TSTP Solution File: SWV601-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV601-1 : 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 : n020.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 : Sun May 5 11:07:46 EDT 2024
% Result : Unsatisfiable 8.67s 1.64s
% Output : Refutation 8.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1733
% Syntax : Number of formulae : 3026 (1150 unt; 0 def)
% Number of atoms : 7829 (1083 equ)
% Maximal formula atoms : 34 ( 2 avg)
% Number of connectives : 8458 (3655 ~;3894 |; 0 &)
% ( 909 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 4 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 963 ( 961 usr; 910 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 7 con; 0-3 aty)
% Number of variables : 3911 (3911 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23627,plain,
$false,
inference(avatar_sat_refutation,[],[f1134,f1139,f1144,f1149,f1154,f1159,f1164,f1169,f1174,f1179,f1184,f1189,f1194,f1199,f1204,f1209,f1214,f1219,f1224,f1229,f1234,f1239,f1244,f1249,f1254,f1259,f1264,f1269,f1274,f1279,f1284,f1289,f1294,f1299,f1304,f1309,f1314,f1319,f1324,f1329,f1334,f1339,f1344,f1349,f1354,f1359,f1364,f1369,f1374,f1379,f1384,f1389,f1394,f1399,f1404,f1409,f1414,f1419,f1424,f1429,f1434,f1439,f1444,f1449,f1454,f1459,f1464,f1469,f1474,f1479,f1484,f1489,f1494,f1499,f1504,f1509,f1514,f1519,f1524,f1529,f1534,f1539,f1544,f1549,f1554,f1559,f1564,f1569,f1574,f1579,f1584,f1589,f1594,f1599,f1604,f1609,f1614,f1619,f1624,f1629,f1634,f1639,f1644,f1649,f1654,f1659,f1664,f1669,f1674,f1679,f1684,f1689,f1694,f1699,f1704,f1709,f1714,f1719,f1724,f1729,f1734,f1739,f1744,f1749,f1754,f1759,f1764,f1769,f1774,f1779,f1784,f1789,f1794,f1799,f1804,f1809,f1814,f1819,f1824,f1829,f1834,f1839,f1844,f1849,f1854,f1859,f1864,f1869,f1874,f1878,f1882,f1887,f1892,f1896,f1901,f1906,f1911,f1916,f1920,f1924,f1928,f1932,f1936,f1940,f1944,f1948,f1953,f1958,f1963,f1968,f1975,f1979,f1983,f1987,f1991,f1995,f2001,f2005,f2009,f2013,f2017,f2021,f2026,f2031,f2035,f2039,f2043,f2047,f2068,f2073,f2077,f2081,f2085,f2089,f2094,f2098,f2102,f2106,f2111,f2115,f2119,f2123,f2127,f2131,f2135,f2140,f2144,f2148,f2152,f2157,f2161,f2165,f2169,f2173,f2177,f2181,f2185,f2189,f2193,f2197,f2284,f2288,f2292,f2296,f2300,f2304,f2308,f2312,f2316,f2320,f2324,f2328,f2332,f2336,f2340,f2345,f2349,f2353,f2357,f2361,f2365,f2369,f2373,f2377,f2381,f2385,f2390,f2395,f2400,f2405,f2410,f2414,f2418,f2422,f2427,f2431,f2435,f2439,f2443,f2447,f2451,f2455,f2459,f2463,f2467,f2472,f2476,f2480,f2504,f2640,f2672,f2688,f2694,f2706,f2710,f2715,f2719,f2723,f2727,f2731,f2735,f2739,f2743,f2747,f2751,f2755,f2762,f2766,f2770,f2774,f2778,f2782,f2786,f2790,f2794,f2798,f2803,f2807,f2811,f2815,f2819,f2823,f2827,f2831,f2835,f2840,f2844,f2848,f2852,f2856,f2908,f3048,f3078,f3082,f3087,f3091,f3095,f3099,f3103,f3107,f3111,f3115,f3119,f3124,f3129,f3134,f3139,f3143,f3147,f3151,f3155,f3159,f3164,f3168,f3172,f3258,f3331,f3335,f3339,f3343,f3347,f3351,f3355,f3359,f3363,f3367,f3371,f3375,f3379,f3383,f3387,f3391,f3395,f3399,f3403,f3417,f3422,f3426,f3430,f3434,f3438,f3442,f3446,f3451,f3455,f3459,f3463,f3468,f3647,f3808,f3824,f3828,f3832,f3836,f3840,f3844,f3848,f3852,f3865,f3869,f3873,f3877,f3881,f3885,f3889,f3893,f3897,f3901,f3914,f3918,f3922,f3926,f3930,f3934,f3938,f3942,f3946,f3950,f3954,f3958,f3962,f3966,f3970,f3974,f3978,f3982,f3986,f3990,f3994,f4005,f4009,f4013,f4017,f4022,f4026,f4030,f4034,f4038,f4042,f4046,f4050,f4054,f4058,f4063,f4067,f4183,f4495,f4830,f4903,f4907,f4930,f4934,f4938,f4942,f4946,f4950,f4954,f4958,f4962,f4966,f4970,f4974,f4978,f4982,f4986,f4990,f4994,f4998,f5002,f5006,f5010,f5015,f5019,f5023,f5028,f5033,f5037,f5041,f5045,f5049,f5053,f5058,f5082,f5269,f5385,f5389,f5393,f5397,f5401,f5405,f5409,f5413,f5417,f5421,f5425,f5429,f5433,f5437,f5441,f5445,f5449,f5465,f5469,f5473,f5477,f5481,f5485,f5490,f5558,f5891,f5895,f5899,f5903,f5907,f5911,f5916,f5921,f5925,f5929,f5933,f5937,f5970,f5974,f5978,f5982,f5986,f5990,f5994,f5998,f6002,f6006,f6010,f6014,f6018,f6022,f6026,f6030,f6120,f6204,f6208,f6212,f6216,f6220,f6224,f6228,f6232,f6236,f6240,f6244,f6248,f6252,f6256,f6260,f6264,f6268,f6272,f6276,f6280,f6284,f6298,f6302,f6306,f6310,f6315,f6387,f6764,f6768,f6772,f6776,f6780,f6784,f6788,f6792,f6796,f6800,f6804,f6820,f6824,f6828,f6832,f6836,f6840,f6844,f6848,f6852,f6856,f6860,f6865,f6869,f6874,f6880,f6885,f7163,f7290,f7312,f7316,f7320,f7324,f7328,f7332,f7336,f7340,f7344,f7348,f7352,f7356,f7360,f7364,f7368,f7372,f7376,f7380,f7384,f7388,f7392,f7413,f7417,f7421,f7425,f7429,f7433,f7437,f7441,f7445,f7449,f7453,f7457,f7461,f7465,f7469,f7473,f7477,f7481,f7485,f7489,f7493,f7509,f7513,f7517,f7521,f7525,f7529,f7533,f7537,f7541,f7545,f7549,f7553,f7557,f7561,f7565,f7569,f7573,f7577,f7581,f7585,f7589,f7612,f7616,f7620,f7624,f7628,f7632,f7636,f7640,f7644,f7648,f7668,f7672,f7676,f7680,f7685,f7769,f8169,f8719,f9057,f9138,f9142,f9146,f9150,f9154,f9158,f9162,f9166,f9170,f9174,f9178,f9182,f9186,f9190,f9194,f9198,f9202,f9206,f9210,f9214,f9218,f9222,f9226,f9230,f9234,f9238,f9242,f9246,f9250,f9254,f9258,f9262,f9266,f9270,f9285,f9289,f9293,f9297,f9301,f9305,f9309,f9313,f9317,f10518,f10805,f10809,f10813,f10817,f10821,f10825,f10829,f10833,f10837,f10841,f10845,f10849,f10853,f10857,f10861,f10865,f10869,f10873,f10877,f10881,f10885,f10889,f10893,f10897,f10901,f10905,f10910,f10918,f10924,f11048,f11499,f11525,f11529,f11533,f11537,f11541,f11545,f11549,f11553,f11557,f11561,f11576,f11580,f11584,f11588,f11592,f12045,f12049,f12054,f12173,f12177,f12181,f12185,f12189,f12193,f12197,f12201,f12308,f12327,f12331,f12335,f12339,f12343,f12347,f12351,f12355,f12359,f12363,f12367,f12371,f12375,f12379,f12383,f12387,f12391,f12395,f12399,f12432,f12708,f12909,f12913,f13006,f13010,f13014,f13018,f13022,f13026,f13030,f13034,f13038,f13060,f13064,f13068,f13072,f13076,f13080,f13084,f13088,f13092,f13096,f13117,f13121,f13125,f13919,f13923,f13927,f13931,f13935,f13941,f13945,f13969,f13973,f14168,f14172,f14176,f14180,f14184,f14188,f14192,f14196,f14200,f14204,f14208,f14212,f14234,f14238,f14242,f14246,f14250,f14254,f14258,f14262,f14266,f14271,f14306,f14311,f14334,f14339,f14374,f14379,f14383,f14390,f14394,f15295,f15356,f15360,f15364,f15368,f15372,f15376,f15380,f15405,f15409,f15413,f15418,f15761,f16035,f16040,f16072,f16181,f16187,f16203,f16208,f16242,f16247,f16252,f16277,f16281,f16285,f16290,f16426,f16430,f16435,f16441,f16537,f16541,f16546,f16746,f17231,f17236,f17240,f17247,f17384,f17390,f17665,f17669,f17673,f17678,f18931,f18936,f18969,f18973,f19545,f19612,f19616,f19816,f19820,f19824,f19829,f20968,f21007,f21011,f21654,f22583,f22588,f22687,f22988,f22995,f23624,f23626]) ).
fof(f23626,plain,
( spl0_158
| ~ spl0_112
| ~ spl0_194
| ~ spl0_215
| ~ spl0_880 ),
inference(avatar_split_clause,[],[f21757,f17233,f2175,f2087,f1686,f1913]) ).
fof(f1913,plain,
( spl0_158
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1686,plain,
( spl0_112
<=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f2087,plain,
( spl0_194
<=> ! [X4,X8] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X8,tc_RealDef_Oreal),X8,tc_RealDef_Oreal) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f2175,plain,
( spl0_215
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f17233,plain,
( spl0_880
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f21757,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ spl0_112
| ~ spl0_194
| ~ spl0_215
| ~ spl0_880 ),
inference(forward_demodulation,[],[f21655,f2265]) ).
fof(f2265,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_112
| ~ spl0_215 ),
inference(resolution,[],[f2176,f1688]) ).
fof(f1688,plain,
( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1686]) ).
fof(f2176,plain,
( ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f2175]) ).
fof(f21655,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_194
| ~ spl0_880 ),
inference(superposition,[],[f2088,f17235]) ).
fof(f17235,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_880 ),
inference(avatar_component_clause,[],[f17233]) ).
fof(f2088,plain,
( ! [X8,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X8,tc_RealDef_Oreal),X8,tc_RealDef_Oreal) = X4
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f2087]) ).
fof(f23624,plain,
( spl0_909
| ~ spl0_102
| ~ spl0_114
| ~ spl0_233
| ~ spl0_252
| ~ spl0_266
| ~ spl0_267
| ~ spl0_273
| ~ spl0_275
| ~ spl0_276
| ~ spl0_571
| ~ spl0_780
| ~ spl0_810
| ~ spl0_855
| ~ spl0_878
| ~ spl0_884 ),
inference(avatar_split_clause,[],[f17512,f17388,f16744,f15415,f13943,f12907,f6877,f2712,f2708,f2691,f2474,f2469,f2412,f2330,f1696,f1636,f23621]) ).
fof(f23621,plain,
( spl0_909
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f1636,plain,
( spl0_102
<=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1696,plain,
( spl0_114
<=> class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f2330,plain,
( spl0_233
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f2412,plain,
( spl0_252
<=> ! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f2469,plain,
( spl0_266
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f2474,plain,
( spl0_267
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f2691,plain,
( spl0_273
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2708,plain,
( spl0_275
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,X3,X0) = c_HOL_Oplus__class_Oplus(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2712,plain,
( spl0_276
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f6877,plain,
( spl0_571
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f12907,plain,
( spl0_780
<=> ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f13943,plain,
( spl0_810
<=> ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f15415,plain,
( spl0_855
<=> c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f16744,plain,
( spl0_878
<=> ! [X6] : c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f17388,plain,
( spl0_884
<=> ! [X4] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f17512,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_102
| ~ spl0_114
| ~ spl0_233
| ~ spl0_252
| ~ spl0_266
| ~ spl0_267
| ~ spl0_273
| ~ spl0_275
| ~ spl0_276
| ~ spl0_571
| ~ spl0_780
| ~ spl0_810
| ~ spl0_855
| ~ spl0_878
| ~ spl0_884 ),
inference(forward_demodulation,[],[f17511,f15417]) ).
fof(f15417,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_855 ),
inference(avatar_component_clause,[],[f15415]) ).
fof(f17511,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_102
| ~ spl0_114
| ~ spl0_233
| ~ spl0_252
| ~ spl0_266
| ~ spl0_267
| ~ spl0_273
| ~ spl0_275
| ~ spl0_276
| ~ spl0_571
| ~ spl0_780
| ~ spl0_810
| ~ spl0_855
| ~ spl0_878
| ~ spl0_884 ),
inference(forward_demodulation,[],[f17510,f17181]) ).
fof(f17181,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_114
| ~ spl0_252
| ~ spl0_267
| ~ spl0_273
| ~ spl0_276
| ~ spl0_878 ),
inference(forward_demodulation,[],[f17180,f2680]) ).
fof(f2680,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_114
| ~ spl0_267 ),
inference(resolution,[],[f2475,f1698]) ).
fof(f1698,plain,
( class_Ring__and__Field_Ofield(tc_RealDef_Oreal)
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1696]) ).
fof(f2475,plain,
( ! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X2,X0) )
| ~ spl0_267 ),
inference(avatar_component_clause,[],[f2474]) ).
fof(f17180,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_114
| ~ spl0_252
| ~ spl0_267
| ~ spl0_273
| ~ spl0_276
| ~ spl0_878 ),
inference(forward_demodulation,[],[f17179,f2701]) ).
fof(f2701,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_252
| ~ spl0_273 ),
inference(trivial_inequality_removal,[],[f2700]) ).
fof(f2700,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_252
| ~ spl0_273 ),
inference(superposition,[],[f2413,f2693]) ).
fof(f2693,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)))
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f2691]) ).
fof(f2413,plain,
( ! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(X2,X3)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3 )
| ~ spl0_252 ),
inference(avatar_component_clause,[],[f2412]) ).
fof(f17179,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_114
| ~ spl0_267
| ~ spl0_276
| ~ spl0_878 ),
inference(forward_demodulation,[],[f17045,f2680]) ).
fof(f17045,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_276
| ~ spl0_878 ),
inference(superposition,[],[f16745,f2714]) ).
fof(f2714,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal))
| ~ spl0_276 ),
inference(avatar_component_clause,[],[f2712]) ).
fof(f16745,plain,
( ! [X6] : c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_878 ),
inference(avatar_component_clause,[],[f16744]) ).
fof(f17510,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_102
| ~ spl0_233
| ~ spl0_266
| ~ spl0_275
| ~ spl0_571
| ~ spl0_780
| ~ spl0_810
| ~ spl0_855
| ~ spl0_884 ),
inference(forward_demodulation,[],[f17509,f16031]) ).
fof(f16031,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_102
| ~ spl0_233
| ~ spl0_275
| ~ spl0_780
| ~ spl0_855 ),
inference(forward_demodulation,[],[f16030,f2331]) ).
fof(f2331,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2330]) ).
fof(f16030,plain,
( 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_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_102
| ~ spl0_275
| ~ spl0_780
| ~ spl0_855 ),
inference(forward_demodulation,[],[f16021,f2861]) ).
fof(f2861,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal)
| ~ spl0_102
| ~ spl0_275 ),
inference(resolution,[],[f2709,f1638]) ).
fof(f1638,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1636]) ).
fof(f2709,plain,
( ! [X2,X3,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,X3,X0) = c_HOL_Oplus__class_Oplus(X3,X2,X0) )
| ~ spl0_275 ),
inference(avatar_component_clause,[],[f2708]) ).
fof(f16021,plain,
( 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_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_780
| ~ spl0_855 ),
inference(superposition,[],[f12908,f15417]) ).
fof(f12908,plain,
( ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_780 ),
inference(avatar_component_clause,[],[f12907]) ).
fof(f17509,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_266
| ~ spl0_571
| ~ spl0_810
| ~ spl0_884 ),
inference(forward_demodulation,[],[f17508,f13944]) ).
fof(f13944,plain,
( ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal))
| ~ spl0_810 ),
inference(avatar_component_clause,[],[f13943]) ).
fof(f17508,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_266
| ~ spl0_571
| ~ spl0_884 ),
inference(forward_demodulation,[],[f17396,f2471]) ).
fof(f2471,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_266 ),
inference(avatar_component_clause,[],[f2469]) ).
fof(f17396,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_571
| ~ spl0_884 ),
inference(superposition,[],[f17389,f6879]) ).
fof(f6879,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_571 ),
inference(avatar_component_clause,[],[f6877]) ).
fof(f17389,plain,
( ! [X4] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_884 ),
inference(avatar_component_clause,[],[f17388]) ).
fof(f22995,plain,
( spl0_908
| ~ spl0_112
| ~ spl0_194
| ~ spl0_215
| ~ spl0_880
| ~ spl0_907 ),
inference(avatar_split_clause,[],[f22991,f22986,f17233,f2175,f2087,f1686,f22993]) ).
fof(f22993,plain,
( spl0_908
<=> ! [X6,X4] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal))
| c_Transcendental_Ocos(X6) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X4) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f22986,plain,
( spl0_907
<=> ! [X6,X4] :
( c_Transcendental_Ocos(X4) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X6) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal))
| c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f22991,plain,
( ! [X6,X4] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal))
| c_Transcendental_Ocos(X6) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X4) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_112
| ~ spl0_194
| ~ spl0_215
| ~ spl0_880
| ~ spl0_907 ),
inference(forward_demodulation,[],[f22990,f21757]) ).
fof(f22990,plain,
( ! [X6,X4] :
( c_Transcendental_Ocos(X6) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X4) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal))
| c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_112
| ~ spl0_194
| ~ spl0_215
| ~ spl0_880
| ~ spl0_907 ),
inference(forward_demodulation,[],[f22989,f21757]) ).
fof(f22989,plain,
( ! [X6,X4] :
( c_Transcendental_Ocos(X4) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X6) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal))
| c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_112
| ~ spl0_194
| ~ spl0_215
| ~ spl0_880
| ~ spl0_907 ),
inference(forward_demodulation,[],[f22987,f21757]) ).
fof(f22987,plain,
( ! [X6,X4] :
( c_Transcendental_Ocos(X4) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X6) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal))
| c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_907 ),
inference(avatar_component_clause,[],[f22986]) ).
fof(f22988,plain,
spl0_907,
inference(avatar_split_clause,[],[f1089,f22986]) ).
fof(f1089,plain,
! [X6,X4] :
( c_Transcendental_Ocos(X4) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X6) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal))
| c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f512,f1030,f1030,f1030,f1030,f1030]) ).
fof(f1030,plain,
! [X4] : c_Transcendental_Otan(X4) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f519,f786]) ).
fof(f786,axiom,
! [X4] : c_Transcendental_Osin(X4) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__cos__eq_0) ).
fof(f519,axiom,
! [X4] : c_Transcendental_Otan(X4) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Osin(X4),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__def_0) ).
fof(f512,axiom,
! [X6,X4] :
( c_Transcendental_Ocos(X4) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X6) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal))
| c_Transcendental_Otan(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_Transcendental_Otan(X4),c_Transcendental_Otan(X6),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Otan(X4),c_Transcendental_Otan(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__add_0) ).
fof(f22687,plain,
spl0_906,
inference(avatar_split_clause,[],[f1091,f22685]) ).
fof(f22685,plain,
( spl0_906
<=> ! [X6,X4] :
( c_HOL_Oord__class_Oless(X6,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f1091,plain,
! [X6,X4] :
( c_HOL_Oord__class_Oless(X6,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f320,f1030,f1030]) ).
fof(f320,axiom,
! [X6,X4] :
( c_HOL_Oord__class_Oless(X6,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(X6),c_Transcendental_Otan(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__monotone_H_1) ).
fof(f22588,plain,
( spl0_905
| ~ spl0_102
| ~ spl0_275
| ~ spl0_904 ),
inference(avatar_split_clause,[],[f22584,f22581,f2708,f1636,f22586]) ).
fof(f22586,plain,
( spl0_905
<=> ! [X4] :
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f22581,plain,
( spl0_904
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Oplus__class_Oplus(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f22584,plain,
( ! [X4] :
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) )
| ~ spl0_102
| ~ spl0_275
| ~ spl0_904 ),
inference(forward_demodulation,[],[f22582,f2861]) ).
fof(f22582,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Oplus__class_Oplus(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_904 ),
inference(avatar_component_clause,[],[f22581]) ).
fof(f22583,plain,
spl0_904,
inference(avatar_split_clause,[],[f1085,f22581]) ).
fof(f1085,plain,
! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Oplus__class_Oplus(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f361,f1030,f786]) ).
fof(f361,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_Transcendental_Otan(X4) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Osin(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_HOL_Oplus__class_Oplus(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__half_0) ).
fof(f21654,plain,
spl0_903,
inference(avatar_split_clause,[],[f1082,f21652]) ).
fof(f21652,plain,
( spl0_903
<=> ! [X6,X4] :
( c_Transcendental_Ocos(X4) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X6) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f1082,plain,
! [X6,X4] :
( c_Transcendental_Ocos(X4) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X6) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f362,f1030,f1030,f786]) ).
fof(f362,axiom,
! [X6,X4] :
( c_Transcendental_Ocos(X4) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X6) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Oplus__class_Oplus(c_Transcendental_Otan(X4),c_Transcendental_Otan(X6),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__tan__eq_0) ).
fof(f21011,plain,
spl0_902,
inference(avatar_split_clause,[],[f1087,f21009]) ).
fof(f21009,plain,
( spl0_902
<=> ! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X6,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f1087,plain,
! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X6,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f318,f1030,f1030]) ).
fof(f318,axiom,
! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X6,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(X6),c_Transcendental_Otan(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__monotone_0) ).
fof(f21007,plain,
spl0_901,
inference(avatar_split_clause,[],[f1083,f21005]) ).
fof(f21005,plain,
( spl0_901
<=> ! [X6,X4] :
( c_Transcendental_Ocos(X4) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X6) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f1083,plain,
! [X6,X4] :
( c_Transcendental_Ocos(X4) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X6) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f513,f1030,f1030]) ).
fof(f513,axiom,
! [X6,X4] :
( c_Transcendental_Ocos(X4) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(X6) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Otan(X4),c_Transcendental_Otan(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__tan__add1_0) ).
fof(f20968,plain,
spl0_900,
inference(avatar_split_clause,[],[f1086,f20966]) ).
fof(f20966,plain,
( spl0_900
<=> ! [X6,X4] :
( ~ c_lessequals(X6,X4,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f1086,plain,
! [X6,X4] :
( ~ c_lessequals(X6,X4,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f523,f786,f786]) ).
fof(f523,axiom,
! [X6,X4] :
( ~ c_lessequals(X6,X4,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Osin(X6),c_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__monotone__2pi_H_0) ).
fof(f19829,plain,
( spl0_899
| ~ spl0_114
| ~ spl0_252
| ~ spl0_267
| ~ spl0_273
| ~ spl0_276
| ~ spl0_878 ),
inference(avatar_split_clause,[],[f17181,f16744,f2712,f2691,f2474,f2412,f1696,f19826]) ).
fof(f19826,plain,
( spl0_899
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f19824,plain,
spl0_898,
inference(avatar_split_clause,[],[f1062,f19822]) ).
fof(f19822,plain,
( spl0_898
<=> ! [X6,X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f1062,plain,
! [X6,X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f518,f786,f786,f786]) ).
fof(f518,axiom,
! [X6,X4] : c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Osin(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__add_0) ).
fof(f19820,plain,
spl0_897,
inference(avatar_split_clause,[],[f1061,f19818]) ).
fof(f19818,plain,
( spl0_897
<=> ! [X6,X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f1061,plain,
! [X6,X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f722,f786,f786,f786]) ).
fof(f722,axiom,
! [X6,X4] : c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X6),c_Transcendental_Osin(X4),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X6),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__diff2_0) ).
fof(f19816,plain,
spl0_896,
inference(avatar_split_clause,[],[f1060,f19814]) ).
fof(f19814,plain,
( spl0_896
<=> ! [X6,X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f1060,plain,
! [X6,X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f723,f786,f786,f786]) ).
fof(f723,axiom,
! [X6,X4] : c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Osin(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__diff_0) ).
fof(f19616,plain,
spl0_895,
inference(avatar_split_clause,[],[f1100,f19614]) ).
fof(f19614,plain,
( spl0_895
<=> ! [X4,X5] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f1100,plain,
! [X4,X5] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1052,f868]) ).
