X0,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_RealVector_Odist__class_Odist(X4,X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) )
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f2198]) ).
fof(f2252,plain,
( ~ spl0_181
| ~ spl0_8
| spl0_170 ),
inference(avatar_split_clause,[],[f2196,f2192,f1376,f2249]) ).
fof(f2192,plain,
( spl0_170
<=> c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f2196,plain,
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Otimes__class_Otimes(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_8
| spl0_170 ),
inference(forward_demodulation,[],[f2194,f1378]) ).
fof(f2194,plain,
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_170 ),
inference(avatar_component_clause,[],[f2192]) ).
fof(f2245,plain,
spl0_180,
inference(avatar_split_clause,[],[f1252,f2243]) ).
fof(f1252,plain,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),X4,tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X4) != c_Transcendental_Osin(v_x) ),
inference(forward_demodulation,[],[f1251,f1092]) ).
fof(f1251,plain,
! [X4] :
( c_NthRoot_Osqrt(X4) != c_Transcendental_Osin(v_x)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f239,f1092]) ).
fof(f239,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__not__eq__zero_0) ).
fof(f2241,plain,
( spl0_179
| ~ spl0_127
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2183,f2162,f1977,f2238]) ).
fof(f2238,plain,
( spl0_179
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_RealVector_Oof__real(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1977,plain,
( spl0_127
<=> class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f2162,plain,
( spl0_164
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_Oof__real(c_Transcendental_Otan(c_Transcendental_Opi),X0)
| ~ class_RealVector_Oreal__algebra__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f2183,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_RealVector_Oof__real(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_127
| ~ spl0_164 ),
inference(forward_demodulation,[],[f2182,f908]) ).
fof(f2182,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Oof__real(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_127
| ~ spl0_164 ),
inference(resolution,[],[f2163,f1979]) ).
fof(f1979,plain,
( class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal)
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1977]) ).
fof(f2163,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_Oof__real(c_Transcendental_Otan(c_Transcendental_Opi),X0) )
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f2162]) ).
fof(f2235,plain,
spl0_178,
inference(avatar_split_clause,[],[f1241,f2233]) ).
fof(f1241,plain,
! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(forward_demodulation,[],[f1054,f1092]) ).
fof(f1054,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_1) ).
fof(f2230,plain,
spl0_177,
inference(avatar_split_clause,[],[f1240,f2228]) ).
fof(f1240,plain,
! [X2,X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Osin(v_x),X2,X0)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(forward_demodulation,[],[f1085,f1092]) ).
fof(f1085,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ozero__left_0) ).
fof(f2225,plain,
spl0_176,
inference(avatar_split_clause,[],[f1239,f2223]) ).
fof(f1239,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(forward_demodulation,[],[f1053,f1092]) ).
fof(f1053,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__norm__iff_0) ).
fof(f2220,plain,
spl0_175,
inference(avatar_split_clause,[],[f1234,f2218]) ).
fof(f1234,plain,
! [X0,X4] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(c_Transcendental_Osin(v_x),X4,X0)
| ~ class_RealVector_Oreal__vector(X0) ),
inference(forward_demodulation,[],[f1086,f1092]) ).
fof(f1086,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_1) ).
fof(f2215,plain,
spl0_174,
inference(avatar_split_clause,[],[f1232,f2213]) ).
fof(f1232,plain,
! [X0,X4] :
( c_lessequals(c_RealVector_Odist__class_Odist(X4,X4,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ),
inference(forward_demodulation,[],[f257,f1092]) ).
fof(f257,axiom,
! [X0,X4] :
( ~ class_RealVector_Ometric__space(X0)
| c_lessequals(c_RealVector_Odist__class_Odist(X4,X4,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__le__zero__iff_1) ).
fof(f2210,plain,
spl0_173,
inference(avatar_split_clause,[],[f1231,f2208]) ).
fof(f1231,plain,
! [X10,X0,X4] :
( c_lessequals(c_Transcendental_Osin(v_x),c_RealVector_Odist__class_Odist(X4,X10,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ),
inference(forward_demodulation,[],[f24,f1092]) ).
fof(f24,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Ometric__space(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X4,X10,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__dist_0) ).
fof(f2205,plain,
spl0_172,
inference(avatar_split_clause,[],[f1230,f2203]) ).
fof(f1230,plain,
! [X10,X0,X4] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(X4,X10,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ),
inference(forward_demodulation,[],[f202,f1092]) ).
fof(f202,axiom,
! [X10,X0,X4] :
( ~ class_RealVector_Ometric__space(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(X4,X10,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__not__less__zero_0) ).
fof(f2200,plain,
spl0_171,
inference(avatar_split_clause,[],[f1229,f2198]) ).
fof(f1229,plain,
! [X0,X4] :
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_RealVector_Odist__class_Odist(X4,X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X0) ),
inference(forward_demodulation,[],[f421,f1092]) ).
fof(f421,axiom,
! [X0,X4] :
( ~ class_RealVector_Ometric__space(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X4,X4,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__dist__iff_0) ).
fof(f2195,plain,
~ spl0_170,
inference(avatar_split_clause,[],[f1227,f2192]) ).
fof(f1227,plain,
~ c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(v_x),c_Transcendental_Osin(v_x),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f575,f1092]) ).
fof(f575,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_1) ).
fof(f2189,plain,
( spl0_169
| ~ spl0_137
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f2181,f2158,f2027,f2187]) ).
fof(f2187,plain,
( spl0_169
<=> ! [X0] : c_Transcendental_Otan(c_Transcendental_Opi) = c_RealVector_Odist__class_Odist(X0,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f2027,plain,
( spl0_137
<=> class_RealVector_Ometric__space(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f2158,plain,
( spl0_163
<=> ! [X4,X0] :
( c_RealVector_Odist__class_Odist(X4,X4,X0) = c_Transcendental_Otan(c_Transcendental_Opi)
| ~ class_RealVector_Ometric__space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f2181,plain,
( ! [X0] : c_Transcendental_Otan(c_Transcendental_Opi) = c_RealVector_Odist__class_Odist(X0,X0,tc_RealDef_Oreal)
| ~ spl0_137
| ~ spl0_163 ),
inference(resolution,[],[f2159,f2029]) ).
fof(f2029,plain,
( class_RealVector_Ometric__space(tc_RealDef_Oreal)
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f2027]) ).
fof(f2159,plain,
( ! [X0,X4] :
( ~ class_RealVector_Ometric__space(X0)
| c_RealVector_Odist__class_Odist(X4,X4,X0) = c_Transcendental_Otan(c_Transcendental_Opi) )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f2158]) ).
fof(f2180,plain,
( spl0_168
| ~ spl0_8
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f2156,f2152,f1376,f2178]) ).
fof(f2178,plain,
( spl0_168
<=> ! [X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X4
| c_NthRoot_Osqrt(X4) != c_Transcendental_Otan(c_Transcendental_Opi) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f2152,plain,
( spl0_162
<=> ! [X4] :
( c_NthRoot_Osqrt(X4) != c_Transcendental_Osin(v_x)
| c_Transcendental_Osin(v_x) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f2156,plain,
( ! [X4] :
( c_Transcendental_Otan(c_Transcendental_Opi) = X4
| c_NthRoot_Osqrt(X4) != c_Transcendental_Otan(c_Transcendental_Opi) )
| ~ spl0_8
| ~ spl0_162 ),
inference(forward_demodulation,[],[f2155,f1378]) ).
fof(f2155,plain,
( ! [X4] :
( c_NthRoot_Osqrt(X4) != c_Transcendental_Otan(c_Transcendental_Opi)
| c_Transcendental_Osin(v_x) = X4 )
| ~ spl0_8
| ~ spl0_162 ),
inference(forward_demodulation,[],[f2153,f1378]) ).
fof(f2153,plain,
( ! [X4] :
( c_NthRoot_Osqrt(X4) != c_Transcendental_Osin(v_x)
| c_Transcendental_Osin(v_x) = X4 )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f2152]) ).
fof(f2176,plain,
( spl0_167
| ~ spl0_8
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2150,f2147,f1376,f2174]) ).
fof(f2147,plain,
( spl0_161
<=> ! [X4,X0] :
( c_lessequals(c_Transcendental_Osin(v_x),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f2150,plain,
( ! [X0,X4] :
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_8
| ~ spl0_161 ),
inference(forward_demodulation,[],[f2148,f1378]) ).
fof(f2148,plain,
( ! [X0,X4] :
( c_lessequals(c_Transcendental_Osin(v_x),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f2147]) ).
fof(f2172,plain,
( spl0_166
| ~ spl0_8
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f2145,f2142,f1376,f2170]) ).
fof(f2142,plain,
( spl0_160
<=> ! [X0] :
( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) = c_Transcendental_Osin(v_x)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f2145,plain,
( ! [X0] :
( c_Transcendental_Otan(c_Transcendental_Opi) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_8
| ~ spl0_160 ),
inference(forward_demodulation,[],[f2143,f1378]) ).
fof(f2143,plain,
( ! [X0] :
( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) = c_Transcendental_Osin(v_x)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f2142]) ).
fof(f2168,plain,
( spl0_165
| ~ spl0_8
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f2140,f2137,f1376,f2166]) ).
fof(f2166,plain,
( spl0_165
<=> ! [X4,X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f2137,plain,
( spl0_159
<=> ! [X4,X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f2140,plain,
( ! [X0,X4] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X0),c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_8
| ~ spl0_159 ),
inference(forward_demodulation,[],[f2138,f1378]) ).
fof(f2138,plain,
( ! [X0,X4] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f2137]) ).
fof(f2164,plain,
( spl0_164
| ~ spl0_8
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f2135,f2132,f1376,f2162]) ).
fof(f2132,plain,
( spl0_158
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_Oof__real(c_Transcendental_Osin(v_x),X0)
| ~ class_RealVector_Oreal__algebra__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f2135,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_Oof__real(c_Transcendental_Otan(c_Transcendental_Opi),X0)
| ~ class_RealVector_Oreal__algebra__1(X0) )
| ~ spl0_8
| ~ spl0_158 ),
inference(forward_demodulation,[],[f2133,f1378]) ).
fof(f2133,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_Oof__real(c_Transcendental_Osin(v_x),X0)
| ~ class_RealVector_Oreal__algebra__1(X0) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f2132]) ).
fof(f2160,plain,
( spl0_163
| ~ spl0_8
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f2130,f2127,f1376,f2158]) ).
fof(f2127,plain,
( spl0_157
<=> ! [X4,X0] :
( c_RealVector_Odist__class_Odist(X4,X4,X0) = c_Transcendental_Osin(v_x)
| ~ class_RealVector_Ometric__space(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f2130,plain,
( ! [X0,X4] :
( c_RealVector_Odist__class_Odist(X4,X4,X0) = c_Transcendental_Otan(c_Transcendental_Opi)
| ~ class_RealVector_Ometric__space(X0) )
| ~ spl0_8
| ~ spl0_157 ),
inference(forward_demodulation,[],[f2128,f1378]) ).
fof(f2128,plain,
( ! [X0,X4] :
( c_RealVector_Odist__class_Odist(X4,X4,X0) = c_Transcendental_Osin(v_x)
| ~ class_RealVector_Ometric__space(X0) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f2127]) ).
fof(f2154,plain,
spl0_162,
inference(avatar_split_clause,[],[f1244,f2152]) ).
fof(f1244,plain,
! [X4] :
( c_NthRoot_Osqrt(X4) != c_Transcendental_Osin(v_x)
| c_Transcendental_Osin(v_x) = X4 ),
inference(forward_demodulation,[],[f1243,f1092]) ).
fof(f1243,plain,
! [X4] :
( c_Transcendental_Osin(v_x) = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X4) ),
inference(forward_demodulation,[],[f1063,f1092]) ).
fof(f1063,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__0__iff_0) ).
fof(f2149,plain,
spl0_161,
inference(avatar_split_clause,[],[f1238,f2147]) ).
fof(f1238,plain,
! [X0,X4] :
( c_lessequals(c_Transcendental_Osin(v_x),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(forward_demodulation,[],[f170,f1092]) ).
fof(f170,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
fof(f2144,plain,
spl0_160,
inference(avatar_split_clause,[],[f1237,f2142]) ).
fof(f1237,plain,
! [X0] :
( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) = c_Transcendental_Osin(v_x)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(forward_demodulation,[],[f1079,f1092]) ).
fof(f1079,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__zero_0) ).
fof(f2139,plain,
spl0_159,
inference(avatar_split_clause,[],[f1236,f2137]) ).
fof(f1236,plain,
! [X0,X4] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X0),c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(forward_demodulation,[],[f456,f1092]) ).
fof(f456,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
fof(f2134,plain,
spl0_158,
inference(avatar_split_clause,[],[f1233,f2132]) ).
fof(f1233,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_RealVector_Oof__real(c_Transcendental_Osin(v_x),X0)
| ~ class_RealVector_Oreal__algebra__1(X0) ),
inference(forward_demodulation,[],[f1082,f1092]) ).
fof(f1082,axiom,
! [X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__0_0) ).
fof(f2129,plain,
spl0_157,
inference(avatar_split_clause,[],[f1228,f2127]) ).
fof(f1228,plain,
! [X0,X4] :
( c_RealVector_Odist__class_Odist(X4,X4,X0) = c_Transcendental_Osin(v_x)
| ~ class_RealVector_Ometric__space(X0) ),
inference(forward_demodulation,[],[f1070,f1092]) ).