fof(f868,axiom,
! [X8,X7] : c_HOL_Otimes__class_Otimes(X8,X7,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X7,X8,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
fof(f1052,plain,
! [X4,X5] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X5,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X5,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f29,f1030,f1030]) ).
fof(f29,axiom,
! [X4,X5] : c_Transcendental_Otan(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X5,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Otan(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__periodic__nat_0) ).
fof(f19612,plain,
spl0_894,
inference(avatar_split_clause,[],[f1099,f19610]) ).
fof(f19610,plain,
( spl0_894
<=> ! [X4,X5] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(X5,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(X5,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f1099,plain,
! [X4,X5] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(X5,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(X5,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1051,f868]) ).
fof(f1051,plain,
! [X4,X5] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f32,f1030,f1030]) ).
fof(f32,axiom,
! [X4,X5] : c_Transcendental_Otan(X4) = c_Transcendental_Otan(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X5,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__periodic__n_0) ).
fof(f19545,plain,
spl0_893,
inference(avatar_split_clause,[],[f1116,f19543]) ).
fof(f19543,plain,
( spl0_893
<=> ! [X2,X3,X31] : c_HOL_Ominus__class_Ominus(hAPP(X31,X3),c_HOL_Otimes__class_Otimes(X3,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X31,X3),hAPP(X31,X2),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(hAPP(X31,X2),c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X31,X3),hAPP(X31,X2),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f1116,plain,
! [X31,X2,X3] : c_HOL_Ominus__class_Ominus(hAPP(X31,X3),c_HOL_Otimes__class_Otimes(X3,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X31,X3),hAPP(X31,X2),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(hAPP(X31,X2),c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X31,X3),hAPP(X31,X2),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1115,f868]) ).
fof(f1115,plain,
! [X31,X2,X3] : c_HOL_Ominus__class_Ominus(hAPP(X31,X2),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X31,X3),hAPP(X31,X2),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(hAPP(X31,X3),c_HOL_Otimes__class_Otimes(X3,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X31,X3),hAPP(X31,X2),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f732,f868]) ).
fof(f732,axiom,
! [X31,X2,X3] : c_HOL_Ominus__class_Ominus(hAPP(X31,X2),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X31,X3),hAPP(X31,X2),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(hAPP(X31,X3),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X31,X3),hAPP(X31,X2),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),X3,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__MVT_0) ).
fof(f18973,plain,
spl0_892,
inference(avatar_split_clause,[],[f1084,f18971]) ).
fof(f18971,plain,
( spl0_892
<=> ! [X4] :
( c_Transcendental_Oarctan(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal)) = X4
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f1084,plain,
! [X4] :
( c_Transcendental_Oarctan(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal)) = X4
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f34,f1030]) ).
fof(f34,axiom,
! [X4] :
( c_Transcendental_Oarctan(c_Transcendental_Otan(X4)) = X4
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan__tan_0) ).
fof(f18969,plain,
spl0_891,
inference(avatar_split_clause,[],[f1070,f18967]) ).
fof(f18967,plain,
( spl0_891
<=> ! [X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f1070,plain,
! [X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f879,f786,f786]) ).
fof(f879,axiom,
! [X4] : c_Transcendental_Osin(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Osin(X4),tc_RealDef_Oreal),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__double_0) ).
fof(f18936,plain,
spl0_890,
inference(avatar_split_clause,[],[f1117,f18933]) ).
fof(f18933,plain,
( spl0_890
<=> c_Transcendental_Oarctan(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),c_Transcendental_Oarctan(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),c_Transcendental_Oarctan(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f1117,plain,
c_Transcendental_Oarctan(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),c_Transcendental_Oarctan(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),c_Transcendental_Oarctan(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f704,f696]) ).
fof(f696,axiom,
c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Oarctan(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan1__eq__pi4_0) ).
fof(f704,axiom,
c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),c_Transcendental_Oarctan(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),c_Transcendental_Oarctan(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_machin_0) ).
fof(f18931,plain,
spl0_889,
inference(avatar_split_clause,[],[f296,f18929]) ).
fof(f18929,plain,
( spl0_889
<=> ! [X3,X4,X0,X6,X2] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X6,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X2,X0),c_HOL_Ominus__class_Ominus(X6,X3,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X2,X0),X3,X0),X0),c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X6,X3,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f296,axiom,
! [X2,X3,X0,X6,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X6,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X2,X0),c_HOL_Ominus__class_Ominus(X6,X3,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X2,X0),X3,X0),X0),c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X6,X3,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
fof(f17678,plain,
( spl0_888
| ~ spl0_101
| ~ spl0_102
| ~ spl0_111
| ~ spl0_112
| ~ spl0_114
| ~ spl0_121
| ~ spl0_169
| ~ spl0_193
| ~ spl0_201
| ~ spl0_216
| ~ spl0_220
| ~ spl0_252
| ~ spl0_266
| ~ spl0_267
| ~ spl0_273
| ~ spl0_275
| ~ spl0_276
| ~ spl0_327
| ~ spl0_361
| ~ spl0_443
| ~ spl0_444
| ~ spl0_453
| ~ spl0_458
| ~ spl0_462
| ~ spl0_645
| ~ spl0_743
| ~ spl0_755
| ~ spl0_774
| ~ spl0_780
| ~ spl0_810
| ~ spl0_877
| ~ spl0_878
| ~ spl0_884 ),
inference(avatar_split_clause,[],[f17578,f17388,f16744,f16544,f13943,f12907,f12385,f12191,f11578,f7638,f5055,f5039,f5017,f4980,f4976,f3436,f3136,f2712,f2708,f2691,f2474,f2469,f2412,f2195,f2179,f2117,f2083,f1960,f1731,f1696,f1686,f1681,f1636,f1631,f17675]) ).
fof(f17675,plain,
( spl0_888
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f1631,plain,
( spl0_101
<=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1681,plain,
( spl0_111
<=> class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1731,plain,
( spl0_121
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1960,plain,
( spl0_169
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f2083,plain,
( spl0_193
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f2117,plain,
( spl0_201
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f2179,plain,
( spl0_216
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f2195,plain,
( spl0_220
<=> ! [X8,X7] : c_HOL_Otimes__class_Otimes(X8,X7,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X7,X8,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f3136,plain,
( spl0_327
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f3436,plain,
( spl0_361
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X2,X3,X0) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f4976,plain,
( spl0_443
<=> ! [X0,X8] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X0) = c_HOL_Oplus__class_Oplus(X8,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f4980,plain,
( spl0_444
<=> ! [X0,X8] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X8,X8,X0) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f5017,plain,
( spl0_453
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f5039,plain,
( spl0_458
<=> ! [X2,X10] : c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X10,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X2,X10,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f5055,plain,
( spl0_462
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f7638,plain,
( spl0_645
<=> ! [X4,X0,X6,X26] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X4,X6,X0),X26,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X26,X0),c_HOL_Oinverse__class_Odivide(X6,X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f11578,plain,
( spl0_743
<=> ! [X6,X8] : c_HOL_Oinverse__class_Odivide(X6,X8,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X6,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X8,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f12191,plain,
( spl0_755
<=> ! [X4] : c_Transcendental_Ocos(X4) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f12385,plain,
( spl0_774
<=> ! [X2,X3] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,X2,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f16544,plain,
( spl0_877
<=> ! [X4] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f17578,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_101
| ~ spl0_102
| ~ spl0_111
| ~ spl0_112
| ~ spl0_114
| ~ spl0_121
| ~ spl0_169
| ~ spl0_193
| ~ spl0_201
| ~ spl0_216
| ~ spl0_220
| ~ spl0_252
| ~ spl0_266
| ~ spl0_267
| ~ spl0_273
| ~ spl0_275
| ~ spl0_276
| ~ spl0_327
| ~ spl0_361
| ~ spl0_443
| ~ spl0_444
| ~ spl0_453
| ~ spl0_458
| ~ spl0_462
| ~ spl0_645
| ~ spl0_743
| ~ spl0_755
| ~ spl0_774
| ~ spl0_780
| ~ spl0_810
| ~ spl0_877
| ~ spl0_878
| ~ spl0_884 ),
inference(forward_demodulation,[],[f17577,f12192]) ).
fof(f12192,plain,
( ! [X4] : c_Transcendental_Ocos(X4) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_755 ),
inference(avatar_component_clause,[],[f12191]) ).
fof(f17577,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_101
| ~ spl0_102
| ~ spl0_111
| ~ spl0_112
| ~ spl0_114
| ~ spl0_121
| ~ spl0_169
| ~ spl0_193
| ~ spl0_201
| ~ spl0_216
| ~ spl0_220
| ~ spl0_252
| ~ spl0_266
| ~ spl0_267
| ~ spl0_273
| ~ spl0_275
| ~ spl0_276
| ~ spl0_327
| ~ spl0_361
| ~ spl0_443
| ~ spl0_444
| ~ spl0_453
| ~ spl0_458
| ~ spl0_462
| ~ spl0_645
| ~ spl0_743
| ~ spl0_755
| ~ spl0_774
| ~ spl0_780
| ~ spl0_810
| ~ spl0_877
| ~ spl0_878
| ~ spl0_884 ),
inference(forward_demodulation,[],[f17576,f17181]) ).
fof(f17576,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_101
| ~ spl0_102
| ~ spl0_111
| ~ spl0_112
| ~ spl0_114
| ~ spl0_121
| ~ spl0_169
| ~ spl0_193
| ~ spl0_201
| ~ spl0_216
| ~ spl0_220
| ~ spl0_266
| ~ spl0_267
| ~ spl0_275
| ~ spl0_327
| ~ spl0_361
| ~ spl0_443
| ~ spl0_444
| ~ spl0_453
| ~ spl0_458
| ~ spl0_462
| ~ spl0_645
| ~ spl0_743
| ~ spl0_755
| ~ spl0_774
| ~ spl0_780
| ~ spl0_810
| ~ spl0_877
| ~ spl0_878
| ~ spl0_884 ),
inference(forward_demodulation,[],[f17575,f17153]) ).
fof(f17153,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_114
| ~ spl0_267
| ~ spl0_462
| ~ spl0_878 ),
inference(forward_demodulation,[],[f17026,f2680]) ).
fof(f17026,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_462
| ~ spl0_878 ),
inference(superposition,[],[f16745,f5057]) ).
fof(f5057,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal))
| ~ spl0_462 ),
inference(avatar_component_clause,[],[f5055]) ).
fof(f17575,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_101
| ~ spl0_102
| ~ spl0_111
| ~ spl0_112
| ~ spl0_114
| ~ spl0_121
| ~ spl0_169
| ~ spl0_193
| ~ spl0_201
| ~ spl0_216
| ~ spl0_220
| ~ spl0_266
| ~ spl0_267
| ~ spl0_275
| ~ spl0_327
| ~ spl0_361
| ~ spl0_443
| ~ spl0_444
| ~ spl0_453
| ~ spl0_458
| ~ spl0_462
| ~ spl0_645
| ~ spl0_743
| ~ spl0_755
| ~ spl0_774
| ~ spl0_780
| ~ spl0_810
| ~ spl0_877
| ~ spl0_878
| ~ spl0_884 ),
inference(forward_demodulation,[],[f17574,f16697]) ).
fof(f16697,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_101
| ~ spl0_111
| ~ spl0_112
| ~ spl0_114
| ~ spl0_121
| ~ spl0_169
| ~ spl0_193
| ~ spl0_201
| ~ spl0_216
| ~ spl0_220
| ~ spl0_267
| ~ spl0_327
| ~ spl0_361
| ~ spl0_443
| ~ spl0_444
| ~ spl0_458
| ~ spl0_645
| ~ spl0_743
| ~ spl0_774
| ~ spl0_877 ),
inference(forward_demodulation,[],[f16696,f1962]) ).
fof(f1962,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f1960]) ).
fof(f16696,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_101
| ~ spl0_111
| ~ spl0_112
| ~ spl0_114
| ~ spl0_121
| ~ spl0_193
| ~ spl0_201
| ~ spl0_216
| ~ spl0_220
| ~ spl0_267
| ~ spl0_327
| ~ spl0_361
| ~ spl0_443
| ~ spl0_444
| ~ spl0_458
| ~ spl0_645
| ~ spl0_743
| ~ spl0_774
| ~ spl0_877 ),
inference(forward_demodulation,[],[f16695,f2680]) ).
fof(f16695,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_101
| ~ spl0_111
| ~ spl0_112
| ~ spl0_114
| ~ spl0_121
| ~ spl0_193
| ~ spl0_201
| ~ spl0_216
| ~ spl0_220
| ~ spl0_267
| ~ spl0_327
| ~ spl0_361
| ~ spl0_443
| ~ spl0_444
| ~ spl0_458
| ~ spl0_645
| ~ spl0_743
| ~ spl0_774
| ~ spl0_877 ),
inference(forward_demodulation,[],[f16694,f2268]) ).
fof(f2268,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,X0,tc_RealDef_Oreal)
| ~ spl0_112
| ~ spl0_216 ),
inference(resolution,[],[f2180,f1688]) ).
fof(f2180,plain,
( ! [X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) )
| ~ spl0_216 ),
inference(avatar_component_clause,[],[f2179]) ).
fof(f16694,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_101
| ~ spl0_111
| ~ spl0_112
| ~ spl0_114
| ~ spl0_121
| ~ spl0_193
| ~ spl0_201
| ~ spl0_220
| ~ spl0_267
| ~ spl0_327
| ~ spl0_361
| ~ spl0_443
| ~ spl0_444
| ~ spl0_458
| ~ spl0_645
| ~ spl0_743
| ~ spl0_774
| ~ spl0_877 ),
inference(forward_demodulation,[],[f16693,f9084]) ).
fof(f9084,plain,
( ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X0,X2,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_101
| ~ spl0_645 ),
inference(resolution,[],[f7639,f1633]) ).
fof(f1633,plain,
( class_RealVector_Oreal__normed__field(tc_RealDef_Oreal)
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f1631]) ).
fof(f7639,plain,
( ! [X0,X6,X26,X4] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X4,X6,X0),X26,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X26,X0),c_HOL_Oinverse__class_Odivide(X6,X26,X0),X0) )
| ~ spl0_645 ),
inference(avatar_component_clause,[],[f7638]) ).
fof(f16693,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_111
| ~ spl0_112
| ~ spl0_114
| ~ spl0_121
| ~ spl0_193
| ~ spl0_201
| ~ spl0_220
| ~ spl0_267
| ~ spl0_327
| ~ spl0_361
| ~ spl0_443
| ~ spl0_444
| ~ spl0_458
| ~ spl0_743
| ~ spl0_774
| ~ spl0_877 ),
inference(forward_demodulation,[],[f16692,f12856]) ).
fof(f12856,plain,
( ! [X0] : c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X0,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_111
| ~ spl0_112
| ~ spl0_114
| ~ spl0_193
| ~ spl0_201
| ~ spl0_267
| ~ spl0_361
| ~ spl0_774 ),
inference(forward_demodulation,[],[f12855,f2220]) ).
fof(f2220,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
| ~ spl0_111
| ~ spl0_201 ),
inference(resolution,[],[f2118,f1683]) ).
fof(f1683,plain,
( class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal)
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1681]) ).
fof(f2118,plain,
( ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f2117]) ).
fof(f12855,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X0,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_112
| ~ spl0_114
| ~ spl0_193
| ~ spl0_267
| ~ spl0_361
| ~ spl0_774 ),
inference(forward_demodulation,[],[f12854,f2680]) ).
fof(f12854,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X0,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_112
| ~ spl0_193
| ~ spl0_361
| ~ spl0_774 ),
inference(forward_demodulation,[],[f12853,f3797]) ).
fof(f3797,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_112
| ~ spl0_361 ),
inference(resolution,[],[f3437,f1688]) ).
fof(f3437,plain,
( ! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X2,X3,X0) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) )
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f3436]) ).
fof(f12853,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_112
| ~ spl0_193
| ~ spl0_361
| ~ spl0_774 ),
inference(forward_demodulation,[],[f12826,f3797]) ).
fof(f12826,plain,
( ! [X0] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_193
| ~ spl0_774 ),
inference(superposition,[],[f12386,f2084]) ).
fof(f2084,plain,
( ! [X4] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f2083]) ).
fof(f12386,plain,
( ! [X2,X3] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,X2,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ spl0_774 ),
inference(avatar_component_clause,[],[f12385]) ).
fof(f16692,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_121
| ~ spl0_220
| ~ spl0_327
| ~ spl0_443
| ~ spl0_444
| ~ spl0_458
| ~ spl0_743
| ~ spl0_877 ),
inference(forward_demodulation,[],[f16691,f5253]) ).
fof(f5253,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,X0,tc_RealDef_Oreal)
| ~ spl0_121
| ~ spl0_444 ),
inference(resolution,[],[f4981,f1733]) ).
fof(f1733,plain,
( class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1731]) ).
fof(f4981,plain,
( ! [X0,X8] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X8,X8,X0) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X8,X0) )
| ~ spl0_444 ),
inference(avatar_component_clause,[],[f4980]) ).
fof(f16691,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_121
| ~ spl0_220
| ~ spl0_327
| ~ spl0_443
| ~ spl0_458
| ~ spl0_743
| ~ spl0_877 ),
inference(forward_demodulation,[],[f16690,f11882]) ).
fof(f11882,plain,
( ! [X0] : c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X0,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X0,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_458
| ~ spl0_743 ),
inference(superposition,[],[f11579,f5040]) ).
fof(f5040,plain,
( ! [X2,X10] : c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X10,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X2,X10,tc_RealDef_Oreal)
| ~ spl0_458 ),
inference(avatar_component_clause,[],[f5039]) ).
fof(f11579,plain,
( ! [X8,X6] : c_HOL_Oinverse__class_Odivide(X6,X8,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X6,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X8,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_743 ),
inference(avatar_component_clause,[],[f11578]) ).
fof(f16690,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_121
| ~ spl0_220
| ~ spl0_327
| ~ spl0_443
| ~ spl0_877 ),
inference(forward_demodulation,[],[f16689,f2196]) ).
fof(f2196,plain,
( ! [X8,X7] : c_HOL_Otimes__class_Otimes(X8,X7,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X7,X8,tc_RealDef_Oreal)
| ~ spl0_220 ),
inference(avatar_component_clause,[],[f2195]) ).
fof(f16689,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_121
| ~ spl0_327
| ~ spl0_443
| ~ spl0_877 ),
inference(forward_demodulation,[],[f16571,f5250]) ).
fof(f5250,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,X0,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_121
| ~ spl0_443 ),
inference(resolution,[],[f4977,f1733]) ).
fof(f4977,plain,
( ! [X0,X8] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X0) = c_HOL_Oplus__class_Oplus(X8,X8,X0) )
| ~ spl0_443 ),
inference(avatar_component_clause,[],[f4976]) ).
fof(f16571,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_327
| ~ spl0_877 ),
inference(superposition,[],[f16545,f3138]) ).
fof(f3138,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_327 ),
inference(avatar_component_clause,[],[f3136]) ).
fof(f16545,plain,
( ! [X4] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal)
| ~ spl0_877 ),
inference(avatar_component_clause,[],[f16544]) ).
fof(f17574,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_102
| ~ spl0_114
| ~ spl0_266
| ~ spl0_267
| ~ spl0_275
| ~ spl0_453
| ~ spl0_462
| ~ spl0_755
| ~ spl0_780
| ~ spl0_810
| ~ spl0_878
| ~ spl0_884 ),
inference(forward_demodulation,[],[f17573,f17153]) ).
fof(f17573,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_102
| ~ spl0_114
| ~ spl0_266
| ~ spl0_275
| ~ spl0_453
| ~ spl0_462
| ~ spl0_755
| ~ spl0_780
| ~ spl0_810
| ~ spl0_884 ),
inference(forward_demodulation,[],[f17572,f5278]) ).
fof(f5278,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ spl0_114
| ~ spl0_453 ),
inference(resolution,[],[f5018,f1698]) ).
fof(f5018,plain,
( ! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) )
| ~ spl0_453 ),
inference(avatar_component_clause,[],[f5017]) ).
fof(f17572,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_102
| ~ spl0_266
| ~ spl0_275
| ~ spl0_462
| ~ spl0_755
| ~ spl0_780
| ~ spl0_810
| ~ spl0_884 ),
inference(forward_demodulation,[],[f17571,f12967]) ).
fof(f12967,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(X0),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_102
| ~ spl0_275
| ~ spl0_755
| ~ spl0_780 ),
inference(forward_demodulation,[],[f12919,f2861]) ).
fof(f12919,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(X0),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_755
| ~ spl0_780 ),
inference(superposition,[],[f12908,f12192]) ).
fof(f17571,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_266
| ~ spl0_462
| ~ spl0_810
| ~ spl0_884 ),
inference(forward_demodulation,[],[f17570,f13944]) ).
fof(f17570,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_266
| ~ spl0_462
| ~ spl0_884 ),
inference(forward_demodulation,[],[f17408,f2471]) ).
fof(f17408,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_462
| ~ spl0_884 ),
inference(superposition,[],[f17389,f5057]) ).
fof(f17673,plain,
spl0_887,
inference(avatar_split_clause,[],[f1065,f17671]) ).
fof(f17671,plain,
( spl0_887
<=> ! [X6,X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f1065,plain,
! [X6,X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f567,f786,f786]) ).
fof(f567,axiom,
! [X6,X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X4),c_Transcendental_Osin(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__add_0) ).
fof(f17669,plain,
spl0_886,
inference(avatar_split_clause,[],[f1064,f17667]) ).
fof(f17667,plain,
( spl0_886
<=> ! [X6,X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f1064,plain,
! [X6,X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f568,f786,f786]) ).
fof(f568,axiom,
! [X6,X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X6),c_Transcendental_Osin(X4),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__diff2_0) ).
fof(f17665,plain,
spl0_885,
inference(avatar_split_clause,[],[f1063,f17663]) ).
fof(f17663,plain,
( spl0_885
<=> ! [X6,X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f1063,plain,
! [X6,X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f569,f786,f786]) ).
fof(f569,axiom,
! [X6,X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X4),c_Transcendental_Osin(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__diff_0) ).
fof(f17390,plain,
( spl0_884
| ~ spl0_246
| ~ spl0_834
| ~ spl0_883 ),
inference(avatar_split_clause,[],[f17386,f17382,f14269,f2383,f17388]) ).
fof(f2383,plain,
( spl0_246
<=> ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f14269,plain,
( spl0_834
<=> ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f17382,plain,
( spl0_883
<=> ! [X4] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f17386,plain,
( ! [X4] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_246
| ~ spl0_834
| ~ spl0_883 ),
inference(forward_demodulation,[],[f17385,f14270]) ).
fof(f14270,plain,
( ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_834 ),
inference(avatar_component_clause,[],[f14269]) ).
fof(f17385,plain,
( ! [X4] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_246
| ~ spl0_883 ),
inference(forward_demodulation,[],[f17383,f2384]) ).
fof(f2384,plain,
( ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(X4),tc_RealDef_Oreal)
| ~ spl0_246 ),
inference(avatar_component_clause,[],[f2383]) ).
fof(f17383,plain,
( ! [X4] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_883 ),
inference(avatar_component_clause,[],[f17382]) ).
fof(f17384,plain,
spl0_883,
inference(avatar_split_clause,[],[f1039,f17382]) ).
fof(f1039,plain,
! [X4] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f196,f1030,f1030]) ).
fof(f196,axiom,
! [X4] : c_Transcendental_Otan(X4) = c_Transcendental_Otan(c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__periodic__pi_0) ).
fof(f17247,plain,
( spl0_882
| ~ spl0_114
| ~ spl0_453
| ~ spl0_881 ),
inference(avatar_split_clause,[],[f17241,f17238,f5017,f1696,f17245]) ).
fof(f17245,plain,
( spl0_882
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f17238,plain,
( spl0_881
<=> ! [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_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f17241,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_114
| ~ spl0_453
| ~ spl0_881 ),
inference(forward_demodulation,[],[f17239,f5278]) ).
fof(f17239,plain,
( ! [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_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) )
| ~ spl0_881 ),
inference(avatar_component_clause,[],[f17238]) ).
fof(f17240,plain,
spl0_881,
inference(avatar_split_clause,[],[f1077,f17238]) ).
fof(f1077,plain,
! [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_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f356,f1030]) ).
fof(f356,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_Transcendental_Otan(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__less__zero_0) ).
fof(f17236,plain,
( spl0_880
| ~ spl0_81
| ~ spl0_252
| ~ spl0_256
| ~ spl0_273
| ~ spl0_276
| ~ spl0_875 ),
inference(avatar_split_clause,[],[f16935,f16535,f2712,f2691,f2429,f2412,f1531,f17233]) ).
fof(f1531,plain,
( spl0_81
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f2429,plain,
( spl0_256
<=> ! [X0,X3] :
( ~ 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),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f16535,plain,
( spl0_875
<=> ! [X4] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f16935,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_81
| ~ spl0_252
| ~ spl0_256
| ~ spl0_273
| ~ spl0_276
| ~ spl0_875 ),
inference(forward_demodulation,[],[f16934,f2647]) ).