fof(f1070,axiom,
! [X0,X4] :
( ~ class_RealVector_Ometric__space(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Odist__class_Odist(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__self_0) ).
fof(f2125,plain,
spl0_156,
inference(avatar_split_clause,[],[f1205,f2122]) ).
fof(f2122,plain,
( spl0_156
<=> class_SEQ_Obanach(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1205,axiom,
class_SEQ_Obanach(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Obanach) ).
fof(f2120,plain,
spl0_155,
inference(avatar_split_clause,[],[f1204,f2117]) ).
fof(f2117,plain,
( spl0_155
<=> class_Power_Opower(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1204,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Power_Opower) ).
fof(f2115,plain,
spl0_154,
inference(avatar_split_clause,[],[f1203,f2112]) ).
fof(f2112,plain,
( spl0_154
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1203,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f2110,plain,
spl0_153,
inference(avatar_split_clause,[],[f1202,f2107]) ).
fof(f1202,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
fof(f2105,plain,
spl0_152,
inference(avatar_split_clause,[],[f1201,f2102]) ).
fof(f1201,axiom,
class_Lattices_Olattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olattice) ).
fof(f2100,plain,
spl0_151,
inference(avatar_split_clause,[],[f1200,f2097]) ).
fof(f1200,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f2095,plain,
spl0_150,
inference(avatar_split_clause,[],[f1199,f2092]) ).
fof(f1199,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f2090,plain,
spl0_149,
inference(avatar_split_clause,[],[f1198,f2087]) ).
fof(f2087,plain,
( spl0_149
<=> class_Ring__and__Field_Odvd(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1198,axiom,
class_Ring__and__Field_Odvd(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odvd) ).
fof(f2085,plain,
spl0_148,
inference(avatar_split_clause,[],[f1197,f2082]) ).
fof(f2082,plain,
( spl0_148
<=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1197,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
fof(f2080,plain,
spl0_147,
inference(avatar_split_clause,[],[f1196,f2077]) ).
fof(f2077,plain,
( spl0_147
<=> class_Ring__and__Field_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1196,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
fof(f2075,plain,
spl0_146,
inference(avatar_split_clause,[],[f1195,f2072]) ).
fof(f2072,plain,
( spl0_146
<=> class_RealVector_Odist__norm(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1195,axiom,
class_RealVector_Odist__norm(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Odist__norm) ).
fof(f2070,plain,
spl0_145,
inference(avatar_split_clause,[],[f1194,f2067]) ).
fof(f2067,plain,
( spl0_145
<=> class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1194,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
fof(f2065,plain,
spl0_144,
inference(avatar_split_clause,[],[f1193,f2062]) ).
fof(f2062,plain,
( spl0_144
<=> class_RealVector_Oreal__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1193,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__field) ).
fof(f2060,plain,
spl0_143,
inference(avatar_split_clause,[],[f1192,f2057]) ).
fof(f2057,plain,
( spl0_143
<=> class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1192,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).
fof(f2055,plain,
spl0_142,
inference(avatar_split_clause,[],[f1191,f2052]) ).
fof(f2052,plain,
( spl0_142
<=> class_Ring__and__Field_Oring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1191,axiom,
class_Ring__and__Field_Oring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1) ).
fof(f2050,plain,
spl0_141,
inference(avatar_split_clause,[],[f1190,f2047]) ).
fof(f2047,plain,
( spl0_141
<=> class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1190,axiom,
class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if) ).
fof(f2045,plain,
spl0_140,
inference(avatar_split_clause,[],[f1189,f2042]) ).
fof(f1189,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f2040,plain,
spl0_139,
inference(avatar_split_clause,[],[f1188,f2037]) ).
fof(f1188,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__vector) ).
fof(f2035,plain,
spl0_138,
inference(avatar_split_clause,[],[f1187,f2032]) ).
fof(f2032,plain,
( spl0_138
<=> class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1187,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
fof(f2030,plain,
spl0_137,
inference(avatar_split_clause,[],[f1186,f2027]) ).
fof(f1186,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Ometric__space) ).
fof(f2025,plain,
spl0_136,
inference(avatar_split_clause,[],[f1185,f2022]) ).
fof(f2022,plain,
( spl0_136
<=> class_RealVector_Oreal__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1185,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra) ).
fof(f2020,plain,
spl0_135,
inference(avatar_split_clause,[],[f1184,f2017]) ).
fof(f2017,plain,
( spl0_135
<=> class_RealVector_Osgn__div__norm(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1184,axiom,
class_RealVector_Osgn__div__norm(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Osgn__div__norm) ).
fof(f2015,plain,
spl0_134,
inference(avatar_split_clause,[],[f1183,f2012]) ).
fof(f2012,plain,
( spl0_134
<=> class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1183,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
fof(f2010,plain,
spl0_133,
inference(avatar_split_clause,[],[f1182,f2007]) ).
fof(f2007,plain,
( spl0_133
<=> class_Lattices_Odistrib__lattice(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1182,axiom,
class_Lattices_Odistrib__lattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Odistrib__lattice) ).
fof(f2005,plain,
spl0_132,
inference(avatar_split_clause,[],[f1181,f2002]) ).
fof(f2002,plain,
( spl0_132
<=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1181,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
fof(f2000,plain,
spl0_131,
inference(avatar_split_clause,[],[f1180,f1997]) ).
fof(f1997,plain,
( spl0_131
<=> class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1180,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring) ).
fof(f1995,plain,
spl0_130,
inference(avatar_split_clause,[],[f1179,f1992]) ).
fof(f1992,plain,
( spl0_130
<=> class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1179,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) ).
fof(f1990,plain,
spl0_129,
inference(avatar_split_clause,[],[f1178,f1987]) ).
fof(f1987,plain,
( spl0_129
<=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1178,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
fof(f1985,plain,
spl0_128,
inference(avatar_split_clause,[],[f1177,f1982]) ).
fof(f1982,plain,
( spl0_128
<=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1177,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
fof(f1980,plain,
spl0_127,
inference(avatar_split_clause,[],[f1176,f1977]) ).
fof(f1176,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).
fof(f1975,plain,
spl0_126,
inference(avatar_split_clause,[],[f1175,f1972]) ).
fof(f1972,plain,
( spl0_126
<=> class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1175,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).
fof(f1970,plain,
spl0_125,
inference(avatar_split_clause,[],[f1174,f1967]) ).
fof(f1174,axiom,
class_Lattices_Olower__semilattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olower__semilattice) ).
fof(f1965,plain,
spl0_124,
inference(avatar_split_clause,[],[f1173,f1962]) ).
fof(f1173,axiom,
class_Lattices_Oupper__semilattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Oupper__semilattice) ).
fof(f1960,plain,
spl0_123,
inference(avatar_split_clause,[],[f1172,f1957]) ).
fof(f1957,plain,
( spl0_123
<=> class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1172,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) ).
fof(f1955,plain,
spl0_122,
inference(avatar_split_clause,[],[f1171,f1952]) ).
fof(f1952,plain,
( spl0_122
<=> class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1171,axiom,
class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__div__algebra) ).
fof(f1950,plain,
spl0_121,
inference(avatar_split_clause,[],[f1170,f1947]) ).
fof(f1947,plain,
( spl0_121
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1170,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
fof(f1945,plain,
spl0_120,
inference(avatar_split_clause,[],[f1169,f1942]) ).
fof(f1942,plain,
( spl0_120
<=> class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1169,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).
fof(f1940,plain,
spl0_119,
inference(avatar_split_clause,[],[f1168,f1937]) ).
fof(f1937,plain,
( spl0_119
<=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1168,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
fof(f1935,plain,
spl0_118,
inference(avatar_split_clause,[],[f1167,f1932]) ).
fof(f1932,plain,
( spl0_118
<=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1167,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(f1930,plain,
spl0_117,
inference(avatar_split_clause,[],[f1166,f1927]) ).
fof(f1927,plain,
( spl0_117
<=> class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1166,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
fof(f1925,plain,
spl0_116,
inference(avatar_split_clause,[],[f1165,f1922]) ).
fof(f1165,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).
fof(f1920,plain,
spl0_115,
inference(avatar_split_clause,[],[f1164,f1917]) ).
fof(f1917,plain,
( spl0_115
<=> class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1164,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) ).
fof(f1915,plain,
spl0_114,
inference(avatar_split_clause,[],[f1163,f1912]) ).
fof(f1912,plain,
( spl0_114
<=> class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1163,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
fof(f1910,plain,
spl0_113,
inference(avatar_split_clause,[],[f1162,f1907]) ).
fof(f1907,plain,
( spl0_113
<=> class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1162,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) ).
fof(f1905,plain,
spl0_112,
inference(avatar_split_clause,[],[f1161,f1902]) ).
fof(f1902,plain,
( spl0_112
<=> class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1161,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
fof(f1900,plain,
spl0_111,
inference(avatar_split_clause,[],[f1160,f1897]) ).
fof(f1897,plain,
( spl0_111
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1160,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1895,plain,
spl0_110,
inference(avatar_split_clause,[],[f1159,f1892]) ).
fof(f1159,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f1890,plain,
spl0_109,
inference(avatar_split_clause,[],[f1158,f1887]) ).
fof(f1887,plain,
( spl0_109
<=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1158,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
fof(f1885,plain,
spl0_108,
inference(avatar_split_clause,[],[f1157,f1882]) ).
fof(f1882,plain,
( spl0_108
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1157,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f1880,plain,
spl0_107,
inference(avatar_split_clause,[],[f1156,f1877]) ).
fof(f1156,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1875,plain,
spl0_106,
inference(avatar_split_clause,[],[f1155,f1872]) ).
fof(f1872,plain,
( spl0_106
<=> class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1155,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
fof(f1870,plain,
spl0_105,
inference(avatar_split_clause,[],[f1154,f1867]) ).
fof(f1154,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
fof(f1865,plain,
spl0_104,
inference(avatar_split_clause,[],[f1153,f1862]) ).
fof(f1862,plain,
( spl0_104
<=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1153,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).
fof(f1860,plain,
spl0_103,
inference(avatar_split_clause,[],[f1152,f1857]) ).
fof(f1857,plain,
( spl0_103
<=> class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1152,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).
fof(f1855,plain,
spl0_102,
inference(avatar_split_clause,[],[f1151,f1852]) ).
fof(f1852,plain,
( spl0_102
<=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1151,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(f1850,plain,
spl0_101,
inference(avatar_split_clause,[],[f1150,f1847]) ).
fof(f1847,plain,
( spl0_101
<=> class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1150,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) ).
fof(f1845,plain,
spl0_100,
inference(avatar_split_clause,[],[f1149,f1842]) ).
fof(f1842,plain,
( spl0_100
<=> class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1149,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) ).
fof(f1840,plain,
spl0_99,
inference(avatar_split_clause,[],[f1148,f1837]) ).
fof(f1837,plain,
( spl0_99
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1148,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1835,plain,
spl0_98,
inference(avatar_split_clause,[],[f1147,f1832]) ).
fof(f1832,plain,
( spl0_98
<=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1147,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
fof(f1830,plain,
spl0_97,
inference(avatar_split_clause,[],[f1146,f1827]) ).
fof(f1827,plain,
( spl0_97
<=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1146,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
fof(f1825,plain,
spl0_96,
inference(avatar_split_clause,[],[f1145,f1822]) ).
fof(f1822,plain,
( spl0_96
<=> class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1145,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
fof(f1820,plain,
spl0_95,
inference(avatar_split_clause,[],[f1144,f1817]) ).
fof(f1817,plain,
( spl0_95
<=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1144,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(f1815,plain,
spl0_94,
inference(avatar_split_clause,[],[f1143,f1812]) ).
fof(f1812,plain,
( spl0_94
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1143,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
fof(f1810,plain,
spl0_93,
inference(avatar_split_clause,[],[f1142,f1807]) ).
fof(f1807,plain,
( spl0_93
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1142,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1805,plain,
spl0_92,
inference(avatar_split_clause,[],[f1141,f1802]) ).
fof(f1802,plain,
( spl0_92
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1141,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1800,plain,
spl0_91,
inference(avatar_split_clause,[],[f1140,f1797]) ).
fof(f1797,plain,
( spl0_91
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1140,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1795,plain,
spl0_90,
inference(avatar_split_clause,[],[f1139,f1792]) ).
fof(f1792,plain,
( spl0_90
<=> class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1139,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).
fof(f1790,plain,
spl0_89,
inference(avatar_split_clause,[],[f1138,f1787]) ).
fof(f1787,plain,
( spl0_89
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1138,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f1785,plain,
spl0_88,
inference(avatar_split_clause,[],[f1137,f1782]) ).
fof(f1782,plain,
( spl0_88
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1137,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1780,plain,
spl0_87,
inference(avatar_split_clause,[],[f1136,f1777]) ).
fof(f1777,plain,
( spl0_87
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1136,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1775,plain,
spl0_86,
inference(avatar_split_clause,[],[f1135,f1772]) ).
fof(f1772,plain,
( spl0_86
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1135,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f1770,plain,
spl0_85,
inference(avatar_split_clause,[],[f1134,f1767]) ).
fof(f1767,plain,
( spl0_85
<=> class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1134,axiom,
class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__join) ).
fof(f1765,plain,
spl0_84,
inference(avatar_split_clause,[],[f1133,f1762]) ).
fof(f1762,plain,
( spl0_84
<=> class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1133,axiom,
class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__meet) ).