fof(f2647,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_81
| ~ spl0_256 ),
inference(resolution,[],[f2430,f1533]) ).
fof(f1533,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal)
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1531]) ).
fof(f2430,plain,
( ! [X3,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),X3,X0) )
| ~ spl0_256 ),
inference(avatar_component_clause,[],[f2429]) ).
fof(f16934,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),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) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ spl0_252
| ~ spl0_273
| ~ spl0_276
| ~ spl0_875 ),
inference(forward_demodulation,[],[f16760,f2701]) ).
fof(f16760,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_276
| ~ spl0_875 ),
inference(superposition,[],[f16536,f2714]) ).
fof(f16536,plain,
( ! [X4] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_875 ),
inference(avatar_component_clause,[],[f16535]) ).
fof(f17231,plain,
spl0_879,
inference(avatar_split_clause,[],[f508,f17229]) ).
fof(f17229,plain,
( spl0_879
<=> ! [X2,X3,X23,X0,X9,X1] :
( ~ class_RealVector_Oreal__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Otimes__class_Otimes(X1,X9,X0),X0),X23,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X3,X9,X0),X23,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X1,X0),X23,X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f508,axiom,
! [X2,X3,X0,X1,X9,X23] :
( ~ class_RealVector_Oreal__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Otimes__class_Otimes(X1,X9,X0),X0),X23,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X3,X9,X0),X23,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X1,X0),X23,X0),X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).
fof(f16746,plain,
spl0_878,
inference(avatar_split_clause,[],[f1108,f16744]) ).
fof(f1108,plain,
! [X6] : c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1059,f1031]) ).
fof(f1031,plain,
! [X4] : c_Transcendental_Ocos(X4) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f785,f786]) ).
fof(f785,axiom,
! [X4] : c_Transcendental_Ocos(X4) = c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__sin__eq_0) ).
fof(f1059,plain,
! [X6] : c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f702,f1030,f1030]) ).
fof(f702,axiom,
! [X6] : c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Otan(X6),tc_RealDef_Oreal) = c_Transcendental_Otan(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__inverse_0) ).
fof(f16546,plain,
( spl0_877
| ~ spl0_112
| ~ spl0_361
| ~ spl0_876 ),
inference(avatar_split_clause,[],[f16542,f16539,f3436,f1686,f16544]) ).
fof(f16539,plain,
( spl0_876
<=> ! [X4] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f16542,plain,
( ! [X4] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal)
| ~ spl0_112
| ~ spl0_361
| ~ spl0_876 ),
inference(forward_demodulation,[],[f16540,f3797]) ).
fof(f16540,plain,
( ! [X4] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal)
| ~ spl0_876 ),
inference(avatar_component_clause,[],[f16539]) ).
fof(f16541,plain,
spl0_876,
inference(avatar_split_clause,[],[f1094,f16539]) ).
fof(f1094,plain,
! [X4] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1040,f676]) ).
fof(f676,axiom,
! [X4] : c_Transcendental_Ocos(X4) = c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__minus_0) ).
fof(f1040,plain,
! [X4] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f262,f1030,f1030]) ).
fof(f262,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/sandbox/benchmark/theBenchmark.p',cls_tan__minus_0) ).
fof(f16537,plain,
spl0_875,
inference(avatar_split_clause,[],[f1056,f16535]) ).
fof(f1056,plain,
! [X4] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f566,f786,f786]) ).
fof(f566,axiom,
! [X4] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X4),c_Transcendental_Osin(X4),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__cos__squared__add3_0) ).
fof(f16441,plain,
( spl0_874
| ~ spl0_861
| ~ spl0_873 ),
inference(avatar_split_clause,[],[f16436,f16432,f16184,f16438]) ).
fof(f16438,plain,
( spl0_874
<=> c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f16184,plain,
( spl0_861
<=> c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f16432,plain,
( spl0_873
<=> c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f16436,plain,
( c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_861
| ~ spl0_873 ),
inference(forward_demodulation,[],[f16434,f16186]) ).
fof(f16186,plain,
( c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_861 ),
inference(avatar_component_clause,[],[f16184]) ).
fof(f16434,plain,
( c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_873 ),
inference(avatar_component_clause,[],[f16432]) ).
fof(f16435,plain,
spl0_873,
inference(avatar_split_clause,[],[f1055,f16432]) ).
fof(f1055,plain,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f690,f1030]) ).
fof(f690,axiom,
c_Transcendental_Otan(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__60_0) ).
fof(f16430,plain,
spl0_872,
inference(avatar_split_clause,[],[f726,f16428]) ).
fof(f16428,plain,
( spl0_872
<=> ! [X4,X0,X6,X8,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X6,X0),c_HOL_Oinverse__class_Odivide(X7,X8,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X8,X0),c_HOL_Otimes__class_Otimes(X7,X6,X0),X0),c_HOL_Otimes__class_Otimes(X6,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f726,axiom,
! [X0,X8,X6,X7,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X6,X0),c_HOL_Oinverse__class_Odivide(X7,X8,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X8,X0),c_HOL_Otimes__class_Otimes(X7,X6,X0),X0),c_HOL_Otimes__class_Otimes(X6,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
fof(f16426,plain,
spl0_871,
inference(avatar_split_clause,[],[f488,f16424]) ).
fof(f16424,plain,
( spl0_871
<=> ! [X4,X0,X6,X8,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X6,X0),c_HOL_Oinverse__class_Odivide(X7,X8,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X8,X0),c_HOL_Otimes__class_Otimes(X7,X6,X0),X0),c_HOL_Otimes__class_Otimes(X6,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f488,axiom,
! [X0,X8,X6,X7,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X6,X0),c_HOL_Oinverse__class_Odivide(X7,X8,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X8,X0),c_HOL_Otimes__class_Otimes(X7,X6,X0),X0),c_HOL_Otimes__class_Otimes(X6,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).
fof(f16290,plain,
( spl0_870
| ~ spl0_121
| ~ spl0_443
| ~ spl0_869 ),
inference(avatar_split_clause,[],[f16286,f16283,f4976,f1731,f16288]) ).
fof(f16288,plain,
( spl0_870
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal))
| c_Transcendental_Ocos(X4) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f16283,plain,
( spl0_869
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal))
| c_Transcendental_Ocos(X4) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f16286,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal))
| c_Transcendental_Ocos(X4) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal) )
| ~ spl0_121
| ~ spl0_443
| ~ spl0_869 ),
inference(forward_demodulation,[],[f16284,f5250]) ).
fof(f16284,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal))
| c_Transcendental_Ocos(X4) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal) )
| ~ spl0_869 ),
inference(avatar_component_clause,[],[f16283]) ).
fof(f16285,plain,
spl0_869,
inference(avatar_split_clause,[],[f1123,f16283]) ).
fof(f1123,plain,
! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal))
| c_Transcendental_Ocos(X4) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1088,f868]) ).
fof(f1088,plain,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal))
| c_Transcendental_Ocos(X4) != c_HOL_Oone__class_Oone(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(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f707,f786]) ).
fof(f707,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Osin(X4)
| c_Transcendental_Ocos(X4) != c_HOL_Oone__class_Oone(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(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__cos__between__zero__two__pi_0) ).
fof(f16281,plain,
spl0_868,
inference(avatar_split_clause,[],[f1079,f16279]) ).
fof(f16279,plain,
( spl0_868
<=> ! [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_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f1079,plain,
! [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_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_Transcendental_Ocos(X4),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f522,f1030]) ).
fof(f522,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_Transcendental_Otan(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__gt__zero_0) ).
fof(f16277,plain,
( spl0_867
| ~ spl0_357
| ~ spl0_856 ),
inference(avatar_split_clause,[],[f16170,f15759,f3419,f16274]) ).
fof(f16274,plain,
( spl0_867
<=> c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f3419,plain,
( spl0_357
<=> 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_357])]) ).
fof(f15759,plain,
( spl0_856
<=> ! [X0] : c_HOL_Oord__class_Oless(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),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f16170,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_357
| ~ spl0_856 ),
inference(superposition,[],[f15760,f3421]) ).
fof(f3421,plain,
( 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)
| ~ spl0_357 ),
inference(avatar_component_clause,[],[f3419]) ).
fof(f15760,plain,
( ! [X0] : c_HOL_Oord__class_Oless(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),tc_RealDef_Oreal)
| ~ spl0_856 ),
inference(avatar_component_clause,[],[f15759]) ).
fof(f16252,plain,
( spl0_866
| ~ spl0_121
| ~ spl0_443
| ~ spl0_865 ),
inference(avatar_split_clause,[],[f16248,f16245,f4976,f1731,f16250]) ).
fof(f16250,plain,
( spl0_866
<=> ! [X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f16245,plain,
( spl0_865
<=> ! [X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f16248,plain,
( ! [X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_121
| ~ spl0_443
| ~ spl0_865 ),
inference(forward_demodulation,[],[f16246,f5250]) ).
fof(f16246,plain,
( ! [X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_865 ),
inference(avatar_component_clause,[],[f16245]) ).
fof(f16247,plain,
spl0_865,
inference(avatar_split_clause,[],[f1103,f16245]) ).
fof(f1103,plain,
! [X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f1054,f868]) ).
fof(f1054,plain,
! [X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f698,f786,f786]) ).
fof(f698,axiom,
! [X4] : c_Transcendental_Osin(X4) = c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__periodic_0) ).
fof(f16242,plain,
spl0_864,
inference(avatar_split_clause,[],[f1050,f16239]) ).
fof(f16239,plain,
( spl0_864
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f1050,plain,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f695,f1030]) ).
fof(f695,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Otan(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__45_0) ).
fof(f16208,plain,
( spl0_863
| ~ spl0_114
| ~ spl0_453
| ~ spl0_862 ),
inference(avatar_split_clause,[],[f16204,f16201,f5017,f1696,f16206]) ).
fof(f16206,plain,
( spl0_863
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f16201,plain,
( spl0_862
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f16204,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_114
| ~ spl0_453
| ~ spl0_862 ),
inference(forward_demodulation,[],[f16202,f5278]) ).
fof(f16202,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) )
| ~ spl0_862 ),
inference(avatar_component_clause,[],[f16201]) ).
fof(f16203,plain,
spl0_862,
inference(avatar_split_clause,[],[f1078,f16201]) ).
fof(f1078,plain,
! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f563,f786]) ).
fof(f563,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_Transcendental_Osin(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__less__zero_0) ).
fof(f16187,plain,
( spl0_861
| ~ spl0_749
| ~ spl0_860 ),
inference(avatar_split_clause,[],[f16182,f16178,f12051,f16184]) ).
fof(f12051,plain,
( spl0_749
<=> c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f16178,plain,
( spl0_860
<=> c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f16182,plain,
( c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_749
| ~ spl0_860 ),
inference(forward_demodulation,[],[f16180,f12053]) ).
fof(f12053,plain,
( c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_749 ),
inference(avatar_component_clause,[],[f12051]) ).
fof(f16180,plain,
( c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_860 ),
inference(avatar_component_clause,[],[f16178]) ).
fof(f16181,plain,
spl0_860,
inference(avatar_split_clause,[],[f1069,f16178]) ).
fof(f1069,plain,
c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f710,f786]) ).
fof(f710,axiom,
c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__60_0) ).
fof(f16072,plain,
( spl0_859
| ~ spl0_170
| ~ spl0_328
| ~ spl0_858 ),
inference(avatar_split_clause,[],[f16041,f16037,f3141,f1965,f16069]) ).
fof(f16069,plain,
( spl0_859
<=> c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f1965,plain,
( spl0_170
<=> 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_170])]) ).
fof(f3141,plain,
( spl0_328
<=> ! [X6,X4] : c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f16037,plain,
( spl0_858
<=> c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f16041,plain,
( c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_170
| ~ spl0_328
| ~ spl0_858 ),
inference(forward_demodulation,[],[f16039,f3274]) ).
fof(f3274,plain,
( ! [X0] : c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ spl0_170
| ~ spl0_328 ),
inference(superposition,[],[f3142,f1967]) ).
fof(f1967,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1965]) ).
fof(f3142,plain,
( ! [X6,X4] : c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal)
| ~ spl0_328 ),
inference(avatar_component_clause,[],[f3141]) ).
fof(f16039,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_858 ),
inference(avatar_component_clause,[],[f16037]) ).
fof(f16040,plain,
spl0_858,
inference(avatar_split_clause,[],[f1111,f16037]) ).
fof(f1111,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1068,f1109]) ).
fof(f1109,plain,
c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f1066,f712]) ).
fof(f712,axiom,
c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__60_0) ).
fof(f1066,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f780,f786]) ).
fof(f780,axiom,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__30_0) ).
fof(f1068,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f703,f1030]) ).
fof(f703,axiom,
c_Transcendental_Otan(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__30_0) ).
fof(f16035,plain,
spl0_857,
inference(avatar_split_clause,[],[f1081,f16033]) ).
fof(f16033,plain,
( spl0_857
<=> ! [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_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f1081,plain,
! [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_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f701,f786]) ).
fof(f701,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_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__gt__zero2_0) ).
fof(f15761,plain,
( spl0_856
| ~ spl0_394
| ~ spl0_844 ),
inference(avatar_split_clause,[],[f15381,f15293,f3932,f15759]) ).
fof(f3932,plain,
( spl0_394
<=> ! [X6,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f15293,plain,
( spl0_844
<=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f15381,plain,
( ! [X0] : c_HOL_Oord__class_Oless(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),tc_RealDef_Oreal)
| ~ spl0_394
| ~ spl0_844 ),
inference(resolution,[],[f15294,f3933]) ).
fof(f3933,plain,
( ! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X6,tc_RealDef_Oreal) )
| ~ spl0_394 ),
inference(avatar_component_clause,[],[f3932]) ).
fof(f15294,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_844 ),
inference(avatar_component_clause,[],[f15293]) ).
fof(f15418,plain,
spl0_855,
inference(avatar_split_clause,[],[f1110,f15415]) ).
fof(f1110,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f1067,f868]) ).
fof(f1067,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f705,f786]) ).
fof(f705,axiom,
c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__3over2__pi_0) ).
fof(f15413,plain,
spl0_854,
inference(avatar_split_clause,[],[f634,f15411]) ).
fof(f15411,plain,
( spl0_854
<=> ! [X3,X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X2 = X3
| X1 = X9
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X9,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f634,axiom,
! [X2,X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X2 = X3
| X1 = X9
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X9,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
fof(f15409,plain,
spl0_853,
inference(avatar_split_clause,[],[f422,f15407]) ).
fof(f15407,plain,
( spl0_853
<=> ! [X2,X16,X3,X0,X9,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(X2,X3,X0),X16,X0),X1,X0),X9,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f422,axiom,
! [X2,X3,X0,X1,X9,X16] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X0),X16,X0),X1,X0),X9,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
fof(f15405,plain,
spl0_852,
inference(avatar_split_clause,[],[f421,f15403]) ).
fof(f15403,plain,
( spl0_852
<=> ! [X2,X16,X3,X0,X9,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(X2,X3,X0),X16,X0),X1,X0),X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f421,axiom,
! [X2,X3,X0,X1,X9,X16] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X0),X16,X0),X1,X0),X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
fof(f15380,plain,
spl0_851,
inference(avatar_split_clause,[],[f420,f15378]) ).
fof(f15378,plain,
( spl0_851
<=> ! [X16,X3,X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X2,X0),X16,X0),X9,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f420,axiom,
! [X2,X3,X0,X1,X9,X16] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X2,X0),X16,X0),X9,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
fof(f15376,plain,
spl0_850,
inference(avatar_split_clause,[],[f419,f15374]) ).
fof(f15374,plain,
( spl0_850
<=> ! [X16,X3,X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X2,X0),X16,X0),X9,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f419,axiom,
! [X2,X3,X0,X1,X9,X16] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X2,X0),X16,X0),X9,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
fof(f15372,plain,
spl0_849,
inference(avatar_split_clause,[],[f215,f15370]) ).
fof(f15370,plain,
( spl0_849
<=> ! [X2,X16,X3,X0,X9,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(X2,X3,X0),X16,X0),X1,X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f215,axiom,
! [X2,X3,X0,X1,X9,X16] :
( ~ 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(X2,X3,X0),X16,X0),X1,X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
fof(f15368,plain,
spl0_848,
inference(avatar_split_clause,[],[f214,f15366]) ).
fof(f15366,plain,
( spl0_848
<=> ! [X2,X16,X3,X0,X9,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(X2,X3,X0),X16,X0),X1,X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f214,axiom,
! [X2,X3,X0,X1,X9,X16] :
( ~ 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(X2,X3,X0),X16,X0),X1,X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
fof(f15364,plain,
spl0_847,
inference(avatar_split_clause,[],[f213,f15362]) ).
fof(f15362,plain,
( spl0_847
<=> ! [X16,X3,X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X2,X0),X16,X0),X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f213,axiom,
! [X2,X3,X0,X1,X9,X16] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X2,X0),X16,X0),X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
fof(f15360,plain,
spl0_846,
inference(avatar_split_clause,[],[f212,f15358]) ).
fof(f15358,plain,
( spl0_846
<=> ! [X16,X3,X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X2,X0),X16,X0),X9,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f212,axiom,
! [X2,X3,X0,X1,X9,X16] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X2,X0),X16,X0),X9,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
fof(f15356,plain,
spl0_845,
inference(avatar_split_clause,[],[f59,f15354]) ).
fof(f15354,plain,
( spl0_845
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Oinverse__class_Odivide(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f59,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Oinverse__class_Odivide(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).
fof(f15295,plain,
( spl0_844
| ~ spl0_286
| ~ spl0_842 ),
inference(avatar_split_clause,[],[f14752,f14388,f2753,f15293]) ).
fof(f2753,plain,
( spl0_286
<=> ! [X6] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f14388,plain,
( spl0_842
<=> ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f14752,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_286
| ~ spl0_842 ),
inference(resolution,[],[f14389,f2754]) ).
fof(f2754,plain,
( ! [X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal) )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f2753]) ).
fof(f14389,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_842 ),
inference(avatar_component_clause,[],[f14388]) ).
fof(f14394,plain,
( spl0_843
| ~ spl0_93
| ~ spl0_102
| ~ spl0_275
| ~ spl0_520
| ~ spl0_810
| ~ spl0_841 ),
inference(avatar_split_clause,[],[f14386,f14381,f13943,f6206,f2708,f1636,f1591,f14392]) ).
fof(f14392,plain,
( spl0_843
<=> ! [X24] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(X24,tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ c_Parity_Oeven__odd__class_Oeven(X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f1591,plain,
( spl0_93
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f6206,plain,
( spl0_520
<=> ! [X2,X0,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X12,X0) = c_HOL_Oplus__class_Oplus(X12,c_HOL_Otimes__class_Otimes(X2,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f14381,plain,
( spl0_841
<=> ! [X24] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X24,tc_nat),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ c_Parity_Oeven__odd__class_Oeven(X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f14386,plain,
( ! [X24] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(X24,tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ c_Parity_Oeven__odd__class_Oeven(X24,tc_nat) )
| ~ spl0_93
| ~ spl0_102
| ~ spl0_275
| ~ spl0_520
| ~ spl0_810
| ~ spl0_841 ),
inference(forward_demodulation,[],[f14385,f2861]) ).
fof(f14385,plain,
( ! [X24] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X24,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ c_Parity_Oeven__odd__class_Oeven(X24,tc_nat) )
| ~ spl0_93
| ~ spl0_520
| ~ spl0_810
| ~ spl0_841 ),
inference(forward_demodulation,[],[f14384,f6321]) ).
fof(f6321,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_93
| ~ spl0_520 ),
inference(resolution,[],[f6207,f1593]) ).
fof(f1593,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1591]) ).
fof(f6207,plain,
( ! [X2,X0,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X12,X0) = c_HOL_Oplus__class_Oplus(X12,c_HOL_Otimes__class_Otimes(X2,X12,X0),X0) )
| ~ spl0_520 ),
inference(avatar_component_clause,[],[f6206]) ).
fof(f14384,plain,
( ! [X24] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X24,tc_nat),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ c_Parity_Oeven__odd__class_Oeven(X24,tc_nat) )
| ~ spl0_810
| ~ spl0_841 ),
inference(forward_demodulation,[],[f14382,f13944]) ).
fof(f14382,plain,
( ! [X24] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X24,tc_nat),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ c_Parity_Oeven__odd__class_Oeven(X24,tc_nat) )
| ~ spl0_841 ),
inference(avatar_component_clause,[],[f14381]) ).
fof(f14390,plain,
( spl0_842
| ~ spl0_174
| ~ spl0_411
| ~ spl0_489 ),
inference(avatar_split_clause,[],[f5755,f5556,f4007,f1985,f14388]) ).
fof(f1985,plain,
( spl0_174
<=> ! [X8] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X8,tc_RealDef_Oreal) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f4007,plain,
( spl0_411
<=> ! [X6,X4] : c_lessequals(X4,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f5556,plain,
( spl0_489
<=> ! [X0] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f5755,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_174
| ~ spl0_411
| ~ spl0_489 ),
inference(forward_demodulation,[],[f5746,f1986]) ).
fof(f1986,plain,
( ! [X8] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X8,tc_RealDef_Oreal) = X8
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f1985]) ).
fof(f5746,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_411
| ~ spl0_489 ),
inference(resolution,[],[f5557,f4008]) ).
fof(f4008,plain,
( ! [X6,X4] : c_lessequals(X4,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_411 ),
inference(avatar_component_clause,[],[f4007]) ).
fof(f5557,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_489 ),
inference(avatar_component_clause,[],[f5556]) ).
fof(f14383,plain,
spl0_841,
inference(avatar_split_clause,[],[f1119,f14381]) ).
fof(f1119,plain,
! [X24] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X24,tc_nat),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ c_Parity_Oeven__odd__class_Oeven(X24,tc_nat) ),
inference(forward_demodulation,[],[f1118,f1058]) ).
fof(f1058,plain,
! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f564,f786]) ).
fof(f564,axiom,
! [X4] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X4),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__sin__cos__eq_0) ).
fof(f1118,plain,
! [X24] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X24,tc_nat),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ c_Parity_Oeven__odd__class_Oeven(X24,tc_nat) ),
inference(forward_demodulation,[],[f1073,f1041]) ).
fof(f1041,plain,
! [X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f679,f786,f786]) ).
fof(f679,axiom,
! [X4] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X4),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__minus_0) ).
fof(f1073,plain,
! [X24] :
( ~ c_Parity_Oeven__odd__class_Oeven(X24,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X24,tc_nat),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
inference(definition_unfolding,[],[f577,f786]) ).
fof(f577,axiom,
! [X24] :
( ~ c_Parity_Oeven__odd__class_Oeven(X24,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X24,tc_nat),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__zero__iff_5) ).
fof(f14379,plain,
spl0_840,
inference(avatar_split_clause,[],[f1109,f14376]) ).
fof(f14376,plain,
( spl0_840
<=> c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f14374,plain,
spl0_839,
inference(avatar_split_clause,[],[f1072,f14372]) ).
fof(f14372,plain,
( spl0_839
<=> ! [X30] :
( ~ c_Parity_Oeven__odd__class_Oeven(X30,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X30,tc_nat),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f1072,plain,
! [X30] :
( ~ c_Parity_Oeven__odd__class_Oeven(X30,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X30,tc_nat),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
inference(definition_unfolding,[],[f708,f786]) ).
fof(f708,axiom,
! [X30] :
( ~ c_Parity_Oeven__odd__class_Oeven(X30,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X30,tc_nat),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__zero__iff_4) ).
fof(f14339,plain,
( spl0_838
| ~ spl0_780
| ~ spl0_837 ),
inference(avatar_split_clause,[],[f14335,f14332,f12907,f14337]) ).
fof(f14337,plain,
( spl0_838
<=> ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f14332,plain,
( spl0_837
<=> ! [X4] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f14335,plain,
( ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_780
| ~ spl0_837 ),
inference(forward_demodulation,[],[f14333,f12908]) ).
fof(f14333,plain,
( ! [X4] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_837 ),
inference(avatar_component_clause,[],[f14332]) ).
fof(f14334,plain,
spl0_837,
inference(avatar_split_clause,[],[f1047,f14332]) ).
fof(f1047,plain,
! [X4] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f520,f786,f786]) ).
fof(f520,axiom,
! [X4] : c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(X4,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X4),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__periodic__pi__diff_0) ).
fof(f14311,plain,
( spl0_836
| ~ spl0_780
| ~ spl0_835 ),
inference(avatar_split_clause,[],[f14307,f14304,f12907,f14309]) ).
fof(f14309,plain,
( spl0_836
<=> ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,X4,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f14304,plain,
( spl0_835
<=> ! [X4] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,X4,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f14307,plain,
( ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,X4,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_780
| ~ spl0_835 ),
inference(forward_demodulation,[],[f14305,f12908]) ).
fof(f14305,plain,
( ! [X4] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,X4,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_835 ),
inference(avatar_component_clause,[],[f14304]) ).
fof(f14306,plain,
spl0_835,
inference(avatar_split_clause,[],[f1046,f14304]) ).
fof(f1046,plain,
! [X4] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,X4,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f677,f786,f786]) ).
fof(f677,axiom,
! [X4] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X4),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,X4,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__periodic__pi2_0) ).
fof(f14271,plain,
( spl0_834
| ~ spl0_780
| ~ spl0_833 ),
inference(avatar_split_clause,[],[f14267,f14264,f12907,f14269]) ).
fof(f14264,plain,
( spl0_833
<=> ! [X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f14267,plain,
( ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_780
| ~ spl0_833 ),
inference(forward_demodulation,[],[f14265,f12908]) ).
fof(f14265,plain,
( ! [X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_833 ),
inference(avatar_component_clause,[],[f14264]) ).
fof(f14266,plain,
spl0_833,
inference(avatar_split_clause,[],[f1045,f14264]) ).
fof(f1045,plain,
! [X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f678,f786,f786]) ).
fof(f678,axiom,
! [X4] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X4),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__periodic__pi_0) ).
fof(f14262,plain,
spl0_832,
inference(avatar_split_clause,[],[f663,f14260]) ).
fof(f14260,plain,
( spl0_832
<=> ! [X4,X0,X6,X8,X7] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,X6,X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,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),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X8,X0),c_HOL_Oinverse__class_Odivide(X6,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f663,axiom,
! [X0,X8,X6,X7,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,X6,X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,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),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X8,X0),c_HOL_Oinverse__class_Odivide(X6,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__less2_0) ).
fof(f14258,plain,
spl0_831,
inference(avatar_split_clause,[],[f660,f14256]) ).
fof(f14256,plain,
( spl0_831
<=> ! [X4,X0,X6,X8,X7] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X7,X8,X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X8,X0),c_HOL_Oinverse__class_Odivide(X6,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f660,axiom,
! [X0,X8,X6,X7,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X7,X8,X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X8,X0),c_HOL_Oinverse__class_Odivide(X6,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__less_0) ).
fof(f14254,plain,
spl0_830,
inference(avatar_split_clause,[],[f657,f14252]) ).
fof(f14252,plain,
( spl0_830
<=> ! [X4,X0,X6,X8,X7] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X7,X8,X0)
| ~ c_lessequals(X4,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X8,X0),c_HOL_Oinverse__class_Odivide(X6,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f657,axiom,
! [X0,X8,X6,X7,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X7,X8,X0)
| ~ c_lessequals(X4,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X7,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X8,X0),c_HOL_Oinverse__class_Odivide(X6,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__le_0) ).
fof(f14250,plain,
spl0_829,
inference(avatar_split_clause,[],[f621,f14248]) ).
fof(f14248,plain,
( spl0_829
<=> ! [X3,X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f621,axiom,
! [X2,X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
fof(f14246,plain,
spl0_828,
inference(avatar_split_clause,[],[f613,f14244]) ).
fof(f14244,plain,
( spl0_828
<=> ! [X3,X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f613,axiom,
! [X2,X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
fof(f14242,plain,
spl0_827,
inference(avatar_split_clause,[],[f611,f14240]) ).
fof(f14240,plain,
( spl0_827
<=> ! [X3,X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,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_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f611,axiom,
! [X2,X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,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_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
fof(f14238,plain,
spl0_826,
inference(avatar_split_clause,[],[f610,f14236]) ).
fof(f14236,plain,
( spl0_826
<=> ! [X2,X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,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_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f610,axiom,
! [X2,X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,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_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
fof(f14234,plain,
spl0_825,
inference(avatar_split_clause,[],[f562,f14232]) ).
fof(f14232,plain,
( spl0_825
<=> ! [X4] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(X4),tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f562,axiom,
! [X4] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(X4),tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__ge__zero_0) ).
fof(f14212,plain,
spl0_824,
inference(avatar_split_clause,[],[f561,f14210]) ).
fof(f14210,plain,
( spl0_824
<=> ! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f561,axiom,
! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__gt__zero__pi_0) ).
fof(f14208,plain,
spl0_823,
inference(avatar_split_clause,[],[f377,f14206]) ).
fof(f14206,plain,
( spl0_823
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f377,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).
fof(f14204,plain,
spl0_822,
inference(avatar_split_clause,[],[f376,f14202]) ).
fof(f14202,plain,
( spl0_822
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f376,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).
fof(f14200,plain,
spl0_821,
inference(avatar_split_clause,[],[f375,f14198]) ).
fof(f14198,plain,
( spl0_821
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f375,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).
fof(f14196,plain,
spl0_820,
inference(avatar_split_clause,[],[f374,f14194]) ).
fof(f14194,plain,
( spl0_820
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f374,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).
fof(f14192,plain,
spl0_819,
inference(avatar_split_clause,[],[f367,f14190]) ).
fof(f14190,plain,
( spl0_819
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f367,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).
fof(f14188,plain,
spl0_818,
inference(avatar_split_clause,[],[f366,f14186]) ).
fof(f14186,plain,
( spl0_818
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f366,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).
fof(f14184,plain,
spl0_817,
inference(avatar_split_clause,[],[f96,f14182]) ).
fof(f14182,plain,
( spl0_817
<=> ! [X3,X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f96,axiom,
! [X2,X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
fof(f14180,plain,
spl0_816,
inference(avatar_split_clause,[],[f95,f14178]) ).
fof(f14178,plain,
( spl0_816
<=> ! [X3,X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f95,axiom,
! [X2,X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).
fof(f14176,plain,
spl0_815,
inference(avatar_split_clause,[],[f52,f14174]) ).
fof(f14174,plain,
( spl0_815
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f52,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).
fof(f14172,plain,
( spl0_814
| ~ spl0_336
| ~ spl0_778 ),
inference(avatar_split_clause,[],[f13450,f12430,f3256,f14170]) ).
fof(f14170,plain,
( spl0_814
<=> ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f3256,plain,
( spl0_336
<=> ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f12430,plain,
( spl0_778
<=> ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f13450,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_336
| ~ spl0_778 ),
inference(resolution,[],[f12431,f3257]) ).
fof(f3257,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_336 ),
inference(avatar_component_clause,[],[f3256]) ).
fof(f12431,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_778 ),
inference(avatar_component_clause,[],[f12430]) ).
fof(f14168,plain,
spl0_813,
inference(avatar_split_clause,[],[f51,f14166]) ).
fof(f14166,plain,
( spl0_813
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f51,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).
fof(f13973,plain,
spl0_812,
inference(avatar_split_clause,[],[f1095,f13971]) ).
fof(f13971,plain,
( spl0_812
<=> ! [X5] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f1095,plain,
! [X5] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1042,f868]) ).
fof(f1042,plain,
! [X5] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X5,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X5,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f565,f1030]) ).
fof(f565,axiom,
! [X5] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Otan(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X5,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__npi_0) ).
fof(f13969,plain,
spl0_811,
inference(avatar_split_clause,[],[f1080,f13967]) ).
fof(f13967,plain,
( spl0_811
<=> ! [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_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f1080,plain,
! [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_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f682,f786]) ).
fof(f682,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_Transcendental_Osin(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__gt__zero_0) ).
fof(f13945,plain,
( spl0_810
| ~ spl0_112
| ~ spl0_361
| ~ spl0_780
| ~ spl0_808 ),
inference(avatar_split_clause,[],[f13937,f13933,f12907,f3436,f1686,f13943]) ).
fof(f13933,plain,
( spl0_808
<=> ! [X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f13937,plain,
( ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal))
| ~ spl0_112
| ~ spl0_361
| ~ spl0_780
| ~ spl0_808 ),
inference(forward_demodulation,[],[f13936,f3797]) ).
fof(f13936,plain,
( ! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_780
| ~ spl0_808 ),
inference(forward_demodulation,[],[f13934,f12908]) ).
fof(f13934,plain,
( ! [X4] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_808 ),
inference(avatar_component_clause,[],[f13933]) ).
fof(f13941,plain,
( spl0_809
| ~ spl0_428
| ~ spl0_778 ),
inference(avatar_split_clause,[],[f13449,f12430,f4828,f13939]) ).
fof(f13939,plain,
( spl0_809
<=> ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f4828,plain,
( spl0_428
<=> ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f13449,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_428
| ~ spl0_778 ),
inference(resolution,[],[f12431,f4829]) ).
fof(f4829,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_428 ),
inference(avatar_component_clause,[],[f4828]) ).
fof(f13935,plain,
spl0_808,
inference(avatar_split_clause,[],[f1041,f13933]) ).
fof(f13931,plain,
spl0_807,
inference(avatar_split_clause,[],[f490,f13929]) ).
fof(f13929,plain,
( spl0_807
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,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_Otimes__class_Otimes(X2,X3,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Oinverse__class_Odivide(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f490,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,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_Otimes__class_Otimes(X2,X3,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Oinverse__class_Odivide(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).
fof(f13927,plain,
spl0_806,
inference(avatar_split_clause,[],[f489,f13925]) ).
fof(f13925,plain,
( spl0_806
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X3,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_Otimes__class_Otimes(X2,X3,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Oinverse__class_Odivide(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f489,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X3,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_Otimes__class_Otimes(X2,X3,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Oinverse__class_Odivide(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).
fof(f13923,plain,
spl0_805,
inference(avatar_split_clause,[],[f300,f13921]) ).
fof(f13921,plain,
( spl0_805
<=> ! [X2,X16,X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X2,X0),X16,X0),X9,X0) = X1
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f300,axiom,
! [X2,X3,X0,X1,X9,X16] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X2,X0),X16,X0),X9,X0) = X1
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),X1,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
fof(f13919,plain,
spl0_804,
inference(avatar_split_clause,[],[f60,f13917]) ).
fof(f13917,plain,
( spl0_804
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Oinverse__class_Odivide(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f60,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Oinverse__class_Odivide(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).
fof(f13125,plain,
spl0_803,
inference(avatar_split_clause,[],[f789,f13123]) ).
fof(f13123,plain,
( spl0_803
<=> ! [X4,X0,X6,X8,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Oinverse__class_Odivide(X4,X6,X0) != c_HOL_Oinverse__class_Odivide(X7,X8,X0)
| c_HOL_Otimes__class_Otimes(X4,X8,X0) = c_HOL_Otimes__class_Otimes(X7,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f789,axiom,
! [X0,X8,X6,X7,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Oinverse__class_Odivide(X4,X6,X0) != c_HOL_Oinverse__class_Odivide(X7,X8,X0)
| c_HOL_Otimes__class_Otimes(X4,X8,X0) = c_HOL_Otimes__class_Otimes(X7,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
fof(f13121,plain,
spl0_802,
inference(avatar_split_clause,[],[f788,f13119]) ).
fof(f13119,plain,
( spl0_802
<=> ! [X4,X0,X6,X8,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Otimes__class_Otimes(X4,X8,X0) != c_HOL_Otimes__class_Otimes(X7,X6,X0)
| c_HOL_Oinverse__class_Odivide(X4,X6,X0) = c_HOL_Oinverse__class_Odivide(X7,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f788,axiom,
! [X0,X8,X6,X7,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X8
| c_HOL_Otimes__class_Otimes(X4,X8,X0) != c_HOL_Otimes__class_Otimes(X7,X6,X0)
| c_HOL_Oinverse__class_Odivide(X4,X6,X0) = c_HOL_Oinverse__class_Odivide(X7,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
fof(f13117,plain,
spl0_801,
inference(avatar_split_clause,[],[f738,f13115]) ).
fof(f13115,plain,
( spl0_801
<=> ! [X11,X0,X3,X2] :
( ~ class_Ring__and__Field_Oring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_Int_Onumber__class_Onumber__of(X11,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X11,X0),X0),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X11,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f738,axiom,
! [X2,X3,X0,X11] :
( ~ class_Ring__and__Field_Oring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_Int_Onumber__class_Onumber__of(X11,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X11,X0),X0),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X11,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).
fof(f13096,plain,
spl0_800,
inference(avatar_split_clause,[],[f737,f13094]) ).
fof(f13094,plain,
( spl0_800
<=> ! [X11,X0,X3,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X11,X0),c_HOL_Ominus__class_Ominus(X3,X1,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X11,X0),X3,X0),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X11,X0),X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f737,axiom,
! [X3,X0,X11,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X11,X0),c_HOL_Ominus__class_Ominus(X3,X1,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X11,X0),X3,X0),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X11,X0),X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).
fof(f13092,plain,
spl0_799,
inference(avatar_split_clause,[],[f487,f13090]) ).
fof(f13090,plain,
( spl0_799
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f487,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).
fof(f13088,plain,
spl0_798,
inference(avatar_split_clause,[],[f486,f13086]) ).
fof(f13086,plain,
( spl0_798
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f486,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).
fof(f13084,plain,
spl0_797,
inference(avatar_split_clause,[],[f485,f13082]) ).
fof(f13082,plain,
( spl0_797
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f485,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).
fof(f13080,plain,
spl0_796,
inference(avatar_split_clause,[],[f484,f13078]) ).
fof(f13078,plain,
( spl0_796
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f484,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).
fof(f13076,plain,
spl0_795,
inference(avatar_split_clause,[],[f483,f13074]) ).
fof(f13074,plain,
( spl0_795
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f483,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).
fof(f13072,plain,
spl0_794,
inference(avatar_split_clause,[],[f482,f13070]) ).
fof(f13070,plain,
( spl0_794
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f482,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).
fof(f13068,plain,
spl0_793,
inference(avatar_split_clause,[],[f481,f13066]) ).
fof(f13066,plain,
( spl0_793
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f481,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).
fof(f13064,plain,
spl0_792,
inference(avatar_split_clause,[],[f480,f13062]) ).
fof(f13062,plain,
( spl0_792
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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(X3,X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f480,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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(X3,X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).
fof(f13060,plain,
spl0_791,
inference(avatar_split_clause,[],[f117,f13058]) ).
fof(f13058,plain,
( spl0_791
<=> ! [X11,X0,X3,X2] :
( ~ class_Ring__and__Field_Osemiring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_Int_Onumber__class_Onumber__of(X11,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X11,X0),X0),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X11,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f117,axiom,
! [X2,X3,X0,X11] :
( ~ class_Ring__and__Field_Osemiring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_Int_Onumber__class_Onumber__of(X11,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X11,X0),X0),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X11,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__distrib__number__of_0) ).
fof(f13038,plain,
spl0_790,
inference(avatar_split_clause,[],[f116,f13036]) ).
fof(f13036,plain,
( spl0_790
<=> ! [X11,X0,X3,X1] :
( ~ class_Ring__and__Field_Osemiring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X11,X0),c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X11,X0),X3,X0),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X11,X0),X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f116,axiom,
! [X3,X0,X11,X1] :
( ~ class_Ring__and__Field_Osemiring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X11,X0),c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X11,X0),X3,X0),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X11,X0),X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__distrib__number__of_0) ).
fof(f13034,plain,
spl0_789,
inference(avatar_split_clause,[],[f50,f13032]) ).
fof(f13032,plain,
( spl0_789
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f50,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).
fof(f13030,plain,
spl0_788,
inference(avatar_split_clause,[],[f49,f13028]) ).
fof(f13028,plain,
( spl0_788
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f49,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).
fof(f13026,plain,
spl0_787,
inference(avatar_split_clause,[],[f48,f13024]) ).
fof(f13024,plain,
( spl0_787
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f48,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).
fof(f13022,plain,
spl0_786,
inference(avatar_split_clause,[],[f47,f13020]) ).
fof(f13020,plain,
( spl0_786
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f47,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).
fof(f13018,plain,
spl0_785,
inference(avatar_split_clause,[],[f46,f13016]) ).
fof(f13016,plain,
( spl0_785
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f46,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).
fof(f13014,plain,
spl0_784,
inference(avatar_split_clause,[],[f45,f13012]) ).
fof(f13012,plain,
( spl0_784
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f45,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).
fof(f13010,plain,
spl0_783,
inference(avatar_split_clause,[],[f44,f13008]) ).
fof(f13008,plain,
( spl0_783
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f44,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).
fof(f13006,plain,
spl0_782,
inference(avatar_split_clause,[],[f43,f13004]) ).
fof(f13004,plain,
( spl0_782
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f43,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).
fof(f12913,plain,
spl0_781,
inference(avatar_split_clause,[],[f1106,f12911]) ).
fof(f12911,plain,
( spl0_781
<=> ! [X5] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f1106,plain,
! [X5] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f1057,f868]) ).
fof(f1057,plain,
! [X5] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f784,f786]) ).
fof(f784,axiom,
! [X5] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__2npi_0) ).
fof(f12909,plain,
spl0_780,
inference(avatar_split_clause,[],[f1058,f12907]) ).
fof(f12708,plain,
( spl0_779
| ~ spl0_192
| ~ spl0_730 ),
inference(avatar_split_clause,[],[f12032,f11046,f2079,f12706]) ).
fof(f12706,plain,
( spl0_779
<=> ! [X0,X1] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f2079,plain,
( spl0_192
<=> ! [X6,X8] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X6,X8,tc_RealDef_Oreal),X8,tc_RealDef_Oreal) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f11046,plain,
( spl0_730
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f12032,plain,
( ! [X0,X1] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_192
| ~ spl0_730 ),
inference(superposition,[],[f11047,f2080]) ).
fof(f2080,plain,
( ! [X8,X6] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X6,X8,tc_RealDef_Oreal),X8,tc_RealDef_Oreal) = X6
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f2079]) ).
fof(f11047,plain,
( ! [X0,X1] :
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_730 ),
inference(avatar_component_clause,[],[f11046]) ).
fof(f12432,plain,
( spl0_778
| ~ spl0_412
| ~ spl0_730 ),
inference(avatar_split_clause,[],[f12019,f11046,f4011,f12430]) ).
fof(f4011,plain,
( spl0_412
<=> ! [X6,X4] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f12019,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_412
| ~ spl0_730 ),
inference(resolution,[],[f11047,f4012]) ).
fof(f4012,plain,
( ! [X6,X4] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X6,tc_RealDef_Oreal) )
| ~ spl0_412 ),
inference(avatar_component_clause,[],[f4011]) ).
fof(f12399,plain,
spl0_777,
inference(avatar_split_clause,[],[f831,f12397]) ).
fof(f12397,plain,
( spl0_777
<=> ! [X0,X3,X1,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Int_Onumber__class_Onumber__of(X7,X0) != c_HOL_Oinverse__class_Odivide(X3,X1,X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X7,X0),X1,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f831,axiom,
! [X3,X0,X1,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Int_Onumber__class_Onumber__of(X7,X0) != c_HOL_Oinverse__class_Odivide(X3,X1,X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X7,X0),X1,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_0) ).
fof(f12395,plain,
spl0_776,
inference(avatar_split_clause,[],[f794,f12393]) ).
fof(f12393,plain,
( spl0_776
<=> ! [X6,X4,X8] :
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) != c_HOL_Oinverse__class_Odivide(X6,X8,tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Odivide(X6,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X8,tc_RealDef_Oreal),tc_RealDef_Oreal) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f794,axiom,
! [X8,X6,X4] :
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal) != c_HOL_Oinverse__class_Odivide(X6,X8,tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Odivide(X6,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X8,tc_RealDef_Oreal),tc_RealDef_Oreal) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__2__times__iff_1) ).
fof(f12391,plain,
spl0_775,
inference(avatar_split_clause,[],[f699,f12389]) ).
fof(f12389,plain,
( spl0_775
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f699,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__double__less__one_0) ).
fof(f12387,plain,
spl0_774,
inference(avatar_split_clause,[],[f689,f12385]) ).
fof(f689,axiom,
! [X2,X3] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,X2,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X2,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__average__minus__second_0) ).
fof(f12383,plain,
spl0_773,
inference(avatar_split_clause,[],[f688,f12381]) ).
fof(f12381,plain,
( spl0_773
<=> ! [X2,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f688,axiom,
! [X2,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X3,X2,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__average__minus__first_0) ).
fof(f12379,plain,
spl0_772,
inference(avatar_split_clause,[],[f667,f12377]) ).
fof(f12377,plain,
( spl0_772
<=> ! [X2,X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_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_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f667,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_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_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).
fof(f12375,plain,
spl0_771,
inference(avatar_split_clause,[],[f666,f12373]) ).
fof(f12373,plain,
( spl0_771
<=> ! [X2,X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_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_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f666,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_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_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).
fof(f12371,plain,
spl0_770,
inference(avatar_split_clause,[],[f665,f12369]) ).
fof(f12369,plain,
( spl0_770
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_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_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f665,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_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_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
fof(f12367,plain,
spl0_769,
inference(avatar_split_clause,[],[f664,f12365]) ).
fof(f12365,plain,
( spl0_769
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_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_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f664,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_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_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
fof(f12363,plain,
( spl0_768
| ~ spl0_336
| ~ spl0_702 ),
inference(avatar_split_clause,[],[f11507,f10807,f3256,f12361]) ).
fof(f12361,plain,
( spl0_768
<=> ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f10807,plain,
( spl0_702
<=> ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f11507,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_336
| ~ spl0_702 ),
inference(resolution,[],[f10808,f3257]) ).
fof(f10808,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_702 ),
inference(avatar_component_clause,[],[f10807]) ).
fof(f12359,plain,
spl0_767,
inference(avatar_split_clause,[],[f656,f12357]) ).
fof(f12357,plain,
( spl0_767
<=> ! [X2,X3,X0,X16,X1] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X1,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X0),X16,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f656,axiom,
! [X2,X3,X0,X1,X16] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X1,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X0),X16,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
fof(f12355,plain,
spl0_766,
inference(avatar_split_clause,[],[f379,f12353]) ).
fof(f12353,plain,
( spl0_766
<=> ! [X4,X0,X6,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X8,X6,X0),X0),X6,X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f379,axiom,
! [X0,X8,X6,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X8,X6,X0),X0),X6,X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
fof(f12351,plain,
spl0_765,
inference(avatar_split_clause,[],[f378,f12349]) ).
fof(f12349,plain,
( spl0_765
<=> ! [X4,X0,X6,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X6,X0),X8,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X8,X6,X0),X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f378,axiom,
! [X0,X8,X6,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X6,X0),X8,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X8,X6,X0),X0),X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
fof(f12347,plain,
spl0_764,
inference(avatar_split_clause,[],[f297,f12345]) ).
fof(f12345,plain,
( spl0_764
<=> ! [X16,X3,X0,X9,X2] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X2,X0),X16,X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f297,axiom,
! [X2,X3,X0,X9,X16] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X16,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X16,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X2,X0),X16,X0),X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
fof(f12343,plain,
spl0_763,
inference(avatar_split_clause,[],[f176,f12341]) ).
fof(f12341,plain,
( spl0_763
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f176,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
fof(f12339,plain,
spl0_762,
inference(avatar_split_clause,[],[f175,f12337]) ).
fof(f12337,plain,
( spl0_762
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f175,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
fof(f12335,plain,
spl0_761,
inference(avatar_split_clause,[],[f174,f12333]) ).
fof(f12333,plain,
( spl0_761
<=> ! [X2,X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,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(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f174,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,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(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
fof(f12331,plain,
spl0_760,
inference(avatar_split_clause,[],[f173,f12329]) ).
fof(f12329,plain,
( spl0_760
<=> ! [X2,X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f173,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
fof(f12327,plain,
spl0_759,
inference(avatar_split_clause,[],[f81,f12325]) ).
fof(f12325,plain,
( spl0_759
<=> ! [X10,X0,X4,X9,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X1 = X9
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X10,X1,X0),X0) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f81,axiom,
! [X10,X0,X1,X9,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X1 = X9
| c_HOL_Ozero__class_Ozero(X0) = X10
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X10,X1,X0),X0) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X10,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(f12308,plain,
( spl0_758
| ~ spl0_428
| ~ spl0_702 ),
inference(avatar_split_clause,[],[f11506,f10807,f4828,f12306]) ).
fof(f12306,plain,
( spl0_758
<=> ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f11506,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_428
| ~ spl0_702 ),
inference(resolution,[],[f10808,f4829]) ).
fof(f12201,plain,
spl0_757,
inference(avatar_split_clause,[],[f1076,f12199]) ).
fof(f12199,plain,
( spl0_757
<=> ! [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_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f1076,plain,
! [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_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f516,f786]) ).
fof(f516,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/sandbox/benchmark/theBenchmark.p',cls_sin__ge__zero_0) ).
fof(f12197,plain,
spl0_756,
inference(avatar_split_clause,[],[f1075,f12195]) ).
fof(f12195,plain,
( spl0_756
<=> ! [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_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f1075,plain,
! [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_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f517,f786]) ).
fof(f517,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/sandbox/benchmark/theBenchmark.p',cls_sin__gt__zero__pi_0) ).
fof(f12193,plain,
spl0_755,
inference(avatar_split_clause,[],[f1031,f12191]) ).
fof(f12189,plain,
spl0_754,
inference(avatar_split_clause,[],[f845,f12187]) ).