fof(f1760,plain,
spl0_83,
inference(avatar_split_clause,[],[f1132,f1757]) ).
fof(f1757,plain,
( spl0_83
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f1132,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1755,plain,
spl0_82,
inference(avatar_split_clause,[],[f1131,f1752]) ).
fof(f1752,plain,
( spl0_82
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f1131,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1750,plain,
spl0_81,
inference(avatar_split_clause,[],[f1130,f1747]) ).
fof(f1747,plain,
( spl0_81
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1130,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1745,plain,
spl0_80,
inference(avatar_split_clause,[],[f1129,f1742]) ).
fof(f1742,plain,
( spl0_80
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1129,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1740,plain,
spl0_79,
inference(avatar_split_clause,[],[f1128,f1737]) ).
fof(f1737,plain,
( spl0_79
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1128,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f1735,plain,
spl0_78,
inference(avatar_split_clause,[],[f1127,f1732]) ).
fof(f1732,plain,
( spl0_78
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1127,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1730,plain,
spl0_77,
inference(avatar_split_clause,[],[f1126,f1727]) ).
fof(f1727,plain,
( spl0_77
<=> class_Lattices_Olattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1126,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
fof(f1725,plain,
spl0_76,
inference(avatar_split_clause,[],[f1125,f1722]) ).
fof(f1722,plain,
( spl0_76
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1125,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1720,plain,
spl0_75,
inference(avatar_split_clause,[],[f1124,f1717]) ).
fof(f1717,plain,
( spl0_75
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1124,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1715,plain,
spl0_74,
inference(avatar_split_clause,[],[f1123,f1712]) ).
fof(f1712,plain,
( spl0_74
<=> class_Ring__and__Field_Odvd(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1123,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
fof(f1710,plain,
spl0_73,
inference(avatar_split_clause,[],[f1122,f1707]) ).
fof(f1707,plain,
( spl0_73
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1122,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
fof(f1705,plain,
spl0_72,
inference(avatar_split_clause,[],[f1121,f1702]) ).
fof(f1702,plain,
( spl0_72
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1121,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f1700,plain,
spl0_71,
inference(avatar_split_clause,[],[f1120,f1697]) ).
fof(f1697,plain,
( spl0_71
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1120,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f1695,plain,
spl0_70,
inference(avatar_split_clause,[],[f1119,f1692]) ).
fof(f1692,plain,
( spl0_70
<=> class_Lattices_Odistrib__lattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1119,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
fof(f1690,plain,
spl0_69,
inference(avatar_split_clause,[],[f1118,f1687]) ).
fof(f1687,plain,
( spl0_69
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1118,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f1685,plain,
spl0_68,
inference(avatar_split_clause,[],[f1117,f1682]) ).
fof(f1682,plain,
( spl0_68
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1117,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f1680,plain,
spl0_67,
inference(avatar_split_clause,[],[f1116,f1677]) ).
fof(f1677,plain,
( spl0_67
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1116,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f1675,plain,
spl0_66,
inference(avatar_split_clause,[],[f1115,f1672]) ).
fof(f1672,plain,
( spl0_66
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1115,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f1670,plain,
spl0_65,
inference(avatar_split_clause,[],[f1114,f1667]) ).
fof(f1667,plain,
( spl0_65
<=> class_Lattices_Olower__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1114,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
fof(f1665,plain,
spl0_64,
inference(avatar_split_clause,[],[f1113,f1662]) ).
fof(f1662,plain,
( spl0_64
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1113,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
fof(f1660,plain,
spl0_63,
inference(avatar_split_clause,[],[f1112,f1657]) ).
fof(f1657,plain,
( spl0_63
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1112,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f1655,plain,
spl0_62,
inference(avatar_split_clause,[],[f1111,f1652]) ).
fof(f1652,plain,
( spl0_62
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1111,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1650,plain,
spl0_61,
inference(avatar_split_clause,[],[f1110,f1647]) ).
fof(f1647,plain,
( spl0_61
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1110,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f1645,plain,
spl0_60,
inference(avatar_split_clause,[],[f1109,f1642]) ).
fof(f1642,plain,
( spl0_60
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1109,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1640,plain,
spl0_59,
inference(avatar_split_clause,[],[f1108,f1637]) ).
fof(f1637,plain,
( spl0_59
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1108,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1635,plain,
( spl0_58
| ~ spl0_36
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f1550,f1544,f1522,f1632]) ).
fof(f1550,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_36
| ~ spl0_41 ),
inference(superposition,[],[f1545,f1523]) ).
fof(f1630,plain,
spl0_57,
inference(avatar_split_clause,[],[f1107,f1627]) ).
fof(f1627,plain,
( spl0_57
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1107,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f1625,plain,
spl0_56,
inference(avatar_split_clause,[],[f1106,f1622]) ).
fof(f1622,plain,
( spl0_56
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f1106,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1620,plain,
spl0_55,
inference(avatar_split_clause,[],[f1105,f1617]) ).
fof(f1617,plain,
( spl0_55
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1105,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f1615,plain,
spl0_54,
inference(avatar_split_clause,[],[f1104,f1612]) ).
fof(f1612,plain,
( spl0_54
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1104,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f1610,plain,
spl0_53,
inference(avatar_split_clause,[],[f1103,f1607]) ).
fof(f1607,plain,
( spl0_53
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1103,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f1605,plain,
spl0_52,
inference(avatar_split_clause,[],[f1102,f1602]) ).
fof(f1602,plain,
( spl0_52
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1102,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f1600,plain,
spl0_51,
inference(avatar_split_clause,[],[f1101,f1597]) ).
fof(f1597,plain,
( spl0_51
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1101,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1595,plain,
spl0_50,
inference(avatar_split_clause,[],[f1100,f1592]) ).
fof(f1592,plain,
( spl0_50
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1100,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1590,plain,
spl0_49,
inference(avatar_split_clause,[],[f1099,f1587]) ).
fof(f1587,plain,
( spl0_49
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f1099,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1585,plain,
spl0_48,
inference(avatar_split_clause,[],[f1098,f1582]) ).
fof(f1582,plain,
( spl0_48
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1098,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1580,plain,
( spl0_47
| ~ spl0_36
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f1549,f1540,f1522,f1577]) ).
fof(f1549,plain,
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_36
| ~ spl0_40 ),
inference(superposition,[],[f1541,f1523]) ).
fof(f1575,plain,
spl0_46,
inference(avatar_split_clause,[],[f1097,f1572]) ).
fof(f1572,plain,
( spl0_46
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f1097,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1570,plain,
spl0_45,
inference(avatar_split_clause,[],[f1096,f1567]) ).
fof(f1567,plain,
( spl0_45
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1096,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1565,plain,
spl0_44,
inference(avatar_split_clause,[],[f1095,f1562]) ).
fof(f1562,plain,
( spl0_44
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1095,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1560,plain,
spl0_43,
inference(avatar_split_clause,[],[f1094,f1557]) ).
fof(f1557,plain,
( spl0_43
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1094,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1555,plain,
spl0_42,
inference(avatar_split_clause,[],[f1093,f1552]) ).
fof(f1552,plain,
( spl0_42
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f1093,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1546,plain,
( spl0_41
| ~ spl0_8
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f1520,f1517,f1376,f1544]) ).
fof(f1517,plain,
( spl0_35
<=> ! [X4,X1] : c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_Log_Opowr(X4,X1),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1520,plain,
( ! [X1,X4] : c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Log_Opowr(X4,X1),tc_RealDef_Oreal)
| ~ spl0_8
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1518,f1378]) ).
fof(f1518,plain,
( ! [X1,X4] : c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_Log_Opowr(X4,X1),tc_RealDef_Oreal)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f1517]) ).
fof(f1542,plain,
( spl0_40
| ~ spl0_8
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f1515,f1512,f1376,f1540]) ).
fof(f1512,plain,
( spl0_34
<=> ! [X4,X10] : c_lessequals(c_Transcendental_Osin(v_x),c_Log_Opowr(X4,X10),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1515,plain,
( ! [X10,X4] : c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_Log_Opowr(X4,X10),tc_RealDef_Oreal)
| ~ spl0_8
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1513,f1378]) ).
fof(f1513,plain,
( ! [X10,X4] : c_lessequals(c_Transcendental_Osin(v_x),c_Log_Opowr(X4,X10),tc_RealDef_Oreal)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f1512]) ).
fof(f1538,plain,
( spl0_39
| ~ spl0_8
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f1510,f1507,f1376,f1536]) ).
fof(f1536,plain,
( spl0_39
<=> ! [X9] : c_Transcendental_Otan(c_Transcendental_Opi) = c_NthRoot_Oroot(X9,c_Transcendental_Otan(c_Transcendental_Opi)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1507,plain,
( spl0_33
<=> ! [X9] : c_Transcendental_Osin(v_x) = c_NthRoot_Oroot(X9,c_Transcendental_Osin(v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1510,plain,
( ! [X9] : c_Transcendental_Otan(c_Transcendental_Opi) = c_NthRoot_Oroot(X9,c_Transcendental_Otan(c_Transcendental_Opi))
| ~ spl0_8
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1508,f1378]) ).
fof(f1508,plain,
( ! [X9] : c_Transcendental_Osin(v_x) = c_NthRoot_Oroot(X9,c_Transcendental_Osin(v_x))
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f1507]) ).
fof(f1534,plain,
( spl0_38
| ~ spl0_8
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f1500,f1496,f1376,f1531]) ).
fof(f1496,plain,
( spl0_31
<=> c_Transcendental_Osin(v_x) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Osin(v_x),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1500,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_8
| ~ spl0_31 ),
inference(forward_demodulation,[],[f1498,f1378]) ).
fof(f1498,plain,
( c_Transcendental_Osin(v_x) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f1496]) ).
fof(f1529,plain,
( spl0_37
| ~ spl0_8
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f1494,f1490,f1376,f1526]) ).
fof(f1526,plain,
( spl0_37
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_HOL_Osgn__class_Osgn(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1490,plain,
( spl0_30
<=> c_Transcendental_Osin(v_x) = c_HOL_Osgn__class_Osgn(c_Transcendental_Osin(v_x),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1494,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_HOL_Osgn__class_Osgn(c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_8
| ~ spl0_30 ),
inference(forward_demodulation,[],[f1492,f1378]) ).
fof(f1492,plain,
( c_Transcendental_Osin(v_x) = c_HOL_Osgn__class_Osgn(c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f1490]) ).
fof(f1524,plain,
( spl0_36
| ~ spl0_8
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f1488,f1485,f1376,f1522]) ).
fof(f1485,plain,
( spl0_29
<=> ! [X4] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Log_Opowr(X4,c_Transcendental_Osin(v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f1488,plain,
( ! [X4] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Log_Opowr(X4,c_Transcendental_Otan(c_Transcendental_Opi))
| ~ spl0_8
| ~ spl0_29 ),
inference(forward_demodulation,[],[f1486,f1378]) ).
fof(f1486,plain,
( ! [X4] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Log_Opowr(X4,c_Transcendental_Osin(v_x))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f1485]) ).
fof(f1519,plain,
spl0_35,
inference(avatar_split_clause,[],[f1226,f1517]) ).
fof(f1226,plain,
! [X1,X4] : c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_Log_Opowr(X4,X1),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f349,f1092]) ).
fof(f349,axiom,
! [X1,X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Log_Opowr(X4,X1),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__gt__zero_0) ).
fof(f1514,plain,
spl0_34,
inference(avatar_split_clause,[],[f1225,f1512]) ).
fof(f1225,plain,
! [X10,X4] : c_lessequals(c_Transcendental_Osin(v_x),c_Log_Opowr(X4,X10),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f789,f1092]) ).
fof(f789,axiom,
! [X10,X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Log_Opowr(X4,X10),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__ge__pzero_0) ).
fof(f1509,plain,
spl0_33,
inference(avatar_split_clause,[],[f1224,f1507]) ).
fof(f1224,plain,
! [X9] : c_Transcendental_Osin(v_x) = c_NthRoot_Oroot(X9,c_Transcendental_Osin(v_x)),
inference(forward_demodulation,[],[f1069,f1092]) ).
fof(f1069,axiom,
! [X9] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Oroot(X9,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__root__zero_0) ).
fof(f1505,plain,
( ~ spl0_32
| ~ spl0_22
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f1483,f1469,f1451,f1502]) ).
fof(f1502,plain,
( spl0_32
<=> c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Ocos(c_Transcendental_Otan(c_Transcendental_Opi)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1483,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) != c_Transcendental_Ocos(c_Transcendental_Otan(c_Transcendental_Opi))
| ~ spl0_22
| ~ spl0_26 ),
inference(superposition,[],[f1452,f1471]) ).
fof(f1499,plain,
spl0_31,
inference(avatar_split_clause,[],[f1223,f1496]) ).
fof(f1223,plain,
c_Transcendental_Osin(v_x) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Osin(v_x),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1067,f1092]) ).
fof(f1067,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INVERSE__ZERO_0) ).
fof(f1493,plain,
spl0_30,
inference(avatar_split_clause,[],[f1222,f1490]) ).
fof(f1222,plain,
c_Transcendental_Osin(v_x) = c_HOL_Osgn__class_Osgn(c_Transcendental_Osin(v_x),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1058,f1092]) ).
fof(f1058,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sgn__def_0) ).
fof(f1487,plain,
spl0_29,
inference(avatar_split_clause,[],[f1221,f1485]) ).