fof(f12187,plain,
( spl0_754
<=> ! [X4,X0,X6,X8,X7] :
( ~ 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,X6,X0),c_HOL_Oinverse__class_Odivide(X8,X7,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X8,X0),c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f845,axiom,
! [X0,X8,X6,X7,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,X6,X0),c_HOL_Oinverse__class_Odivide(X8,X7,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X8,X0),c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
fof(f12185,plain,
( spl0_753
| ~ spl0_394
| ~ spl0_700 ),
inference(avatar_split_clause,[],[f11270,f10516,f3932,f12183]) ).
fof(f12183,plain,
( spl0_753
<=> ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f10516,plain,
( spl0_700
<=> ! [X0,X1] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f11270,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_394
| ~ spl0_700 ),
inference(resolution,[],[f10517,f3933]) ).
fof(f10517,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_700 ),
inference(avatar_component_clause,[],[f10516]) ).
fof(f12181,plain,
spl0_752,
inference(avatar_split_clause,[],[f654,f12179]) ).
fof(f12179,plain,
( spl0_752
<=> ! [X4,X0,X6,X8] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X6,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X8,X0),c_HOL_Otimes__class_Otimes(X4,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f654,axiom,
! [X0,X8,X6,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X6,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X8,X0),c_HOL_Otimes__class_Otimes(X4,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
fof(f12177,plain,
spl0_751,
inference(avatar_split_clause,[],[f358,f12175]) ).
fof(f12175,plain,
( spl0_751
<=> ! [X6,X4] :
( ~ c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X6,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(X6,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f358,axiom,
! [X6,X4] :
( ~ c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X6,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(X6,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__add__half__cancel_1) ).
fof(f12173,plain,
spl0_750,
inference(avatar_split_clause,[],[f357,f12171]) ).
fof(f12171,plain,
( spl0_750
<=> ! [X6,X4] :
( c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X6,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(X6,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f357,axiom,
! [X6,X4] :
( c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X6,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oinverse__class_Odivide(X6,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__add__half__cancel_0) ).
fof(f12054,plain,
spl0_749,
inference(avatar_split_clause,[],[f714,f12051]) ).
fof(f714,axiom,
c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__30_0) ).
fof(f12049,plain,
spl0_748,
inference(avatar_split_clause,[],[f364,f12047]) ).
fof(f12047,plain,
( spl0_748
<=> ! [X6,X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X6,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),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X6,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f364,axiom,
! [X0,X6,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X6,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),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X6,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
fof(f12045,plain,
spl0_747,
inference(avatar_split_clause,[],[f363,f12043]) ).
fof(f12043,plain,
( spl0_747
<=> ! [X6,X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X6,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),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f363,axiom,
! [X0,X6,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X6,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),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X4,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
fof(f11592,plain,
spl0_746,
inference(avatar_split_clause,[],[f876,f11590]) ).
fof(f11590,plain,
( spl0_746
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f876,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
fof(f11588,plain,
spl0_745,
inference(avatar_split_clause,[],[f875,f11586]) ).
fof(f11586,plain,
( spl0_745
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f875,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
fof(f11584,plain,
spl0_744,
inference(avatar_split_clause,[],[f854,f11582]) ).
fof(f11582,plain,
( spl0_744
<=> ! [X37,X34,X0,X36,X35] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X37,X0),c_HOL_Otimes__class_Otimes(X35,X36,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X0),c_HOL_Otimes__class_Otimes(X37,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f854,axiom,
! [X0,X36,X37,X34,X35] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X37,X0),c_HOL_Otimes__class_Otimes(X35,X36,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X0),c_HOL_Otimes__class_Otimes(X37,X36,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f11580,plain,
spl0_743,
inference(avatar_split_clause,[],[f824,f11578]) ).
fof(f824,axiom,
! [X8,X6] : c_HOL_Oinverse__class_Odivide(X6,X8,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X6,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X8,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__2__times__iff_0) ).
fof(f11576,plain,
spl0_742,
inference(avatar_split_clause,[],[f579,f11574]) ).
fof(f11574,plain,
( spl0_742
<=> ! [X0,X10] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber__ring(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(X10,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f579,axiom,
! [X10,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber__ring(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(X10,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_half__gt__zero_0) ).
fof(f11561,plain,
spl0_741,
inference(avatar_split_clause,[],[f578,f11559]) ).
fof(f11559,plain,
( spl0_741
<=> ! [X0,X10] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber__ring(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(X10,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f578,axiom,
! [X10,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber__ring(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(X10,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_half__gt__zero__iff_0) ).
fof(f11557,plain,
spl0_740,
inference(avatar_split_clause,[],[f464,f11555]) ).
fof(f11555,plain,
( spl0_740
<=> ! [X2,X3,X0,X9,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ominus__class_Ominus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f464,axiom,
! [X2,X3,X0,X1,X9] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ominus__class_Ominus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
fof(f11553,plain,
spl0_739,
inference(avatar_split_clause,[],[f415,f11551]) ).
fof(f11551,plain,
( spl0_739
<=> ! [X6,X4,X0] :
( ~ 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),X6,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X4,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f415,axiom,
! [X0,X6,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),X6,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X4,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
fof(f11549,plain,
spl0_738,
inference(avatar_split_clause,[],[f414,f11547]) ).
fof(f11547,plain,
( spl0_738
<=> ! [X6,X4,X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X4,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f414,axiom,
! [X0,X6,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X4,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
fof(f11545,plain,
spl0_737,
inference(avatar_split_clause,[],[f370,f11543]) ).
fof(f11543,plain,
( spl0_737
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f370,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).
fof(f11541,plain,
spl0_736,
inference(avatar_split_clause,[],[f368,f11539]) ).
fof(f11539,plain,
( spl0_736
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f368,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).
fof(f11537,plain,
spl0_735,
inference(avatar_split_clause,[],[f256,f11535]) ).
fof(f11535,plain,
( spl0_735
<=> ! [X2,X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f256,axiom,
! [X2,X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f11533,plain,
spl0_734,
inference(avatar_split_clause,[],[f172,f11531]) ).
fof(f11531,plain,
( spl0_734
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),c_HOL_Oinverse__class_Odivide(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f172,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),c_HOL_Oinverse__class_Odivide(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
fof(f11529,plain,
spl0_733,
inference(avatar_split_clause,[],[f171,f11527]) ).
fof(f11527,plain,
( spl0_733
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f171,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
fof(f11525,plain,
spl0_732,
inference(avatar_split_clause,[],[f58,f11523]) ).
fof(f11523,plain,
( spl0_732
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f58,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X2,X0)
| c_lessequals(X3,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).
fof(f11499,plain,
spl0_731,
inference(avatar_split_clause,[],[f56,f11497]) ).
fof(f11497,plain,
( spl0_731
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f56,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(X2,c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).
fof(f11048,plain,
( spl0_730
| ~ spl0_177
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f10090,f9228,f1999,f11046]) ).
fof(f1999,plain,
( spl0_177
<=> ! [X7,X8] :
( c_lessequals(X8,X7,tc_RealDef_Oreal)
| c_lessequals(X7,X8,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f9228,plain,
( spl0_680
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f10090,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_177
| ~ spl0_680 ),
inference(resolution,[],[f9229,f2000]) ).
fof(f2000,plain,
( ! [X8,X7] :
( c_lessequals(X8,X7,tc_RealDef_Oreal)
| c_lessequals(X7,X8,tc_RealDef_Oreal) )
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f1999]) ).
fof(f9229,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_680 ),
inference(avatar_component_clause,[],[f9228]) ).
fof(f10924,plain,
( spl0_729
| ~ spl0_121
| ~ spl0_443
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f10919,f10915,f4976,f1731,f10921]) ).
fof(f10921,plain,
( spl0_729
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f10915,plain,
( spl0_728
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f10919,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_121
| ~ spl0_443
| ~ spl0_728 ),
inference(forward_demodulation,[],[f10917,f5250]) ).
fof(f10917,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_728 ),
inference(avatar_component_clause,[],[f10915]) ).
fof(f10918,plain,
spl0_728,
inference(avatar_split_clause,[],[f1098,f10915]) ).
fof(f1098,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f1049,f868]) ).
fof(f1049,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f715,f786]) ).
fof(f715,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__two__pi_0) ).
fof(f10910,plain,
spl0_727,
inference(avatar_split_clause,[],[f1048,f10907]) ).
fof(f10907,plain,
( spl0_727
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f1048,plain,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f709,f786]) ).
fof(f709,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__pi__half_0) ).
fof(f10905,plain,
spl0_726,
inference(avatar_split_clause,[],[f700,f10903]) ).
fof(f10903,plain,
( spl0_726
<=> ! [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_Transcendental_Ocos(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f700,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_Transcendental_Ocos(X4),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__gt__zero_0) ).
fof(f10901,plain,
spl0_725,
inference(avatar_split_clause,[],[f289,f10899]) ).
fof(f10899,plain,
( spl0_725
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f289,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
fof(f10897,plain,
( spl0_724
| ~ spl0_400
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f10088,f9228,f3956,f10895]) ).
fof(f10895,plain,
( spl0_724
<=> ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f3956,plain,
( spl0_400
<=> ! [X6,X4] :
( ~ c_lessequals(X6,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f10088,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_400
| ~ spl0_680 ),
inference(resolution,[],[f9229,f3957]) ).
fof(f3957,plain,
( ! [X6,X4] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X6,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_400 ),
inference(avatar_component_clause,[],[f3956]) ).
fof(f10893,plain,
spl0_723,
inference(avatar_split_clause,[],[f288,f10891]) ).
fof(f10891,plain,
( spl0_723
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f288,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).
fof(f10889,plain,
spl0_722,
inference(avatar_split_clause,[],[f287,f10887]) ).
fof(f10887,plain,
( spl0_722
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f287,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
fof(f10885,plain,
spl0_721,
inference(avatar_split_clause,[],[f286,f10883]) ).
fof(f10883,plain,
( spl0_721
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f286,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
fof(f10881,plain,
spl0_720,
inference(avatar_split_clause,[],[f285,f10879]) ).
fof(f10879,plain,
( spl0_720
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f285,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
fof(f10877,plain,
spl0_719,
inference(avatar_split_clause,[],[f284,f10875]) ).
fof(f10875,plain,
( spl0_719
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f284,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
fof(f10873,plain,
spl0_718,
inference(avatar_split_clause,[],[f170,f10871]) ).
fof(f10871,plain,
( spl0_718
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f170,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
fof(f10869,plain,
spl0_717,
inference(avatar_split_clause,[],[f169,f10867]) ).
fof(f10867,plain,
( spl0_717
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f169,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
fof(f10865,plain,
spl0_716,
inference(avatar_split_clause,[],[f168,f10863]) ).
fof(f10863,plain,
( spl0_716
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X3,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(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f168,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X3,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(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
fof(f10861,plain,
spl0_715,
inference(avatar_split_clause,[],[f167,f10859]) ).
fof(f10859,plain,
( spl0_715
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f167,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
fof(f10857,plain,
spl0_714,
inference(avatar_split_clause,[],[f166,f10855]) ).
fof(f10855,plain,
( spl0_714
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f166,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
fof(f10853,plain,
( spl0_713
| ~ spl0_192
| ~ spl0_669 ),
inference(avatar_split_clause,[],[f9738,f9184,f2079,f10851]) ).
fof(f10851,plain,
( spl0_713
<=> ! [X0,X1] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f9184,plain,
( spl0_669
<=> ! [X0,X1] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f9738,plain,
( ! [X0,X1] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_192
| ~ spl0_669 ),
inference(superposition,[],[f9185,f2080]) ).
fof(f9185,plain,
( ! [X0,X1] :
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_669 ),
inference(avatar_component_clause,[],[f9184]) ).
fof(f10849,plain,
spl0_712,
inference(avatar_split_clause,[],[f165,f10847]) ).
fof(f10847,plain,
( spl0_712
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f165,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
fof(f10845,plain,
spl0_711,
inference(avatar_split_clause,[],[f163,f10843]) ).
fof(f10843,plain,
( spl0_711
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f163,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
fof(f10841,plain,
spl0_710,
inference(avatar_split_clause,[],[f162,f10839]) ).
fof(f10839,plain,
( spl0_710
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f162,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
fof(f10837,plain,
spl0_709,
inference(avatar_split_clause,[],[f161,f10835]) ).
fof(f10835,plain,
( spl0_709
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X3,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(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f161,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X3,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(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
fof(f10833,plain,
spl0_708,
inference(avatar_split_clause,[],[f160,f10831]) ).
fof(f10831,plain,
( spl0_708
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f160,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
fof(f10829,plain,
spl0_707,
inference(avatar_split_clause,[],[f159,f10827]) ).
fof(f10827,plain,
( spl0_707
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f159,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
fof(f10825,plain,
spl0_706,
inference(avatar_split_clause,[],[f158,f10823]) ).
fof(f10823,plain,
( spl0_706
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X3,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_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f158,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X3,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_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
fof(f10821,plain,
spl0_705,
inference(avatar_split_clause,[],[f157,f10819]) ).
fof(f10819,plain,
( spl0_705
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f157,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
fof(f10817,plain,
spl0_704,
inference(avatar_split_clause,[],[f156,f10815]) ).
fof(f10815,plain,
( spl0_704
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f156,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(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(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
fof(f10813,plain,
spl0_703,
inference(avatar_split_clause,[],[f98,f10811]) ).
fof(f10811,plain,
( spl0_703
<=> ! [X2,X0,X1,X3] :
( ~ 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(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f98,axiom,
! [X2,X3,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(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
fof(f10809,plain,
( spl0_702
| ~ spl0_412
| ~ spl0_669 ),
inference(avatar_split_clause,[],[f9728,f9184,f4011,f10807]) ).
fof(f9728,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_412
| ~ spl0_669 ),
inference(resolution,[],[f9185,f4012]) ).
fof(f10805,plain,
spl0_701,
inference(avatar_split_clause,[],[f97,f10803]) ).
fof(f10803,plain,
( spl0_701
<=> ! [X0,X3,X2,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(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f97,axiom,
! [X2,X3,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(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
fof(f10518,plain,
( spl0_700
| ~ spl0_194
| ~ spl0_656 ),
inference(avatar_split_clause,[],[f9280,f9055,f2087,f10516]) ).
fof(f9055,plain,
( spl0_656
<=> ! [X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f9280,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_194
| ~ spl0_656 ),
inference(superposition,[],[f9056,f2088]) ).
fof(f9056,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal) )
| ~ spl0_656 ),
inference(avatar_component_clause,[],[f9055]) ).
fof(f9317,plain,
spl0_699,
inference(avatar_split_clause,[],[f860,f9315]) ).
fof(f9315,plain,
( spl0_699
<=> ! [X0,X7,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(X7,X0)
| c_Int_Onumber__class_Onumber__of(X7,X0) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f860,axiom,
! [X3,X0,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(X7,X0)
| c_Int_Onumber__class_Onumber__of(X7,X0) != c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_1) ).
fof(f9313,plain,
spl0_698,
inference(avatar_split_clause,[],[f627,f9311]) ).
fof(f9311,plain,
( spl0_698
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f627,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
fof(f9309,plain,
spl0_697,
inference(avatar_split_clause,[],[f626,f9307]) ).
fof(f9307,plain,
( spl0_697
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f626,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
fof(f9305,plain,
spl0_696,
inference(avatar_split_clause,[],[f625,f9303]) ).
fof(f9303,plain,
( spl0_696
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f625,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
fof(f9301,plain,
spl0_695,
inference(avatar_split_clause,[],[f624,f9299]) ).
fof(f9299,plain,
( spl0_695
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f624,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
fof(f9297,plain,
spl0_694,
inference(avatar_split_clause,[],[f623,f9295]) ).
fof(f9295,plain,
( spl0_694
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f623,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
fof(f9293,plain,
spl0_693,
inference(avatar_split_clause,[],[f622,f9291]) ).
fof(f9291,plain,
( spl0_693
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f622,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
fof(f9289,plain,
spl0_692,
inference(avatar_split_clause,[],[f619,f9287]) ).
fof(f9287,plain,
( spl0_692
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f619,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
fof(f9285,plain,
spl0_691,
inference(avatar_split_clause,[],[f618,f9283]) ).
fof(f9283,plain,
( spl0_691
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f618,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
fof(f9270,plain,
spl0_690,
inference(avatar_split_clause,[],[f617,f9268]) ).
fof(f9268,plain,
( spl0_690
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f617,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
fof(f9266,plain,
spl0_689,
inference(avatar_split_clause,[],[f616,f9264]) ).
fof(f9264,plain,
( spl0_689
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f616,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
fof(f9262,plain,
spl0_688,
inference(avatar_split_clause,[],[f514,f9260]) ).
fof(f9260,plain,
( spl0_688
<=> ! [X4] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f514,axiom,
! [X4] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__squared__diff__one__factored_0) ).
fof(f9258,plain,
spl0_687,
inference(avatar_split_clause,[],[f373,f9256]) ).
fof(f9256,plain,
( spl0_687
<=> ! [X4,X0,X6,X8] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X6,X0),X4,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f373,axiom,
! [X0,X8,X6,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X6,X0),X4,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
fof(f9254,plain,
spl0_686,
inference(avatar_split_clause,[],[f372,f9252]) ).
fof(f9252,plain,
( spl0_686
<=> ! [X4,X0,X6,X8] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X8,X6,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X6,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f372,axiom,
! [X0,X8,X6,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X8,X6,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X6,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).
fof(f9250,plain,
spl0_685,
inference(avatar_split_clause,[],[f283,f9248]) ).
fof(f9248,plain,
( spl0_685
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f283,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
fof(f9246,plain,
spl0_684,
inference(avatar_split_clause,[],[f282,f9244]) ).
fof(f9244,plain,
( spl0_684
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f282,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
fof(f9242,plain,
spl0_683,
inference(avatar_split_clause,[],[f258,f9240]) ).
fof(f9240,plain,
( spl0_683
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f258,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
fof(f9238,plain,
spl0_682,
inference(avatar_split_clause,[],[f257,f9236]) ).
fof(f9236,plain,
( spl0_682
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,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_682])]) ).
fof(f257,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
fof(f9234,plain,
spl0_681,
inference(avatar_split_clause,[],[f244,f9232]) ).
fof(f9232,plain,
( spl0_681
<=> ! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X6,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),X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f244,axiom,
! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X6,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),X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__monotone__minus__pi__0_0) ).
fof(f9230,plain,
( spl0_680
| ~ spl0_194
| ~ spl0_653 ),
inference(avatar_split_clause,[],[f7969,f7767,f2087,f9228]) ).
fof(f7767,plain,
( spl0_653
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f7969,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) )
| ~ spl0_194
| ~ spl0_653 ),
inference(superposition,[],[f7768,f2088]) ).
fof(f7768,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) )
| ~ spl0_653 ),
inference(avatar_component_clause,[],[f7767]) ).
fof(f9226,plain,
spl0_679,
inference(avatar_split_clause,[],[f111,f9224]) ).
fof(f9224,plain,
( spl0_679
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f111,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
fof(f9222,plain,
spl0_678,
inference(avatar_split_clause,[],[f110,f9220]) ).
fof(f9220,plain,
( spl0_678
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f110,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
fof(f9218,plain,
spl0_677,
inference(avatar_split_clause,[],[f109,f9216]) ).
fof(f9216,plain,
( spl0_677
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f109,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
fof(f9214,plain,
spl0_676,
inference(avatar_split_clause,[],[f108,f9212]) ).
fof(f9212,plain,
( spl0_676
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X2,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_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f108,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X2,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_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
fof(f9210,plain,
spl0_675,
inference(avatar_split_clause,[],[f80,f9208]) ).
fof(f9208,plain,
( spl0_675
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f80,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
fof(f9206,plain,
spl0_674,
inference(avatar_split_clause,[],[f54,f9204]) ).
fof(f9204,plain,
( spl0_674
<=> ! [X4,X0,X6,X8] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X8,X6,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X6,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f54,axiom,
! [X0,X8,X6,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_lessequals(X4,c_HOL_Otimes__class_Otimes(X8,X6,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X6,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).
fof(f9202,plain,
spl0_673,
inference(avatar_split_clause,[],[f53,f9200]) ).
fof(f9200,plain,
( spl0_673
<=> ! [X4,X0,X6,X8] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X6,X0),X4,X0)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f53,axiom,
! [X0,X8,X6,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X6,X0),X4,X0)
| c_lessequals(X8,c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).
fof(f9198,plain,
spl0_672,
inference(avatar_split_clause,[],[f31,f9196]) ).
fof(f9196,plain,
( spl0_672
<=> ! [X6,X4] :
( ~ c_lessequals(X6,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),X6,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f31,axiom,
! [X6,X4] :
( ~ c_lessequals(X6,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),X6,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__monotone__minus__pi__0_H_0) ).
fof(f9194,plain,
spl0_671,
inference(avatar_split_clause,[],[f28,f9192]) ).
fof(f9192,plain,
( spl0_671
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f28,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
fof(f9190,plain,
spl0_670,
inference(avatar_split_clause,[],[f26,f9188]) ).
fof(f9188,plain,
( spl0_670
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X3,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_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f26,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X3,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_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
fof(f9186,plain,
( spl0_669
| ~ spl0_177
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f7651,f4044,f1999,f9184]) ).
fof(f4044,plain,
( spl0_420
<=> ! [X0,X1] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f7651,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_177
| ~ spl0_420 ),
inference(resolution,[],[f4045,f2000]) ).
fof(f4045,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_420 ),
inference(avatar_component_clause,[],[f4044]) ).
fof(f9182,plain,
spl0_668,
inference(avatar_split_clause,[],[f24,f9180]) ).
fof(f9180,plain,
( spl0_668
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f24,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
fof(f9178,plain,
spl0_667,
inference(avatar_split_clause,[],[f23,f9176]) ).
fof(f9176,plain,
( spl0_667
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,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_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f23,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,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_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
fof(f9174,plain,
spl0_666,
inference(avatar_split_clause,[],[f22,f9172]) ).
fof(f9172,plain,
( spl0_666
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,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_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f22,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,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_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
fof(f9170,plain,
spl0_665,
inference(avatar_split_clause,[],[f19,f9168]) ).
fof(f9168,plain,
( spl0_665
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f19,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
fof(f9166,plain,
spl0_664,
inference(avatar_split_clause,[],[f18,f9164]) ).
fof(f9164,plain,
( spl0_664
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
fof(f9162,plain,
spl0_663,
inference(avatar_split_clause,[],[f17,f9160]) ).
fof(f9160,plain,
( spl0_663
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f17,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
fof(f9158,plain,
spl0_662,
inference(avatar_split_clause,[],[f16,f9156]) ).
fof(f9156,plain,
( spl0_662
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,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_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,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_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
fof(f9154,plain,
spl0_661,
inference(avatar_split_clause,[],[f4,f9152]) ).
fof(f9152,plain,
( spl0_661
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
fof(f9150,plain,
spl0_660,
inference(avatar_split_clause,[],[f3,f9148]) ).
fof(f9148,plain,
( spl0_660
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
fof(f9146,plain,
spl0_659,
inference(avatar_split_clause,[],[f2,f9144]) ).
fof(f9144,plain,
( spl0_659
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
fof(f9142,plain,
( spl0_658
| ~ spl0_400
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f7649,f4044,f3956,f9140]) ).
fof(f9140,plain,
( spl0_658
<=> ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f7649,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_400
| ~ spl0_420 ),
inference(resolution,[],[f4045,f3957]) ).
fof(f9138,plain,
spl0_657,
inference(avatar_split_clause,[],[f1,f9136]) ).
fof(f9136,plain,
( spl0_657
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
fof(f9057,plain,
( spl0_656
| ~ spl0_335
| ~ spl0_491 ),
inference(avatar_split_clause,[],[f5941,f5893,f3170,f9055]) ).
fof(f3170,plain,
( spl0_335
<=> ! [X18,X19] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X19,X18,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X18,X19,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f5893,plain,
( spl0_491
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f5941,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal) )
| ~ spl0_335
| ~ spl0_491 ),
inference(resolution,[],[f5894,f3171]) ).
fof(f3171,plain,
( ! [X18,X19] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X19,X18,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X18,X19,tc_RealDef_Oreal) )
| ~ spl0_335 ),
inference(avatar_component_clause,[],[f3170]) ).
fof(f5894,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_491 ),
inference(avatar_component_clause,[],[f5893]) ).
fof(f8719,plain,
( ~ spl0_117
| ~ spl0_655
| ~ spl0_240
| ~ spl0_452 ),
inference(avatar_split_clause,[],[f5187,f5012,f2359,f8716,f1711]) ).
fof(f1711,plain,
( spl0_117
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f8716,plain,
( spl0_655
<=> c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f2359,plain,
( spl0_240
<=> ! [X6,X4,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X6,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f5012,plain,
( spl0_452
<=> c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f5187,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl0_240
| ~ spl0_452 ),
inference(resolution,[],[f5014,f2360]) ).