fof(f1221,plain,
! [X4] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Log_Opowr(X4,c_Transcendental_Osin(v_x)),
inference(forward_demodulation,[],[f697,f1092]) ).
fof(f697,axiom,
! [X4] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Log_Opowr(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__zero__eq__one_0) ).
fof(f1482,plain,
( spl0_28
| ~ spl0_8
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f1449,f1445,f1376,f1479]) ).
fof(f1445,plain,
( spl0_21
<=> c_Transcendental_Osin(v_x) = c_NthRoot_Osqrt(c_Transcendental_Osin(v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f1449,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_NthRoot_Osqrt(c_Transcendental_Otan(c_Transcendental_Opi))
| ~ spl0_8
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1447,f1378]) ).
fof(f1447,plain,
( c_Transcendental_Osin(v_x) = c_NthRoot_Osqrt(c_Transcendental_Osin(v_x))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f1445]) ).
fof(f1477,plain,
( spl0_27
| ~ spl0_8
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f1443,f1439,f1376,f1474]) ).
fof(f1439,plain,
( spl0_20
<=> c_Transcendental_Osin(v_x) = c_Transcendental_Osin(c_Transcendental_Osin(v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f1443,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Osin(c_Transcendental_Otan(c_Transcendental_Opi))
| ~ spl0_8
| ~ spl0_20 ),
inference(forward_demodulation,[],[f1441,f1378]) ).
fof(f1441,plain,
( c_Transcendental_Osin(v_x) = c_Transcendental_Osin(c_Transcendental_Osin(v_x))
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f1439]) ).
fof(f1472,plain,
( spl0_26
| ~ spl0_8
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f1437,f1433,f1376,f1469]) ).
fof(f1433,plain,
( spl0_19
<=> c_Transcendental_Osin(v_x) = c_Transcendental_Oarctan(c_Transcendental_Osin(v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1437,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Oarctan(c_Transcendental_Otan(c_Transcendental_Opi))
| ~ spl0_8
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1435,f1378]) ).
fof(f1435,plain,
( c_Transcendental_Osin(v_x) = c_Transcendental_Oarctan(c_Transcendental_Osin(v_x))
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f1433]) ).
fof(f1467,plain,
( spl0_25
| ~ spl0_8
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f1431,f1427,f1376,f1464]) ).
fof(f1427,plain,
( spl0_18
<=> c_Transcendental_Osin(v_x) = c_Transcendental_Otan(c_Transcendental_Osin(v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1431,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Otan(c_Transcendental_Otan(c_Transcendental_Opi))
| ~ spl0_8
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1429,f1378]) ).
fof(f1429,plain,
( c_Transcendental_Osin(v_x) = c_Transcendental_Otan(c_Transcendental_Osin(v_x))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f1427]) ).
fof(f1462,plain,
( spl0_24
| ~ spl0_8
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f1425,f1421,f1376,f1459]) ).
fof(f1459,plain,
( spl0_24
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Transcendental_Otan(c_Transcendental_Opi)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1421,plain,
( spl0_17
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Transcendental_Osin(v_x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1425,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Transcendental_Otan(c_Transcendental_Opi))
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1423,f1378]) ).
fof(f1423,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Transcendental_Osin(v_x))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f1421]) ).
fof(f1457,plain,
( spl0_23
| ~ spl0_8
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f1419,f1416,f1376,f1455]) ).
fof(f1416,plain,
( spl0_16
<=> ! [X4,X1] : c_Log_Opowr(X4,X1) != c_Transcendental_Osin(v_x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1419,plain,
( ! [X1,X4] : c_Log_Opowr(X4,X1) != c_Transcendental_Otan(c_Transcendental_Opi)
| ~ spl0_8
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1417,f1378]) ).
fof(f1417,plain,
( ! [X1,X4] : c_Log_Opowr(X4,X1) != c_Transcendental_Osin(v_x)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f1416]) ).
fof(f1453,plain,
( spl0_22
| ~ spl0_8
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f1414,f1411,f1376,f1451]) ).
fof(f1411,plain,
( spl0_15
<=> ! [X4] : c_Transcendental_Ocos(c_Transcendental_Oarctan(X4)) != c_Transcendental_Osin(v_x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1414,plain,
( ! [X4] : c_Transcendental_Ocos(c_Transcendental_Oarctan(X4)) != c_Transcendental_Otan(c_Transcendental_Opi)
| ~ spl0_8
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1412,f1378]) ).
fof(f1412,plain,
( ! [X4] : c_Transcendental_Ocos(c_Transcendental_Oarctan(X4)) != c_Transcendental_Osin(v_x)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f1411]) ).
fof(f1448,plain,
spl0_21,
inference(avatar_split_clause,[],[f1220,f1445]) ).
fof(f1220,plain,
c_Transcendental_Osin(v_x) = c_NthRoot_Osqrt(c_Transcendental_Osin(v_x)),
inference(forward_demodulation,[],[f1066,f1092]) ).
fof(f1066,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__zero_0) ).
fof(f1442,plain,
spl0_20,
inference(avatar_split_clause,[],[f1219,f1439]) ).
fof(f1219,plain,
c_Transcendental_Osin(v_x) = c_Transcendental_Osin(c_Transcendental_Osin(v_x)),
inference(forward_demodulation,[],[f1089,f1092]) ).
fof(f1089,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__zero_0) ).
fof(f1436,plain,
spl0_19,
inference(avatar_split_clause,[],[f1218,f1433]) ).
fof(f1218,plain,
c_Transcendental_Osin(v_x) = c_Transcendental_Oarctan(c_Transcendental_Osin(v_x)),
inference(forward_demodulation,[],[f1068,f1092]) ).
fof(f1068,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Oarctan(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arctan__zero__zero_0) ).
fof(f1430,plain,
spl0_18,
inference(avatar_split_clause,[],[f1217,f1427]) ).
fof(f1217,plain,
c_Transcendental_Osin(v_x) = c_Transcendental_Otan(c_Transcendental_Osin(v_x)),
inference(forward_demodulation,[],[f1062,f1092]) ).
fof(f1062,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Otan(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__zero_0) ).
fof(f1424,plain,
spl0_17,
inference(avatar_split_clause,[],[f1216,f1421]) ).
fof(f1216,plain,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Transcendental_Osin(v_x)),
inference(forward_demodulation,[],[f381,f1092]) ).
fof(f381,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__zero_0) ).
fof(f1418,plain,
spl0_16,
inference(avatar_split_clause,[],[f1215,f1416]) ).
fof(f1215,plain,
! [X1,X4] : c_Log_Opowr(X4,X1) != c_Transcendental_Osin(v_x),
inference(forward_demodulation,[],[f1059,f1092]) ).
fof(f1059,axiom,
! [X1,X4] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Log_Opowr(X4,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_powr__not__zero_0) ).
fof(f1413,plain,
spl0_15,
inference(avatar_split_clause,[],[f1214,f1411]) ).
fof(f1214,plain,
! [X4] : c_Transcendental_Ocos(c_Transcendental_Oarctan(X4)) != c_Transcendental_Osin(v_x),
inference(forward_demodulation,[],[f307,f1092]) ).
fof(f307,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(c_Transcendental_Oarctan(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__arctan__not__zero_0) ).
fof(f1409,plain,
( spl0_14
| ~ spl0_1
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f1374,f1370,f1334,f1406]) ).
fof(f1334,plain,
( spl0_1
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(v_x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1370,plain,
( spl0_7
<=> c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1374,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_1
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1372,f1338]) ).
fof(f1338,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Osin(v_x)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1336,f908]) ).
fof(f1336,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(v_x)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f1334]) ).
fof(f1372,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f1370]) ).
fof(f1404,plain,
( spl0_13
| ~ spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f1368,f1364,f1334,f1401]) ).
fof(f1364,plain,
( spl0_6
<=> c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),v_x,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1368,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi),v_x,tc_RealDef_Oreal)
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f1366,f1338]) ).
fof(f1366,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),v_x,tc_RealDef_Oreal)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f1364]) ).
fof(f1399,plain,
( spl0_12
| ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f1362,f1358,f1334,f1396]) ).
fof(f1358,plain,
( spl0_5
<=> c_lessequals(c_Transcendental_Osin(v_x),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1362,plain,
( c_lessequals(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f1360,f1338]) ).
fof(f1360,plain,
( c_lessequals(c_Transcendental_Osin(v_x),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f1358]) ).
fof(f1394,plain,
( spl0_11
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f1356,f1352,f1334,f1391]) ).
fof(f1352,plain,
( spl0_4
<=> c_Transcendental_Osin(c_Transcendental_Opi) = c_Transcendental_Osin(v_x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1356,plain,
( c_Transcendental_Otan(c_Transcendental_Opi) = c_Transcendental_Osin(c_Transcendental_Opi)
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f1354,f1338]) ).
fof(f1354,plain,
( c_Transcendental_Osin(c_Transcendental_Opi) = c_Transcendental_Osin(v_x)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f1352]) ).
fof(f1389,plain,
( ~ spl0_10
| ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f1350,f1346,f1334,f1386]) ).
fof(f1386,plain,
( spl0_10
<=> c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1346,plain,
( spl0_3
<=> c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_Transcendental_Osin(v_x),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1350,plain,
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_Transcendental_Otan(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_1
| spl0_3 ),
inference(forward_demodulation,[],[f1348,f1338]) ).
fof(f1348,plain,
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_Transcendental_Osin(v_x),tc_RealDef_Oreal)
| spl0_3 ),
inference(avatar_component_clause,[],[f1346]) ).
fof(f1384,plain,
( ~ spl0_9
| ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f1344,f1340,f1334,f1381]) ).
fof(f1340,plain,
( spl0_2
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Osin(v_x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1344,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Otan(c_Transcendental_Opi)
| ~ spl0_1
| spl0_2 ),
inference(forward_demodulation,[],[f1342,f1338]) ).
fof(f1342,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Osin(v_x)
| spl0_2 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f1379,plain,
( spl0_8
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f1338,f1334,f1376]) ).
fof(f1373,plain,
spl0_7,
inference(avatar_split_clause,[],[f1213,f1370]) ).
fof(f1213,plain,
c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),c_Transcendental_Opi,tc_RealDef_Oreal),
inference(forward_demodulation,[],[f965,f1092]) ).
fof(f965,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__gt__zero_0) ).
fof(f1367,plain,
spl0_6,
inference(avatar_split_clause,[],[f1211,f1364]) ).
fof(f1211,plain,
c_HOL_Oord__class_Oless(c_Transcendental_Osin(v_x),v_x,tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1088,f1092]) ).
fof(f1088,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_0_0) ).
fof(f1361,plain,
spl0_5,
inference(avatar_split_clause,[],[f1210,f1358]) ).
fof(f1210,plain,
c_lessequals(c_Transcendental_Osin(v_x),c_Transcendental_Opi,tc_RealDef_Oreal),
inference(forward_demodulation,[],[f923,f1092]) ).
fof(f923,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__ge__zero_0) ).
fof(f1355,plain,
spl0_4,
inference(avatar_split_clause,[],[f1209,f1352]) ).
fof(f1209,plain,
c_Transcendental_Osin(c_Transcendental_Opi) = c_Transcendental_Osin(v_x),
inference(forward_demodulation,[],[f1087,f1092]) ).
fof(f1087,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_Transcendental_Opi),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__pi_0) ).
fof(f1349,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f1208,f1346]) ).
fof(f1208,plain,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_Transcendental_Osin(v_x),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f609,f1092]) ).
fof(f609,axiom,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__not__less__zero_0) ).
fof(f1343,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f1207,f1340]) ).
fof(f1207,plain,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Osin(v_x),
inference(forward_demodulation,[],[f1065,f1092]) ).
fof(f1065,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
fof(f1337,plain,
spl0_1,
inference(avatar_split_clause,[],[f1092,f1334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV594-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n013.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Apr 30 04:53:49 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (15859)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.39 % (15861)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.39 % (15862)WARNING: value z3 for option sas not known
% 0.17/0.40 % (15862)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.17/0.40 % (15865)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.17/0.40 % (15866)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.17/0.40 % (15860)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.40 % (15864)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.17/0.40 % (15863)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.51 TRYING [1]
% 0.17/0.53 TRYING [2]
% 3.23/0.85 TRYING [1]
% 3.23/0.86 TRYING [3]
% 3.47/0.87 TRYING [2]
% 4.75/1.07 TRYING [1]
% 4.75/1.08 TRYING [3]
% 5.73/1.20 TRYING [2]
% 12.00/2.11 % (15864)First to succeed.
% 12.40/2.18 % (15864)Refutation found. Thanks to Tanya!
% 12.40/2.18 % SZS status Unsatisfiable for theBenchmark
% 12.40/2.18 % SZS output start Proof for theBenchmark
% See solution above
% 12.40/2.21 % (15864)------------------------------
% 12.40/2.21 % (15864)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 12.40/2.21 % (15864)Termination reason: Refutation
% 12.40/2.21
% 12.40/2.21 % (15864)Memory used [KB]: 16309
% 12.40/2.21 % (15864)Time elapsed: 1.777 s
% 12.40/2.21 % (15864)Instructions burned: 3309 (million)
% 12.40/2.21 % (15864)------------------------------
% 12.40/2.21 % (15864)------------------------------
% 12.40/2.21 % (15859)Success in time 1.874 s
%------------------------------------------------------------------------------