fof(f2360,plain,
( ! [X0,X6,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| ~ c_lessequals(X6,X4,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_240 ),
inference(avatar_component_clause,[],[f2359]) ).
fof(f5014,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_452 ),
inference(avatar_component_clause,[],[f5012]) ).
fof(f8169,plain,
( ~ spl0_654
| ~ spl0_119
| ~ spl0_221
| ~ spl0_452 ),
inference(avatar_split_clause,[],[f5182,f5012,f2282,f1721,f8166]) ).
fof(f8166,plain,
( spl0_654
<=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f1721,plain,
( spl0_119
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f2282,plain,
( spl0_221
<=> ! [X2,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f5182,plain,
( ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_221
| ~ spl0_452 ),
inference(resolution,[],[f5014,f2283]) ).
fof(f2283,plain,
( ! [X2,X3,X0] :
( ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0) )
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f2282]) ).
fof(f7769,plain,
( spl0_653
| ~ spl0_318
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f4915,f4828,f3097,f7767]) ).
fof(f3097,plain,
( spl0_318
<=> ! [X6,X4] :
( ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f4915,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) )
| ~ spl0_318
| ~ spl0_428 ),
inference(resolution,[],[f4829,f3098]) ).
fof(f3098,plain,
( ! [X6,X4] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X4,X6,tc_RealDef_Oreal) )
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f3097]) ).
fof(f7685,plain,
spl0_652,
inference(avatar_split_clause,[],[f1093,f7682]) ).
fof(f7682,plain,
( spl0_652
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f1093,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1036,f776]) ).
fof(f776,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__zero_0) ).
fof(f1036,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f220,f1030]) ).
fof(f220,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Otan(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__zero_0) ).
fof(f7680,plain,
spl0_651,
inference(avatar_split_clause,[],[f1074,f7678]) ).
fof(f7678,plain,
( spl0_651
<=> ! [X4] :
( c_Transcendental_Ocos(X4) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f1074,plain,
! [X4] :
( c_Transcendental_Ocos(X4) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X4,tc_RealDef_Oreal)) ),
inference(definition_unfolding,[],[f740,f786]) ).
fof(f740,axiom,
! [X4] :
( c_Transcendental_Ocos(X4) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__one__sin__zero_0) ).
fof(f7676,plain,
spl0_650,
inference(avatar_split_clause,[],[f1043,f7674]) ).
fof(f7674,plain,
( spl0_650
<=> ! [X5] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f1043,plain,
! [X5] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f721,f786]) ).
fof(f721,axiom,
! [X5] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__npi2_0) ).
fof(f7672,plain,
spl0_649,
inference(avatar_split_clause,[],[f1035,f7670]) ).
fof(f7670,plain,
( spl0_649
<=> ! [X6] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Oarctan(X6),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_Transcendental_Oarctan(X6)),tc_RealDef_Oreal) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f1035,plain,
! [X6] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Oarctan(X6),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_Transcendental_Oarctan(X6)),tc_RealDef_Oreal) = X6,
inference(definition_unfolding,[],[f427,f1030]) ).
fof(f427,axiom,
! [X6] : c_Transcendental_Otan(c_Transcendental_Oarctan(X6)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan_2) ).
fof(f7668,plain,
spl0_648,
inference(avatar_split_clause,[],[f754,f7666]) ).
fof(f7666,plain,
( spl0_648
<=> ! [X24,X4,X0,X6] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X24,c_HOL_Ominus__class_Ominus(X4,X6,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X24,X4,X0),c_HOL_Otimes__class_Otimes(X24,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f754,axiom,
! [X0,X6,X4,X24] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X24,c_HOL_Ominus__class_Ominus(X4,X6,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X24,X4,X0),c_HOL_Otimes__class_Otimes(X24,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
fof(f7648,plain,
spl0_647,
inference(avatar_split_clause,[],[f752,f7646]) ).
fof(f7646,plain,
( spl0_647
<=> ! [X2,X0,X3,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X25,X0),X3,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Otimes__class_Otimes(X25,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f752,axiom,
! [X2,X3,X0,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X25,X0),X3,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Otimes__class_Otimes(X25,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
fof(f7644,plain,
spl0_646,
inference(avatar_split_clause,[],[f749,f7642]) ).
fof(f7642,plain,
( spl0_646
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X0),X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f749,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X3,X0),X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X2,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
fof(f7640,plain,
spl0_645,
inference(avatar_split_clause,[],[f748,f7638]) ).
fof(f748,axiom,
! [X0,X6,X26,X4] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X4,X6,X0),X26,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X26,X0),c_HOL_Oinverse__class_Odivide(X6,X26,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
fof(f7636,plain,
spl0_644,
inference(avatar_split_clause,[],[f719,f7634]) ).
fof(f7634,plain,
( spl0_644
<=> ! [X4] : c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f719,axiom,
! [X4] : c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__minus__half__eq_0) ).
fof(f7632,plain,
spl0_643,
inference(avatar_split_clause,[],[f706,f7630]) ).
fof(f7630,plain,
( spl0_643
<=> ! [X30] :
( c_Parity_Oeven__odd__class_Oeven(X30,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X30,tc_nat),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f706,axiom,
! [X30] :
( c_Parity_Oeven__odd__class_Oeven(X30,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X30,tc_nat),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__zero__iff_4) ).
fof(f7628,plain,
spl0_642,
inference(avatar_split_clause,[],[f673,f7626]) ).
fof(f7626,plain,
( spl0_642
<=> ! [X4,X0,X6,X26] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X6,X0),X26,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X26,X0),c_HOL_Oinverse__class_Odivide(X6,X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f673,axiom,
! [X0,X6,X26,X4] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X6,X0),X26,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X26,X0),c_HOL_Oinverse__class_Odivide(X6,X26,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
fof(f7624,plain,
spl0_641,
inference(avatar_split_clause,[],[f672,f7622]) ).
fof(f7622,plain,
( spl0_641
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,X0),X1,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X2,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f672,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X2,X3,X0),X1,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X2,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
fof(f7620,plain,
spl0_640,
inference(avatar_split_clause,[],[f662,f7618]) ).
fof(f7618,plain,
( spl0_640
<=> ! [X6,X4,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f662,axiom,
! [X0,X6,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).
fof(f7616,plain,
spl0_639,
inference(avatar_split_clause,[],[f661,f7614]) ).
fof(f7614,plain,
( spl0_639
<=> ! [X6,X4,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_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f661,axiom,
! [X0,X6,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),X6,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
fof(f7612,plain,
spl0_638,
inference(avatar_split_clause,[],[f659,f7610]) ).
fof(f7610,plain,
( spl0_638
<=> ! [X6,X4,X0] :
( ~ 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),X6,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f659,axiom,
! [X0,X6,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),X6,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
fof(f7589,plain,
spl0_637,
inference(avatar_split_clause,[],[f658,f7587]) ).
fof(f7587,plain,
( spl0_637
<=> ! [X6,X4,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f658,axiom,
! [X0,X6,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
fof(f7585,plain,
spl0_636,
inference(avatar_split_clause,[],[f650,f7583]) ).
fof(f7583,plain,
( spl0_636
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X0),X1,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f650,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X0),X1,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f7581,plain,
spl0_635,
inference(avatar_split_clause,[],[f649,f7579]) ).
fof(f7579,plain,
( spl0_635
<=> ! [X24,X4,X0,X6] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X24,c_HOL_Oplus__class_Oplus(X4,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X4,X0),c_HOL_Otimes__class_Otimes(X24,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f649,axiom,
! [X0,X6,X4,X24] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X24,c_HOL_Oplus__class_Oplus(X4,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X24,X4,X0),c_HOL_Otimes__class_Otimes(X24,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
fof(f7577,plain,
spl0_634,
inference(avatar_split_clause,[],[f647,f7575]) ).
fof(f7575,plain,
( spl0_634
<=> ! [X4,X0,X6,X26] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X6,X0),X26,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X26,X0),c_HOL_Otimes__class_Otimes(X6,X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f647,axiom,
! [X0,X6,X26,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X6,X0),X26,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X26,X0),c_HOL_Otimes__class_Otimes(X6,X26,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
fof(f7573,plain,
spl0_633,
inference(avatar_split_clause,[],[f645,f7571]) ).
fof(f7571,plain,
( spl0_633
<=> ! [X4,X0,X6,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oplus__class_Oplus(X6,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X6,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f645,axiom,
! [X0,X8,X6,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oplus__class_Oplus(X6,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X6,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
fof(f7569,plain,
spl0_632,
inference(avatar_split_clause,[],[f644,f7567]) ).
fof(f7567,plain,
( spl0_632
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X0),X1,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f644,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X0),X1,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
fof(f7565,plain,
spl0_631,
inference(avatar_split_clause,[],[f636,f7563]) ).
fof(f7563,plain,
( spl0_631
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f636,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
fof(f7561,plain,
spl0_630,
inference(avatar_split_clause,[],[f635,f7559]) ).
fof(f7559,plain,
( spl0_630
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f635,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
fof(f7557,plain,
spl0_629,
inference(avatar_split_clause,[],[f631,f7555]) ).
fof(f7555,plain,
( spl0_629
<=> ! [X6,X4,X0] :
( ~ 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(X6,X6,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f631,axiom,
! [X0,X6,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(X6,X6,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
fof(f7553,plain,
spl0_628,
inference(avatar_split_clause,[],[f630,f7551]) ).
fof(f7551,plain,
( spl0_628
<=> ! [X6,X4,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| 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(X6,X6,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f630,axiom,
! [X0,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| 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(X6,X6,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
fof(f7549,plain,
( spl0_627
| ~ spl0_291
| ~ spl0_606 ),
inference(avatar_split_clause,[],[f7494,f7451,f2776,f7547]) ).
fof(f7547,plain,
( spl0_627
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f2776,plain,
( spl0_291
<=> ! [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_291])]) ).
fof(f7451,plain,
( spl0_606
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f7494,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_291
| ~ spl0_606 ),
inference(resolution,[],[f7452,f2777]) ).
fof(f2777,plain,
( ! [X4] :
( ~ c_lessequals(c_NthRoot_Osqrt(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f2776]) ).
fof(f7452,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_606 ),
inference(avatar_component_clause,[],[f7451]) ).
fof(f7545,plain,
spl0_626,
inference(avatar_split_clause,[],[f629,f7543]) ).
fof(f7543,plain,
( spl0_626
<=> ! [X6,X4,X0] :
( ~ 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(X6,X6,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f629,axiom,
! [X0,X6,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(X6,X6,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
fof(f7541,plain,
spl0_625,
inference(avatar_split_clause,[],[f628,f7539]) ).
fof(f7539,plain,
( spl0_625
<=> ! [X6,X4,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f628,axiom,
! [X0,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
fof(f7537,plain,
spl0_624,
inference(avatar_split_clause,[],[f614,f7535]) ).
fof(f7535,plain,
( spl0_624
<=> ! [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_624])]) ).
fof(f614,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/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
fof(f7533,plain,
spl0_623,
inference(avatar_split_clause,[],[f612,f7531]) ).
fof(f7531,plain,
( spl0_623
<=> ! [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_623])]) ).
fof(f612,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/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
fof(f7529,plain,
spl0_622,
inference(avatar_split_clause,[],[f584,f7527]) ).
fof(f7527,plain,
( spl0_622
<=> ! [X3,X0,X9,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f584,axiom,
! [X2,X3,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
fof(f7525,plain,
spl0_621,
inference(avatar_split_clause,[],[f583,f7523]) ).
fof(f7523,plain,
( spl0_621
<=> ! [X2,X3,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f583,axiom,
! [X2,X3,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
fof(f7521,plain,
spl0_620,
inference(avatar_split_clause,[],[f573,f7519]) ).
fof(f7519,plain,
( spl0_620
<=> ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f573,axiom,
! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__of__halves_0) ).
fof(f7517,plain,
spl0_619,
inference(avatar_split_clause,[],[f463,f7515]) ).
fof(f7515,plain,
( spl0_619
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f463,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f7513,plain,
spl0_618,
inference(avatar_split_clause,[],[f453,f7511]) ).
fof(f7511,plain,
( spl0_618
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f453,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
fof(f7509,plain,
spl0_617,
inference(avatar_split_clause,[],[f424,f7507]) ).
fof(f7507,plain,
( spl0_617
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f424,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f7493,plain,
spl0_616,
inference(avatar_split_clause,[],[f423,f7491]) ).
fof(f7491,plain,
( spl0_616
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f423,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f7489,plain,
spl0_615,
inference(avatar_split_clause,[],[f407,f7487]) ).
fof(f7487,plain,
( spl0_615
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X3,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(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f407,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X3,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(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
fof(f7485,plain,
spl0_614,
inference(avatar_split_clause,[],[f406,f7483]) ).
fof(f7483,plain,
( spl0_614
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f406,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
fof(f7481,plain,
spl0_613,
inference(avatar_split_clause,[],[f291,f7479]) ).
fof(f7479,plain,
( spl0_613
<=> ! [X6,X4,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X6,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,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f291,axiom,
! [X0,X6,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X6,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,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
fof(f7477,plain,
spl0_612,
inference(avatar_split_clause,[],[f290,f7475]) ).
fof(f7475,plain,
( spl0_612
<=> ! [X6,X4,X0] :
( ~ 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),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f290,axiom,
! [X0,X6,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),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X4,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
fof(f7473,plain,
spl0_611,
inference(avatar_split_clause,[],[f243,f7471]) ).
fof(f7471,plain,
( spl0_611
<=> ! [X2,X0,X3] :
( ~ 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),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f243,axiom,
! [X2,X3,X0] :
( ~ 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),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
fof(f7469,plain,
spl0_610,
inference(avatar_split_clause,[],[f242,f7467]) ).
fof(f7467,plain,
( spl0_610
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,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(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f242,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,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(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
fof(f7465,plain,
spl0_609,
inference(avatar_split_clause,[],[f239,f7463]) ).
fof(f7463,plain,
( spl0_609
<=> ! [X17,X4,X0,X6,X8] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X4,X8,X0) = X17
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X6,X8,X0),X0) != c_HOL_Oplus__class_Oplus(X6,X17,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f239,axiom,
! [X0,X8,X6,X4,X17] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X4,X8,X0) = X17
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X6,X8,X0),X0) != c_HOL_Oplus__class_Oplus(X6,X17,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
fof(f7461,plain,
spl0_608,
inference(avatar_split_clause,[],[f238,f7459]) ).
fof(f7459,plain,
( spl0_608
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f238,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f7457,plain,
spl0_607,
inference(avatar_split_clause,[],[f235,f7455]) ).
fof(f7455,plain,
( spl0_607
<=> ! [X3,X0,X9,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f235,axiom,
! [X2,X3,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f7453,plain,
( spl0_606
| ~ spl0_182
| ~ spl0_585 ),
inference(avatar_split_clause,[],[f7394,f7350,f2019,f7451]) ).
fof(f2019,plain,
( spl0_182
<=> ! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| c_lessequals(X4,X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f7350,plain,
( spl0_585
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f7394,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_182
| ~ spl0_585 ),
inference(resolution,[],[f7351,f2020]) ).
fof(f2020,plain,
( ! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| c_lessequals(X4,X6,tc_RealDef_Oreal) )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f2019]) ).
fof(f7351,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_585 ),
inference(avatar_component_clause,[],[f7350]) ).
fof(f7449,plain,
spl0_605,
inference(avatar_split_clause,[],[f232,f7447]) ).
fof(f7447,plain,
( spl0_605
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f232,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
fof(f7445,plain,
spl0_604,
inference(avatar_split_clause,[],[f203,f7443]) ).
fof(f7443,plain,
( spl0_604
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(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),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f203,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(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),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f7441,plain,
spl0_603,
inference(avatar_split_clause,[],[f202,f7439]) ).
fof(f7439,plain,
( spl0_603
<=> ! [X3,X0,X9,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f202,axiom,
! [X2,X3,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f7437,plain,
spl0_602,
inference(avatar_split_clause,[],[f178,f7435]) ).
fof(f7435,plain,
( spl0_602
<=> ! [X6,X4,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_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f178,axiom,
! [X0,X6,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),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
fof(f7433,plain,
spl0_601,
inference(avatar_split_clause,[],[f177,f7431]) ).
fof(f7431,plain,
( spl0_601
<=> ! [X6,X4,X0] :
( ~ 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(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f177,axiom,
! [X0,X6,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(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
fof(f7429,plain,
spl0_600,
inference(avatar_split_clause,[],[f146,f7427]) ).
fof(f7427,plain,
( spl0_600
<=> ! [X5,X0,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X12,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X12,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f146,axiom,
! [X0,X5,X12] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X12,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X12,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
fof(f7425,plain,
spl0_599,
inference(avatar_split_clause,[],[f105,f7423]) ).
fof(f7423,plain,
( spl0_599
<=> ! [X2,X0,X3] :
( ~ 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),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f105,axiom,
! [X2,X3,X0] :
( ~ 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),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
fof(f7421,plain,
spl0_598,
inference(avatar_split_clause,[],[f104,f7419]) ).
fof(f7419,plain,
( spl0_598
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f104,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
fof(f7417,plain,
spl0_597,
inference(avatar_split_clause,[],[f101,f7415]) ).
fof(f7415,plain,
( spl0_597
<=> ! [X2,X0,X3] :
( ~ 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),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f101,axiom,
! [X2,X3,X0] :
( ~ 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),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
fof(f7413,plain,
spl0_596,
inference(avatar_split_clause,[],[f100,f7411]) ).
fof(f7411,plain,
( spl0_596
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f100,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
fof(f7392,plain,
spl0_595,
inference(avatar_split_clause,[],[f94,f7390]) ).
fof(f7390,plain,
( spl0_595
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f94,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
fof(f7388,plain,
spl0_594,
inference(avatar_split_clause,[],[f93,f7386]) ).
fof(f7386,plain,
( spl0_594
<=> ! [X2,X0,X3] :
( ~ 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),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f93,axiom,
! [X2,X3,X0] :
( ~ 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),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
fof(f7384,plain,
spl0_593,
inference(avatar_split_clause,[],[f92,f7382]) ).
fof(f7382,plain,
( spl0_593
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,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(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f92,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,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(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
fof(f7380,plain,
spl0_592,
inference(avatar_split_clause,[],[f91,f7378]) ).
fof(f7378,plain,
( spl0_592
<=> ! [X2,X0,X3] :
( ~ 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(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f91,axiom,
! [X2,X3,X0] :
( ~ 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(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
fof(f7376,plain,
spl0_591,
inference(avatar_split_clause,[],[f90,f7374]) ).
fof(f7374,plain,
( spl0_591
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f90,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
fof(f7372,plain,
spl0_590,
inference(avatar_split_clause,[],[f89,f7370]) ).
fof(f7370,plain,
( spl0_590
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f89,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
fof(f7368,plain,
spl0_589,
inference(avatar_split_clause,[],[f88,f7366]) ).
fof(f7366,plain,
( spl0_589
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f88,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
fof(f7364,plain,
spl0_588,
inference(avatar_split_clause,[],[f85,f7362]) ).
fof(f7362,plain,
( spl0_588
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f85,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
fof(f7360,plain,
spl0_587,
inference(avatar_split_clause,[],[f84,f7358]) ).
fof(f7358,plain,
( spl0_587
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f84,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
fof(f7356,plain,
spl0_586,
inference(avatar_split_clause,[],[f78,f7354]) ).
fof(f7354,plain,
( spl0_586
<=> ! [X2,X3,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X1,X0),X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f78,axiom,
! [X2,X3,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X1,X0),X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
fof(f7352,plain,
( spl0_585
| ~ spl0_282
| ~ spl0_573 ),
inference(avatar_split_clause,[],[f7303,f7161,f2737,f7350]) ).
fof(f2737,plain,
( spl0_282
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f7161,plain,
( spl0_573
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f7303,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_282
| ~ spl0_573 ),
inference(resolution,[],[f7162,f2738]) ).
fof(f2738,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_282 ),
inference(avatar_component_clause,[],[f2737]) ).
fof(f7162,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_573 ),
inference(avatar_component_clause,[],[f7161]) ).
fof(f7348,plain,
spl0_584,
inference(avatar_split_clause,[],[f76,f7346]) ).
fof(f7346,plain,
( spl0_584
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f76,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f7344,plain,
spl0_583,
inference(avatar_split_clause,[],[f15,f7342]) ).
fof(f7342,plain,
( spl0_583
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f15,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
fof(f7340,plain,
spl0_582,
inference(avatar_split_clause,[],[f14,f7338]) ).
fof(f7338,plain,
( spl0_582
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(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),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f14,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(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),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
fof(f7336,plain,
spl0_581,
inference(avatar_split_clause,[],[f13,f7334]) ).
fof(f7334,plain,
( spl0_581
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(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),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f13,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(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),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
fof(f7332,plain,
spl0_580,
inference(avatar_split_clause,[],[f12,f7330]) ).
fof(f7330,plain,
( spl0_580
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(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),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f12,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(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),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
fof(f7328,plain,
spl0_579,
inference(avatar_split_clause,[],[f11,f7326]) ).
fof(f7326,plain,
( spl0_579
<=> ! [X2,X0,X3] :
( ~ 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(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f11,axiom,
! [X2,X3,X0] :
( ~ 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(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
fof(f7324,plain,
spl0_578,
inference(avatar_split_clause,[],[f10,f7322]) ).
fof(f7322,plain,
( spl0_578
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f10,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
fof(f7320,plain,
spl0_577,
inference(avatar_split_clause,[],[f9,f7318]) ).
fof(f7318,plain,
( spl0_577
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f9,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
fof(f7316,plain,
spl0_576,
inference(avatar_split_clause,[],[f8,f7314]) ).
fof(f7314,plain,
( spl0_576
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f8,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
fof(f7312,plain,
spl0_575,
inference(avatar_split_clause,[],[f7,f7310]) ).
fof(f7310,plain,
( spl0_575
<=> ! [X2,X0,X3] :
( ~ 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),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f7,axiom,
! [X2,X3,X0] :
( ~ 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),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
fof(f7290,plain,
spl0_574,
inference(avatar_split_clause,[],[f6,f7288]) ).
fof(f7288,plain,
( spl0_574
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,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(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f6,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,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(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
fof(f7163,plain,
( ~ spl0_117
| spl0_573
| ~ spl0_311
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f4727,f4003,f2905,f7161,f1711]) ).
fof(f2905,plain,
( spl0_311
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f4003,plain,
( spl0_410
<=> ! [X4,X0,X6,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X8,X0)
| c_HOL_Oord__class_Oless(X4,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f4727,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_311
| ~ spl0_410 ),
inference(resolution,[],[f4004,f2907]) ).
fof(f2907,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_311 ),
inference(avatar_component_clause,[],[f2905]) ).
fof(f4004,plain,
( ! [X0,X8,X6,X4] :
( ~ c_HOL_Oord__class_Oless(X6,X8,X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X4,X8,X0) )
| ~ spl0_410 ),
inference(avatar_component_clause,[],[f4003]) ).
fof(f6885,plain,
spl0_572,
inference(avatar_split_clause,[],[f1114,f6882]) ).
fof(f6882,plain,
( spl0_572
<=> c_Transcendental_Ocos(c_Transcendental_Oarctan(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Oarctan(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f1114,plain,
c_Transcendental_Ocos(c_Transcendental_Oarctan(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Oarctan(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f1113,f1112]) ).
fof(f1112,plain,
c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Transcendental_Oarctan(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))),
inference(forward_demodulation,[],[f713,f696]) ).
fof(f713,axiom,
c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__45_0) ).
fof(f1113,plain,
c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Oarctan(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f1071,f696]) ).
fof(f1071,plain,
c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f781,f786]) ).
fof(f781,axiom,
c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__45_0) ).
fof(f6880,plain,
spl0_571,
inference(avatar_split_clause,[],[f1107,f6877]) ).
fof(f1107,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f782,f868]) ).
fof(f782,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__3over2__pi_0) ).
fof(f6874,plain,
spl0_570,
inference(avatar_split_clause,[],[f1033,f6871]) ).
fof(f6871,plain,
( spl0_570
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f1033,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f327,f1030]) ).
fof(f327,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Otan(c_Transcendental_Opi),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__pi_0) ).
fof(f6869,plain,
spl0_569,
inference(avatar_split_clause,[],[f878,f6867]) ).
fof(f6867,plain,
( spl0_569
<=> ! [X4,X0,X6,X8] :
( ~ 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,X6,X0),X8,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X8,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f878,axiom,
! [X0,X8,X6,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,X6,X0),X8,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X8,X0),X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
fof(f6865,plain,
spl0_568,
inference(avatar_split_clause,[],[f712,f6862]) ).
fof(f6862,plain,
( spl0_568
<=> c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f6860,plain,
( spl0_567
| ~ spl0_284
| ~ spl0_546 ),
inference(avatar_split_clause,[],[f6805,f6762,f2745,f6858]) ).
fof(f6858,plain,
( spl0_567
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f2745,plain,
( spl0_284
<=> ! [X6] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f6762,plain,
( spl0_546
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f6805,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_284
| ~ spl0_546 ),
inference(resolution,[],[f6763,f2746]) ).
fof(f2746,plain,
( ! [X6] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal) )
| ~ spl0_284 ),
inference(avatar_component_clause,[],[f2745]) ).
fof(f6763,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_546 ),
inference(avatar_component_clause,[],[f6762]) ).
fof(f6856,plain,
spl0_566,
inference(avatar_split_clause,[],[f691,f6854]) ).
fof(f6854,plain,
( spl0_566
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f691,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_half_0) ).
fof(f6852,plain,
spl0_565,
inference(avatar_split_clause,[],[f653,f6850]) ).
fof(f6850,plain,
( spl0_565
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oidom(X0)
| X2 = X3
| c_HOL_Ouminus__class_Ouminus(X3,X0) = X2
| c_HOL_Otimes__class_Otimes(X2,X2,X0) != c_HOL_Otimes__class_Otimes(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f653,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| X2 = X3
| c_HOL_Ouminus__class_Ouminus(X3,X0) = X2
| c_HOL_Otimes__class_Otimes(X2,X2,X0) != c_HOL_Otimes__class_Otimes(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
fof(f6848,plain,
spl0_564,
inference(avatar_split_clause,[],[f515,f6846]) ).
fof(f6846,plain,
( spl0_564
<=> ! [X6,X4] :
( ~ c_lessequals(X6,X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f515,axiom,
! [X6,X4] :
( ~ c_lessequals(X6,X4,tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__monotone__0__pi_H_0) ).
fof(f6844,plain,
spl0_563,
inference(avatar_split_clause,[],[f507,f6842]) ).
fof(f6842,plain,
( spl0_563
<=> ! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X7),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X7,X0),X0),c_Int_Onumber__class_Onumber__of(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f507,axiom,
! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X7),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X7,X0),X0),c_Int_Onumber__class_Onumber__of(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Bit1_0) ).
fof(f6840,plain,
spl0_562,
inference(avatar_split_clause,[],[f457,f6838]) ).
fof(f6838,plain,
( spl0_562
<=> ! [X6,X4,X8] :
( c_lessequals(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f457,axiom,
! [X8,X6,X4] :
( c_lessequals(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_0) ).
fof(f6836,plain,
spl0_561,
inference(avatar_split_clause,[],[f456,f6834]) ).
fof(f6834,plain,
( spl0_561
<=> ! [X6,X4,X8] :
( ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f456,axiom,
! [X8,X6,X4] :
( ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_1) ).
fof(f6832,plain,
spl0_560,
inference(avatar_split_clause,[],[f455,f6830]) ).
fof(f6830,plain,
( spl0_560
<=> ! [X6,X4,X8] :
( c_lessequals(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X8,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f455,axiom,
! [X8,X6,X4] :
( c_lessequals(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X8,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_0) ).
fof(f6828,plain,
spl0_559,
inference(avatar_split_clause,[],[f454,f6826]) ).
fof(f6826,plain,
( spl0_559
<=> ! [X6,X4,X8] :
( ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X8,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f454,axiom,
! [X8,X6,X4] :
( ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X8,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_1) ).
fof(f6824,plain,
spl0_558,
inference(avatar_split_clause,[],[f365,f6822]) ).
fof(f6822,plain,
( spl0_558
<=> ! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X7),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_Int_Onumber__class_Onumber__of(X7,X0),X0),c_Int_Onumber__class_Onumber__of(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f365,axiom,
! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X7),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_Int_Onumber__class_Onumber__of(X7,X0),X0),c_Int_Onumber__class_Onumber__of(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Bit0_0) ).
fof(f6820,plain,
spl0_557,
inference(avatar_split_clause,[],[f303,f6818]) ).
fof(f6818,plain,
( spl0_557
<=> ! [X6,X4,X8] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X8,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f303,axiom,
! [X8,X6,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X8,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__less__mono2_0) ).
fof(f6804,plain,
spl0_556,
inference(avatar_split_clause,[],[f302,f6802]) ).
fof(f6802,plain,
( spl0_556
<=> ! [X6,X4,X8] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f302,axiom,
! [X8,X6,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__less__iff1_1) ).
fof(f6800,plain,
spl0_555,
inference(avatar_split_clause,[],[f301,f6798]) ).
fof(f6798,plain,
( spl0_555
<=> ! [X6,X4,X8] :
( c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f301,axiom,
! [X8,X6,X4] :
( c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__less__iff1_0) ).
fof(f6796,plain,
spl0_554,
inference(avatar_split_clause,[],[f281,f6794]) ).
fof(f6794,plain,
( spl0_554
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f281,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
fof(f6792,plain,
spl0_553,
inference(avatar_split_clause,[],[f276,f6790]) ).
fof(f6790,plain,
( spl0_553
<=> ! [X4,X0,X21,X6,X22] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| c_HOL_Oord__class_Oless(X21,X22,X0)
| c_HOL_Ominus__class_Ominus(X4,X6,X0) != c_HOL_Ominus__class_Ominus(X21,X22,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f276,axiom,
! [X21,X0,X6,X4,X22] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| c_HOL_Oord__class_Oless(X21,X22,X0)
| c_HOL_Ominus__class_Ominus(X4,X6,X0) != c_HOL_Ominus__class_Ominus(X21,X22,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
fof(f6788,plain,
spl0_552,
inference(avatar_split_clause,[],[f275,f6786]) ).
fof(f6786,plain,
( spl0_552
<=> ! [X4,X0,X21,X6,X22] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X22,X21,X0)
| c_lessequals(X6,X4,X0)
| c_HOL_Ominus__class_Ominus(X4,X6,X0) != c_HOL_Ominus__class_Ominus(X21,X22,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f275,axiom,
! [X21,X0,X6,X4,X22] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X22,X21,X0)
| c_lessequals(X6,X4,X0)
| c_HOL_Ominus__class_Ominus(X4,X6,X0) != c_HOL_Ominus__class_Ominus(X21,X22,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
fof(f6784,plain,
spl0_551,
inference(avatar_split_clause,[],[f164,f6782]) ).
fof(f6782,plain,
( spl0_551
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f164,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
fof(f6780,plain,
spl0_550,
inference(avatar_split_clause,[],[f107,f6778]) ).
fof(f6778,plain,
( spl0_550
<=> ! [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_550])]) ).
fof(f107,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/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
fof(f6776,plain,
spl0_549,
inference(avatar_split_clause,[],[f83,f6774]) ).
fof(f6774,plain,
( spl0_549
<=> ! [X6,X4,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f83,axiom,
! [X0,X6,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
fof(f6772,plain,
spl0_548,
inference(avatar_split_clause,[],[f82,f6770]) ).
fof(f6770,plain,
( spl0_548
<=> ! [X6,X4,X0] :
( ~ 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(X6,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f82,axiom,
! [X0,X6,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(X6,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
fof(f6768,plain,
spl0_547,
inference(avatar_split_clause,[],[f30,f6766]) ).
fof(f6766,plain,
( spl0_547
<=> ! [X6,X4] :
( ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X6,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f30,axiom,
! [X6,X4] :
( ~ c_lessequals(X4,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X6,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(X4),c_Transcendental_Ocos(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__monotone__0__pi_0) ).
fof(f6764,plain,
( spl0_546
| ~ spl0_182
| ~ spl0_545 ),
inference(avatar_split_clause,[],[f6555,f6385,f2019,f6762]) ).
fof(f6385,plain,
( spl0_545
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f6555,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal) )
| ~ spl0_182
| ~ spl0_545 ),
inference(resolution,[],[f6386,f2020]) ).
fof(f6386,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_545 ),
inference(avatar_component_clause,[],[f6385]) ).
fof(f6387,plain,
( spl0_545
| ~ spl0_288
| ~ spl0_529 ),
inference(avatar_split_clause,[],[f6286,f6242,f2764,f6385]) ).
fof(f2764,plain,
( spl0_288
<=> ! [X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f6242,plain,
( spl0_529
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f6286,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_288
| ~ spl0_529 ),
inference(resolution,[],[f6243,f2765]) ).
fof(f2765,plain,
( ! [X6] :
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X6,tc_RealDef_Oreal) )
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f2764]) ).
fof(f6243,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_529 ),
inference(avatar_component_clause,[],[f6242]) ).
fof(f6315,plain,
spl0_544,
inference(avatar_split_clause,[],[f1112,f6312]) ).
fof(f6312,plain,
( spl0_544
<=> c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Transcendental_Oarctan(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f6310,plain,
spl0_543,
inference(avatar_split_clause,[],[f674,f6308]) ).
fof(f6308,plain,
( spl0_543
<=> ! [X29,X28,X7] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X28,X29,tc_RealDef_Oreal),X7,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X28,X7,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X29,X7,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f674,axiom,
! [X28,X29,X7] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X28,X29,tc_RealDef_Oreal),X7,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X28,X7,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X29,X7,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__mult__distrib_0) ).
fof(f6306,plain,
spl0_542,
inference(avatar_split_clause,[],[f560,f6304]) ).
fof(f6304,plain,
( spl0_542
<=> ! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X7),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),c_Int_Onumber__class_Onumber__of(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f560,axiom,
! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X7),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),c_Int_Onumber__class_Onumber__of(X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__number__of__Bit0_0) ).
fof(f6302,plain,
spl0_541,
inference(avatar_split_clause,[],[f506,f6300]) ).
fof(f6300,plain,
( spl0_541
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f506,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
fof(f6298,plain,
spl0_540,
inference(avatar_split_clause,[],[f505,f6296]) ).
fof(f6296,plain,
( spl0_540
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f505,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
fof(f6284,plain,
spl0_539,
inference(avatar_split_clause,[],[f504,f6282]) ).
fof(f6282,plain,
( spl0_539
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f504,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
fof(f6280,plain,
spl0_538,
inference(avatar_split_clause,[],[f503,f6278]) ).
fof(f6278,plain,
( spl0_538
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f503,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
fof(f6276,plain,
spl0_537,
inference(avatar_split_clause,[],[f502,f6274]) ).
fof(f6274,plain,
( spl0_537
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f502,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).
fof(f6272,plain,
spl0_536,
inference(avatar_split_clause,[],[f501,f6270]) ).
fof(f6270,plain,
( spl0_536
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f501,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
fof(f6268,plain,
spl0_535,
inference(avatar_split_clause,[],[f500,f6266]) ).
fof(f6266,plain,
( spl0_535
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f500,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
fof(f6264,plain,
spl0_534,
inference(avatar_split_clause,[],[f499,f6262]) ).
fof(f6262,plain,
( spl0_534
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f499,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).
fof(f6260,plain,
spl0_533,
inference(avatar_split_clause,[],[f466,f6258]) ).
fof(f6258,plain,
( spl0_533
<=> ! [X6,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_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f466,axiom,
! [X6,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_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__square__gt__zero_0) ).
fof(f6256,plain,
spl0_532,
inference(avatar_split_clause,[],[f465,f6254]) ).
fof(f6254,plain,
( spl0_532
<=> ! [X6,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f465,axiom,
! [X6,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__square__gt__zero2_0) ).
fof(f6252,plain,
spl0_531,
inference(avatar_split_clause,[],[f360,f6250]) ).
fof(f6250,plain,
( spl0_531
<=> ! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f360,axiom,
! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__half__sum_0) ).
fof(f6248,plain,
spl0_530,
inference(avatar_split_clause,[],[f359,f6246]) ).
fof(f6246,plain,
( spl0_530
<=> ! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f359,axiom,
! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__gt__half__sum_0) ).
fof(f6244,plain,
( ~ spl0_119
| spl0_529
| ~ spl0_311
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f4694,f3992,f2905,f6242,f1721]) ).
fof(f3992,plain,
( spl0_409
<=> ! [X4,X0,X6,X8] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X4,X0)
| ~ c_HOL_Oord__class_Oless(X8,X6,X0)
| c_HOL_Oord__class_Oless(X8,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f4694,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_311
| ~ spl0_409 ),
inference(resolution,[],[f3993,f2907]) ).
fof(f3993,plain,
( ! [X0,X8,X6,X4] :
( ~ c_HOL_Oord__class_Oless(X8,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X4,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X8,X4,X0) )
| ~ spl0_409 ),
inference(avatar_component_clause,[],[f3992]) ).
fof(f6240,plain,
spl0_528,
inference(avatar_split_clause,[],[f317,f6238]) ).
fof(f6238,plain,
( spl0_528
<=> ! [X6,X4] :
( ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f317,axiom,
! [X6,X4] :
( ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_5) ).
fof(f6236,plain,
spl0_527,
inference(avatar_split_clause,[],[f316,f6234]) ).
fof(f6234,plain,
( spl0_527
<=> ! [X6,X4] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,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_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f316,axiom,
! [X6,X4] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,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_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_4) ).
fof(f6232,plain,
spl0_526,
inference(avatar_split_clause,[],[f315,f6230]) ).
fof(f6230,plain,
( spl0_526
<=> ! [X6,X4] :
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f315,axiom,
! [X6,X4] :
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_3) ).
fof(f6228,plain,
spl0_525,
inference(avatar_split_clause,[],[f314,f6226]) ).
fof(f6226,plain,
( spl0_525
<=> ! [X6,X4] :
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),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_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f314,axiom,
! [X6,X4] :
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),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_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_2) ).
fof(f6224,plain,
spl0_524,
inference(avatar_split_clause,[],[f313,f6222]) ).
fof(f6222,plain,
( spl0_524
<=> ! [X6,X4] :
( c_lessequals(X6,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),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_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f313,axiom,
! [X6,X4] :
( c_lessequals(X6,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),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_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_1) ).
fof(f6220,plain,
spl0_523,
inference(avatar_split_clause,[],[f312,f6218]) ).
fof(f6218,plain,
( spl0_523
<=> ! [X6,X4] :
( c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f312,axiom,
! [X6,X4] :
( c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_0) ).
fof(f6216,plain,
spl0_522,
inference(avatar_split_clause,[],[f304,f6214]) ).
fof(f6214,plain,
( spl0_522
<=> ! [X6,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),X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f304,axiom,
! [X6,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),X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__order_0) ).
fof(f6212,plain,
spl0_521,
inference(avatar_split_clause,[],[f278,f6210]) ).
fof(f6210,plain,
( spl0_521
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f278,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f6208,plain,
spl0_520,
inference(avatar_split_clause,[],[f150,f6206]) ).
fof(f150,axiom,
! [X2,X0,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X12,X0) = c_HOL_Oplus__class_Oplus(X12,c_HOL_Otimes__class_Otimes(X2,X12,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(f6204,plain,
spl0_519,
inference(avatar_split_clause,[],[f149,f6202]) ).
fof(f6202,plain,
( spl0_519
<=> ! [X2,X0,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X12,X0),X12,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f149,axiom,
! [X2,X0,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X12,X0),X12,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(f6120,plain,
( spl0_518
| ~ spl0_286
| ~ spl0_491 ),
inference(avatar_split_clause,[],[f5940,f5893,f2753,f6118]) ).
fof(f6118,plain,
( spl0_518
<=> ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f5940,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_286
| ~ spl0_491 ),
inference(resolution,[],[f5894,f2754]) ).
fof(f6030,plain,
spl0_517,
inference(avatar_split_clause,[],[f1105,f6028]) ).
fof(f6028,plain,
( spl0_517
<=> ! [X5] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f1105,plain,
! [X5] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f783,f868]) ).
fof(f783,axiom,
! [X5] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__2npi_0) ).
fof(f6026,plain,
spl0_516,
inference(avatar_split_clause,[],[f1092,f6024]) ).
fof(f6024,plain,
( spl0_516
<=> ! [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_516])]) ).
fof(f1092,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,[],[f433]) ).
fof(f433,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/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f6022,plain,
spl0_515,
inference(avatar_split_clause,[],[f858,f6020]) ).
fof(f6020,plain,
( spl0_515
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f858,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
fof(f6018,plain,
spl0_514,
inference(avatar_split_clause,[],[f856,f6016]) ).
fof(f6016,plain,
( spl0_514
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f856,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
fof(f6014,plain,
spl0_513,
inference(avatar_split_clause,[],[f838,f6012]) ).
fof(f6012,plain,
( spl0_513
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X0),X1,X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f838,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X0),X1,X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f6010,plain,
( spl0_512
| ~ spl0_292
| ~ spl0_489 ),
inference(avatar_split_clause,[],[f5742,f5556,f2780,f6008]) ).
fof(f6008,plain,
( spl0_512
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f2780,plain,
( spl0_292
<=> ! [X6] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f5742,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_292
| ~ spl0_489 ),
inference(resolution,[],[f5557,f2781]) ).
fof(f2781,plain,
( ! [X6] :
( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X6,tc_RealDef_Oreal) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f2780]) ).
fof(f6006,plain,
spl0_511,
inference(avatar_split_clause,[],[f837,f6004]) ).
fof(f6004,plain,
( spl0_511
<=> ! [X37,X34,X0,X35] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X37,X0),X35,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X0),X37,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f837,axiom,
! [X0,X37,X34,X35] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X37,X0),X35,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X34,X35,X0),X37,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f6002,plain,
spl0_510,
inference(avatar_split_clause,[],[f834,f6000]) ).
fof(f6000,plain,
( spl0_510
<=> ! [X35,X34,X0,X36] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X34,c_HOL_Otimes__class_Otimes(X35,X36,X0),X0) = c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(X34,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f834,axiom,
! [X0,X36,X34,X35] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X34,c_HOL_Otimes__class_Otimes(X35,X36,X0),X0) = c_HOL_Otimes__class_Otimes(X35,c_HOL_Otimes__class_Otimes(X34,X36,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f5998,plain,
spl0_509,
inference(avatar_split_clause,[],[f832,f5996]) ).
fof(f5996,plain,
( spl0_509
<=> ! [X4,X0,X6,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(X6,X8,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X4,X6,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f832,axiom,
! [X0,X8,X6,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(X6,X8,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X4,X6,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
fof(f5994,plain,
spl0_508,
inference(avatar_split_clause,[],[f809,f5992]) ).
fof(f5992,plain,
( spl0_508
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X1,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f809,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X1,X0),X1,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
fof(f5990,plain,
spl0_507,
inference(avatar_split_clause,[],[f694,f5988]) ).
fof(f5988,plain,
( spl0_507
<=> ! [X17] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X17,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X17,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal),X17,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f694,axiom,
! [X17] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X17,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X17,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal),X17,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__real__divide__sqrt__less_0) ).
fof(f5986,plain,
spl0_506,
inference(avatar_split_clause,[],[f670,f5984]) ).
fof(f5984,plain,
( spl0_506
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f670,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(X2,X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
fof(f5982,plain,
spl0_505,
inference(avatar_split_clause,[],[f669,f5980]) ).
fof(f5980,plain,
( spl0_505
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f669,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
fof(f5978,plain,
spl0_504,
inference(avatar_split_clause,[],[f444,f5976]) ).
fof(f5976,plain,
( spl0_504
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f444,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(f5974,plain,
spl0_503,
inference(avatar_split_clause,[],[f443,f5972]) ).
fof(f5972,plain,
( spl0_503
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f443,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f5970,plain,
spl0_502,
inference(avatar_split_clause,[],[f442,f5968]) ).
fof(f5968,plain,
( spl0_502
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X1,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f442,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X1,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X1,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f5937,plain,
spl0_501,
inference(avatar_split_clause,[],[f440,f5935]) ).
fof(f5935,plain,
( spl0_501
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f440,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f5933,plain,
spl0_500,
inference(avatar_split_clause,[],[f439,f5931]) ).
fof(f5931,plain,
( spl0_500
<=> ! [X4,X0,X6,X8] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X6,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f439,axiom,
! [X0,X8,X6,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X6,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f5929,plain,
spl0_499,
inference(avatar_split_clause,[],[f437,f5927]) ).
fof(f5927,plain,
( spl0_499
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f437,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f5925,plain,
spl0_498,
inference(avatar_split_clause,[],[f436,f5923]) ).
fof(f5923,plain,
( spl0_498
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f436,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f5921,plain,
spl0_497,
inference(avatar_split_clause,[],[f322,f5919]) ).
fof(f5919,plain,
( spl0_497
<=> ! [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_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f322,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_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__is__one_0) ).
fof(f5916,plain,
spl0_496,
inference(avatar_split_clause,[],[f310,f5913]) ).
fof(f5913,plain,
( spl0_496
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),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) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f310,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),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/sandbox/benchmark/theBenchmark.p',cls_real__two__squares__add__zero__iff_2) ).
fof(f5911,plain,
spl0_495,
inference(avatar_split_clause,[],[f306,f5909]) ).
fof(f5909,plain,
( spl0_495
<=> ! [X6,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f306,axiom,
! [X6,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__squares__cancel2_0) ).
fof(f5907,plain,
spl0_494,
inference(avatar_split_clause,[],[f305,f5905]) ).
fof(f5905,plain,
( spl0_494
<=> ! [X6,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f305,axiom,
! [X6,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__squares__cancel_0) ).
fof(f5903,plain,
spl0_493,
inference(avatar_split_clause,[],[f191,f5901]) ).
fof(f5901,plain,
( spl0_493
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f191,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
fof(f5899,plain,
spl0_492,
inference(avatar_split_clause,[],[f68,f5897]) ).
fof(f5897,plain,
( spl0_492
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f68,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
fof(f5895,plain,
( spl0_491
| ~ spl0_177
| ~ spl0_489 ),
inference(avatar_split_clause,[],[f5744,f5556,f1999,f5893]) ).
fof(f5744,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_177
| ~ spl0_489 ),
inference(resolution,[],[f5557,f2000]) ).
fof(f5891,plain,
spl0_490,
inference(avatar_split_clause,[],[f67,f5889]) ).
fof(f5889,plain,
( spl0_490
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f67,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
fof(f5558,plain,
( ~ spl0_119
| spl0_489
| ~ spl0_311
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f4168,f3838,f2905,f5556,f1721]) ).
fof(f3838,plain,
( spl0_375
<=> ! [X4,X0,X6,X8] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X6,X4,X0)
| ~ c_HOL_Oord__class_Oless(X8,X6,X0)
| c_HOL_Oord__class_Oless(X8,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f4168,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_311
| ~ spl0_375 ),
inference(resolution,[],[f3839,f2907]) ).
fof(f3839,plain,
( ! [X0,X8,X6,X4] :
( ~ c_HOL_Oord__class_Oless(X8,X6,X0)
| ~ c_lessequals(X6,X4,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X8,X4,X0) )
| ~ spl0_375 ),
inference(avatar_component_clause,[],[f3838]) ).
fof(f5490,plain,
spl0_488,
inference(avatar_split_clause,[],[f1037,f5487]) ).
fof(f5487,plain,
( spl0_488
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f1037,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f739,f786]) ).
fof(f739,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__zero_0) ).
fof(f5485,plain,
spl0_487,
inference(avatar_split_clause,[],[f747,f5483]) ).
fof(f5483,plain,
( spl0_487
<=> ! [X2,X1,X3] :
( X2 = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X3,X1,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f747,axiom,
! [X2,X3,X1] :
( X2 = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X3,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__right__cancel_0) ).
fof(f5481,plain,
spl0_486,
inference(avatar_split_clause,[],[f746,f5479]) ).
fof(f5479,plain,
( spl0_486
<=> ! [X2,X1,X3] :
( X2 = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f746,axiom,
! [X2,X3,X1] :
( X2 = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__left__cancel_0) ).
fof(f5477,plain,
spl0_485,
inference(avatar_split_clause,[],[f736,f5475]) ).
fof(f5475,plain,
( spl0_485
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| X2 = X3
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Odivide(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f736,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| X2 = X3
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Odivide(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
fof(f5473,plain,
spl0_484,
inference(avatar_split_clause,[],[f620,f5471]) ).
fof(f5471,plain,
( spl0_484
<=> ! [X6,X4,X0] :
( ~ 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(X6,X6,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f620,axiom,
! [X0,X6,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(X6,X6,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
fof(f5469,plain,
spl0_483,
inference(avatar_split_clause,[],[f615,f5467]) ).
fof(f5467,plain,
( spl0_483
<=> ! [X6,X4,X0] :
( ~ 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(X6,X6,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f615,axiom,
! [X0,X6,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(X6,X6,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
fof(f5465,plain,
spl0_482,
inference(avatar_split_clause,[],[f469,f5463]) ).
fof(f5463,plain,
( spl0_482
<=> ! [X4,X0,X6,X8] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X8,X0) = X4
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X6,X8,X0),X0) != X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f469,axiom,
! [X0,X8,X6,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X8,X0) = X4
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X6,X8,X0),X0) != X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
fof(f5449,plain,
spl0_481,
inference(avatar_split_clause,[],[f392,f5447]) ).
fof(f5447,plain,
( spl0_481
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f392,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f5445,plain,
spl0_480,
inference(avatar_split_clause,[],[f391,f5443]) ).
fof(f5443,plain,
( spl0_480
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f391,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f5441,plain,
spl0_479,
inference(avatar_split_clause,[],[f390,f5439]) ).
fof(f5439,plain,
( spl0_479
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f390,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f5437,plain,
spl0_478,
inference(avatar_split_clause,[],[f389,f5435]) ).
fof(f5435,plain,
( spl0_478
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f389,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f5433,plain,
spl0_477,
inference(avatar_split_clause,[],[f388,f5431]) ).
fof(f5431,plain,
( spl0_477
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f388,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f5429,plain,
spl0_476,
inference(avatar_split_clause,[],[f387,f5427]) ).
fof(f5427,plain,
( spl0_476
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f387,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f5425,plain,
spl0_475,
inference(avatar_split_clause,[],[f384,f5423]) ).
fof(f5423,plain,
( spl0_475
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f384,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
fof(f5421,plain,
spl0_474,
inference(avatar_split_clause,[],[f383,f5419]) ).
fof(f5419,plain,
( spl0_474
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f383,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
fof(f5417,plain,
spl0_473,
inference(avatar_split_clause,[],[f248,f5415]) ).
fof(f5415,plain,
( spl0_473
<=> ! [X4,X0,X6,X8] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X6 = X8
| c_HOL_Oplus__class_Oplus(X4,X6,X0) != c_HOL_Oplus__class_Oplus(X4,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f248,axiom,
! [X0,X8,X6,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X6 = X8
| c_HOL_Oplus__class_Oplus(X4,X6,X0) != c_HOL_Oplus__class_Oplus(X4,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f5413,plain,
spl0_472,
inference(avatar_split_clause,[],[f190,f5411]) ).
fof(f5411,plain,
( spl0_472
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f190,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f5409,plain,
( spl0_471
| ~ spl0_295
| ~ spl0_441 ),
inference(avatar_split_clause,[],[f5061,f4968,f2792,f5407]) ).
fof(f5407,plain,
( spl0_471
<=> ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f2792,plain,
( spl0_295
<=> ! [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_295])]) ).
fof(f4968,plain,
( spl0_441
<=> ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f5061,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_295
| ~ spl0_441 ),
inference(resolution,[],[f4969,f2793]) ).
fof(f2793,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f2792]) ).
fof(f4969,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_441 ),
inference(avatar_component_clause,[],[f4968]) ).
fof(f5405,plain,
spl0_470,
inference(avatar_split_clause,[],[f189,f5403]) ).
fof(f5403,plain,
( spl0_470
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f189,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f5401,plain,
spl0_469,
inference(avatar_split_clause,[],[f188,f5399]) ).
fof(f5399,plain,
( spl0_469
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f188,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f5397,plain,
spl0_468,
inference(avatar_split_clause,[],[f187,f5395]) ).
fof(f5395,plain,
( spl0_468
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f187,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f5393,plain,
spl0_467,
inference(avatar_split_clause,[],[f186,f5391]) ).
fof(f5391,plain,
( spl0_467
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f186,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f5389,plain,
spl0_466,
inference(avatar_split_clause,[],[f185,f5387]) ).
fof(f5387,plain,
( spl0_466
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f185,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X1,X0),c_HOL_Oplus__class_Oplus(X3,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f5385,plain,
spl0_465,
inference(avatar_split_clause,[],[f148,f5383]) ).
fof(f5383,plain,
( spl0_465
<=> ! [X0,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X12,X12,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f148,axiom,
! [X0,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X12,X12,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(f5269,plain,
( spl0_464
| ~ spl0_280
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f4914,f4828,f2729,f5267]) ).
fof(f5267,plain,
( spl0_464
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f2729,plain,
( spl0_280
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f4914,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_280
| ~ spl0_428 ),
inference(resolution,[],[f4829,f2730]) ).
fof(f2730,plain,
( ! [X4] :
( c_lessequals(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_280 ),
inference(avatar_component_clause,[],[f2729]) ).
fof(f5082,plain,
spl0_463,
inference(avatar_split_clause,[],[f1104,f5080]) ).
fof(f5080,plain,
( spl0_463
<=> ! [X4] : c_Transcendental_Ocos(X4) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f1104,plain,
! [X4] : c_Transcendental_Ocos(X4) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f697,f868]) ).
fof(f697,axiom,
! [X4] : c_Transcendental_Ocos(X4) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__periodic_0) ).
fof(f5058,plain,
spl0_462,
inference(avatar_split_clause,[],[f1034,f5055]) ).
fof(f1034,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f731,f786]) ).
fof(f731,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_Transcendental_Opi),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__pi_0) ).
fof(f5053,plain,
spl0_461,
inference(avatar_split_clause,[],[f846,f5051]) ).
fof(f5051,plain,
( spl0_461
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X1,X0),X1,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f846,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X1,X0),X1,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
fof(f5049,plain,
spl0_460,
inference(avatar_split_clause,[],[f833,f5047]) ).
fof(f5047,plain,
( spl0_460
<=> ! [X29,X28,X33] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X29,tc_RealDef_Oreal),X33,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X28,c_HOL_Otimes__class_Otimes(X29,X33,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f833,axiom,
! [X28,X29,X33] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X28,X29,tc_RealDef_Oreal),X33,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X28,c_HOL_Otimes__class_Otimes(X29,X33,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__assoc_0) ).
fof(f5045,plain,
spl0_459,
inference(avatar_split_clause,[],[f823,f5043]) ).
fof(f5043,plain,
( spl0_459
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f823,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__Numeral0_0) ).
fof(f5041,plain,
spl0_458,
inference(avatar_split_clause,[],[f817,f5039]) ).
fof(f817,axiom,
! [X2,X10] : c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X10,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X10,X10,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X2,X10,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__divide__square__eq_0) ).
fof(f5037,plain,
spl0_457,
inference(avatar_split_clause,[],[f787,f5035]) ).
fof(f5035,plain,
( spl0_457
<=> ! [X0,X1] :
( ~ 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),X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f787,axiom,
! [X0,X1] :
( ~ 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),X1,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
fof(f5033,plain,
spl0_456,
inference(avatar_split_clause,[],[f686,f5030]) ).
fof(f5030,plain,
( spl0_456
<=> c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f686,axiom,
c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__less__two_0) ).
fof(f5028,plain,
spl0_455,
inference(avatar_split_clause,[],[f685,f5025]) ).
fof(f5025,plain,
( spl0_455
<=> c_lessequals(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f685,axiom,
c_lessequals(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__le__two_0) ).
fof(f5023,plain,
spl0_454,
inference(avatar_split_clause,[],[f671,f5021]) ).
fof(f5021,plain,
( spl0_454
<=> ! [X6,X4,X0] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X0),X6,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f671,axiom,
! [X0,X6,X4] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X0),X6,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
fof(f5019,plain,
spl0_453,
inference(avatar_split_clause,[],[f668,f5017]) ).
fof(f668,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
fof(f5015,plain,
( spl0_452
| ~ spl0_248
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f4913,f4828,f2392,f5012]) ).
fof(f2392,plain,
( spl0_248
<=> c_lessequals(c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f4913,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_248
| ~ spl0_428 ),
inference(resolution,[],[f4829,f2394]) ).
fof(f2394,plain,
( c_lessequals(c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2392]) ).
fof(f5010,plain,
spl0_451,
inference(avatar_split_clause,[],[f652,f5008]) ).
fof(f5008,plain,
( spl0_451
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f652,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
fof(f5006,plain,
spl0_450,
inference(avatar_split_clause,[],[f651,f5004]) ).
fof(f5004,plain,
( spl0_450
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f651,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
fof(f5002,plain,
spl0_449,
inference(avatar_split_clause,[],[f641,f5000]) ).
fof(f5000,plain,
( spl0_449
<=> ! [X6,X4,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X0),X6,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f641,axiom,
! [X0,X6,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X0),X6,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
fof(f4998,plain,
spl0_448,
inference(avatar_split_clause,[],[f640,f4996]) ).
fof(f4996,plain,
( spl0_448
<=> ! [X2,X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f640,axiom,
! [X2,X3,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
fof(f4994,plain,
spl0_447,
inference(avatar_split_clause,[],[f638,f4992]) ).
fof(f4992,plain,
( spl0_447
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Otimes__class_Otimes(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f638,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Otimes__class_Otimes(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
fof(f4990,plain,
spl0_446,
inference(avatar_split_clause,[],[f637,f4988]) ).
fof(f4988,plain,
( spl0_446
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X2,X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f637,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X2,X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
fof(f4986,plain,
spl0_445,
inference(avatar_split_clause,[],[f632,f4984]) ).
fof(f4984,plain,
( spl0_445
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f632,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
fof(f4982,plain,
spl0_444,
inference(avatar_split_clause,[],[f571,f4980]) ).
fof(f571,axiom,
! [X0,X8] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X8,X8,X0) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__2_0) ).
fof(f4978,plain,
spl0_443,
inference(avatar_split_clause,[],[f570,f4976]) ).
fof(f570,axiom,
! [X0,X8] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Otimes__class_Otimes(X8,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X0) = c_HOL_Oplus__class_Oplus(X8,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__2__right_0) ).
fof(f4974,plain,
spl0_442,
inference(avatar_split_clause,[],[f413,f4972]) ).
fof(f4972,plain,
( spl0_442
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f413,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
fof(f4970,plain,
( spl0_441
| ~ spl0_177
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f4909,f4828,f1999,f4968]) ).
fof(f4909,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_177
| ~ spl0_428 ),
inference(resolution,[],[f4829,f2000]) ).
fof(f4966,plain,
spl0_440,
inference(avatar_split_clause,[],[f412,f4964]) ).
fof(f4964,plain,
( spl0_440
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f412,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
fof(f4962,plain,
spl0_439,
inference(avatar_split_clause,[],[f411,f4960]) ).
fof(f4960,plain,
( spl0_439
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f411,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(f4958,plain,
spl0_438,
inference(avatar_split_clause,[],[f410,f4956]) ).
fof(f4956,plain,
( spl0_438
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f410,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(f4954,plain,
spl0_437,
inference(avatar_split_clause,[],[f308,f4952]) ).
fof(f4952,plain,
( spl0_437
<=> ! [X6,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f308,axiom,
! [X6,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_1) ).
fof(f4950,plain,
spl0_436,
inference(avatar_split_clause,[],[f307,f4948]) ).
fof(f4948,plain,
( spl0_436
<=> ! [X6,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(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f307,axiom,
! [X6,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(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_0) ).
fof(f4946,plain,
spl0_435,
inference(avatar_split_clause,[],[f261,f4944]) ).
fof(f4944,plain,
( spl0_435
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(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(X2,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f261,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(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(X2,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(f4942,plain,
spl0_434,
inference(avatar_split_clause,[],[f260,f4940]) ).
fof(f4940,plain,
( spl0_434
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(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(X2,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f260,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(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(X2,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(f4938,plain,
spl0_433,
inference(avatar_split_clause,[],[f234,f4936]) ).
fof(f4936,plain,
( spl0_433
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f234,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f4934,plain,
spl0_432,
inference(avatar_split_clause,[],[f233,f4932]) ).
fof(f4932,plain,
( spl0_432
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f233,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X2,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f4930,plain,
spl0_431,
inference(avatar_split_clause,[],[f193,f4928]) ).
fof(f4928,plain,
( spl0_431
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f193,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f4907,plain,
spl0_430,
inference(avatar_split_clause,[],[f192,f4905]) ).
fof(f4905,plain,
( spl0_430
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f192,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f4903,plain,
spl0_429,
inference(avatar_split_clause,[],[f33,f4901]) ).
fof(f4901,plain,
( spl0_429
<=> ! [X6,X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f33,axiom,
! [X6,X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__mult__self__sum__ge__zero_0) ).
fof(f4830,plain,
( ~ spl0_119
| spl0_428
| ~ spl0_311
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f4141,f3834,f2905,f4828,f1721]) ).
fof(f3834,plain,
( spl0_374
<=> ! [X4,X0,X6,X8] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X8,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X4,X0)
| c_HOL_Oord__class_Oless(X8,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f4141,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_311
| ~ spl0_374 ),
inference(resolution,[],[f3835,f2907]) ).
fof(f3835,plain,
( ! [X0,X8,X6,X4] :
( ~ c_HOL_Oord__class_Oless(X6,X4,X0)
| ~ c_lessequals(X8,X6,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X8,X4,X0) )
| ~ spl0_374 ),
inference(avatar_component_clause,[],[f3834]) ).
fof(f4495,plain,
( spl0_427
| ~ spl0_292
| ~ spl0_426 ),
inference(avatar_split_clause,[],[f4365,f4181,f2780,f4493]) ).
fof(f4493,plain,
( spl0_427
<=> ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f4181,plain,
( spl0_426
<=> ! [X0] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f4365,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_292
| ~ spl0_426 ),
inference(resolution,[],[f4182,f2781]) ).
fof(f4182,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_426 ),
inference(avatar_component_clause,[],[f4181]) ).
fof(f4183,plain,
( ~ spl0_119
| spl0_426
| ~ spl0_297
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f4111,f3830,f2800,f4181,f1721]) ).
fof(f2800,plain,
( spl0_297
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f3830,plain,
( spl0_373
<=> ! [X4,X0,X6,X8] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X6,X4,X0)
| ~ c_lessequals(X8,X6,X0)
| c_lessequals(X8,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f4111,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_297
| ~ spl0_373 ),
inference(resolution,[],[f3831,f2802]) ).
fof(f2802,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_297 ),
inference(avatar_component_clause,[],[f2800]) ).
fof(f3831,plain,
( ! [X0,X8,X6,X4] :
( ~ c_lessequals(X8,X6,X0)
| ~ c_lessequals(X6,X4,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X8,X4,X0) )
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f3830]) ).
fof(f4067,plain,
spl0_425,
inference(avatar_split_clause,[],[f870,f4065]) ).
fof(f4065,plain,
( spl0_425
<=> ! [X6,X4,X0] :
( ~ class_Int_Oring__char__0(X0)
| ~ class_Int_Onumber__ring(X0)
| X4 = X6
| c_Int_Onumber__class_Onumber__of(X4,X0) != c_Int_Onumber__class_Onumber__of(X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f870,axiom,
! [X0,X6,X4] :
( ~ class_Int_Oring__char__0(X0)
| ~ class_Int_Onumber__ring(X0)
| X4 = X6
| c_Int_Onumber__class_Onumber__of(X4,X0) != c_Int_Onumber__class_Onumber__of(X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
fof(f4063,plain,
~ spl0_424,
inference(avatar_split_clause,[],[f825,f4060]) ).
fof(f4060,plain,
( spl0_424
<=> c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f825,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal) != c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__neq__two_0) ).
fof(f4058,plain,
spl0_423,
inference(avatar_split_clause,[],[f772,f4056]) ).
fof(f4056,plain,
( spl0_423
<=> ! [X4,X0,X21,X22] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X21 = X22
| c_HOL_Ominus__class_Ominus(X21,X22,X0) != c_HOL_Ominus__class_Ominus(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f772,axiom,
! [X21,X0,X4,X22] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X21 = X22
| c_HOL_Ominus__class_Ominus(X21,X22,X0) != c_HOL_Ominus__class_Ominus(X4,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
fof(f4054,plain,
spl0_422,
inference(avatar_split_clause,[],[f761,f4052]) ).
fof(f4052,plain,
( spl0_422
<=> ! [X6,X4,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X4 = X6
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X4,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f761,axiom,
! [X0,X6,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X4 = X6
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X4,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f4050,plain,
spl0_421,
inference(avatar_split_clause,[],[f599,f4048]) ).
fof(f4048,plain,
( spl0_421
<=> ! [X2,X0,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(X4,X2,X0) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f599,axiom,
! [X2,X0,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(X4,X2,X0) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f4046,plain,
( spl0_420
| ~ spl0_194
| ~ spl0_399 ),
inference(avatar_split_clause,[],[f4001,f3952,f2087,f4044]) ).
fof(f3952,plain,
( spl0_399
<=> ! [X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f4001,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) )
| ~ spl0_194
| ~ spl0_399 ),
inference(superposition,[],[f3953,f2088]) ).
fof(f3953,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) )
| ~ spl0_399 ),
inference(avatar_component_clause,[],[f3952]) ).
fof(f4042,plain,
spl0_419,
inference(avatar_split_clause,[],[f591,f4040]) ).
fof(f4040,plain,
( spl0_419
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f591,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
fof(f4038,plain,
spl0_418,
inference(avatar_split_clause,[],[f589,f4036]) ).
fof(f4036,plain,
( spl0_418
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f589,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
fof(f4034,plain,
spl0_417,
inference(avatar_split_clause,[],[f588,f4032]) ).
fof(f4032,plain,
( spl0_417
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f588,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
fof(f4030,plain,
spl0_416,
inference(avatar_split_clause,[],[f586,f4028]) ).
fof(f4028,plain,
( spl0_416
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f586,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
fof(f4026,plain,
spl0_415,
inference(avatar_split_clause,[],[f572,f4024]) ).
fof(f4024,plain,
( spl0_415
<=> ! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f572,axiom,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__add__one__is__two_0) ).
fof(f4022,plain,
spl0_414,
inference(avatar_split_clause,[],[f521,f4019]) ).
fof(f4019,plain,
( spl0_414
<=> c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f521,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__pi__half__less__zero_0) ).
fof(f4017,plain,
spl0_413,
inference(avatar_split_clause,[],[f474,f4015]) ).
fof(f4015,plain,
( spl0_413
<=> ! [X6,X4] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f474,axiom,
! [X6,X4] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__add__iff_1) ).
fof(f4013,plain,
spl0_412,
inference(avatar_split_clause,[],[f473,f4011]) ).
fof(f473,axiom,
! [X6,X4] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__add__iff_0) ).
fof(f4009,plain,
spl0_411,
inference(avatar_split_clause,[],[f468,f4007]) ).
fof(f468,axiom,
! [X6,X4] : c_lessequals(X4,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__real__sqrt__sumsq_0) ).
fof(f4005,plain,
spl0_410,
inference(avatar_split_clause,[],[f435,f4003]) ).
fof(f435,axiom,
! [X0,X8,X6,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X8,X0)
| c_HOL_Oord__class_Oless(X4,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f3994,plain,
spl0_409,
inference(avatar_split_clause,[],[f434,f3992]) ).
fof(f434,axiom,
! [X0,X8,X6,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X4,X0)
| ~ c_HOL_Oord__class_Oless(X8,X6,X0)
| c_HOL_Oord__class_Oless(X8,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f3990,plain,
spl0_408,
inference(avatar_split_clause,[],[f429,f3988]) ).
fof(f3988,plain,
( spl0_408
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f429,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
fof(f3986,plain,
spl0_407,
inference(avatar_split_clause,[],[f428,f3984]) ).
fof(f3984,plain,
( spl0_407
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f428,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
fof(f3982,plain,
spl0_406,
inference(avatar_split_clause,[],[f426,f3980]) ).
fof(f3980,plain,
( spl0_406
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f426,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
fof(f3978,plain,
spl0_405,
inference(avatar_split_clause,[],[f425,f3976]) ).
fof(f3976,plain,
( spl0_405
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f425,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
fof(f3974,plain,
spl0_404,
inference(avatar_split_clause,[],[f417,f3972]) ).
fof(f3972,plain,
( spl0_404
<=> ! [X6,X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f417,axiom,
! [X6,X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__self__sum__ge__zero_0) ).
fof(f3970,plain,
spl0_403,
inference(avatar_split_clause,[],[f409,f3968]) ).
fof(f3968,plain,
( spl0_403
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f409,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
fof(f3966,plain,
spl0_402,
inference(avatar_split_clause,[],[f408,f3964]) ).
fof(f3964,plain,
( spl0_402
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f408,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
fof(f3962,plain,
spl0_401,
inference(avatar_split_clause,[],[f393,f3960]) ).
fof(f3960,plain,
( spl0_401
<=> ! [X6,X4,X8] :
( ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X4,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X8,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f393,axiom,
! [X8,X6,X4] :
( ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X4,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X8,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__left__mono_0) ).
fof(f3958,plain,
spl0_400,
inference(avatar_split_clause,[],[f386,f3956]) ).
fof(f386,axiom,
! [X6,X4] :
( ~ c_lessequals(X6,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__le__0__iff_1) ).
fof(f3954,plain,
( spl0_399
| ~ spl0_318
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f3310,f3256,f3097,f3952]) ).
fof(f3310,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) )
| ~ spl0_318
| ~ spl0_336 ),
inference(resolution,[],[f3257,f3098]) ).
fof(f3950,plain,
spl0_398,
inference(avatar_split_clause,[],[f385,f3948]) ).
fof(f3948,plain,
( spl0_398
<=> ! [X6,X4] :
( c_lessequals(X6,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f385,axiom,
! [X6,X4] :
( c_lessequals(X6,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__le__0__iff_0) ).
fof(f3946,plain,
spl0_397,
inference(avatar_split_clause,[],[f381,f3944]) ).
fof(f3944,plain,
( spl0_397
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f381,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
fof(f3942,plain,
spl0_396,
inference(avatar_split_clause,[],[f380,f3940]) ).
fof(f3940,plain,
( spl0_396
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f380,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
fof(f3938,plain,
spl0_395,
inference(avatar_split_clause,[],[f321,f3936]) ).
fof(f3936,plain,
( spl0_395
<=> ! [X6] : c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Oarctan(X6),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f321,axiom,
! [X6] : c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Oarctan(X6),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan_0) ).
fof(f3934,plain,
spl0_394,
inference(avatar_split_clause,[],[f264,f3932]) ).
fof(f264,axiom,
! [X6,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__less__add__iff_0) ).
fof(f3930,plain,
spl0_393,
inference(avatar_split_clause,[],[f263,f3928]) ).
fof(f3928,plain,
( spl0_393
<=> ! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f263,axiom,
! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__less__add__iff_1) ).
fof(f3926,plain,
spl0_392,
inference(avatar_split_clause,[],[f247,f3924]) ).
fof(f3924,plain,
( spl0_392
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X1 = X3
| c_HOL_Oplus__class_Oplus(X2,X3,X0) != c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f247,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X1 = X3
| c_HOL_Oplus__class_Oplus(X2,X3,X0) != c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f3922,plain,
spl0_391,
inference(avatar_split_clause,[],[f246,f3920]) ).
fof(f3920,plain,
( spl0_391
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X3
| c_HOL_Oplus__class_Oplus(X2,X3,X0) != c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f246,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X3
| c_HOL_Oplus__class_Oplus(X2,X3,X0) != c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f3918,plain,
spl0_390,
inference(avatar_split_clause,[],[f245,f3916]) ).
fof(f3916,plain,
( spl0_390
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X3
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f245,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X3
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X3,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f3914,plain,
spl0_389,
inference(avatar_split_clause,[],[f241,f3912]) ).
fof(f3912,plain,
( spl0_389
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f241,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
fof(f3901,plain,
spl0_388,
inference(avatar_split_clause,[],[f240,f3899]) ).
fof(f3899,plain,
( spl0_388
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f240,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
fof(f3897,plain,
spl0_387,
inference(avatar_split_clause,[],[f222,f3895]) ).
fof(f3895,plain,
( spl0_387
<=> ! [X6,X4] :
( c_HOL_Oord__class_Oless(X6,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f222,axiom,
! [X6,X4] :
( c_HOL_Oord__class_Oless(X6,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__less__0__iff_0) ).
fof(f3893,plain,
spl0_386,
inference(avatar_split_clause,[],[f221,f3891]) ).
fof(f3891,plain,
( spl0_386
<=> ! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f221,axiom,
! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__less__0__iff_1) ).
fof(f3889,plain,
spl0_385,
inference(avatar_split_clause,[],[f210,f3887]) ).
fof(f3887,plain,
( spl0_385
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f210,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
fof(f3885,plain,
spl0_384,
inference(avatar_split_clause,[],[f209,f3883]) ).
fof(f3883,plain,
( spl0_384
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X3,X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f209,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X3,X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
fof(f3881,plain,
spl0_383,
inference(avatar_split_clause,[],[f204,f3879]) ).
fof(f3879,plain,
( spl0_383
<=> ! [X6,X4,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X6,X0)
| c_lessequals(X6,X4,X0)
| c_HOL_Oord__class_Oless(X4,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f204,axiom,
! [X0,X6,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X6,X0)
| c_lessequals(X6,X4,X0)
| c_HOL_Oord__class_Oless(X4,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f3877,plain,
spl0_382,
inference(avatar_split_clause,[],[f180,f3875]) ).
fof(f3875,plain,
( spl0_382
<=> ! [X4,X0,X6,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X8,X0)
| c_HOL_Oord__class_Oless(X4,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f180,axiom,
! [X0,X8,X6,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X8,X0)
| c_HOL_Oord__class_Oless(X4,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f3873,plain,
spl0_381,
inference(avatar_split_clause,[],[f155,f3871]) ).
fof(f3871,plain,
( spl0_381
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f155,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
fof(f3869,plain,
spl0_380,
inference(avatar_split_clause,[],[f154,f3867]) ).
fof(f3867,plain,
( spl0_380
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f154,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
fof(f3865,plain,
spl0_379,
inference(avatar_split_clause,[],[f153,f3863]) ).
fof(f3863,plain,
( spl0_379
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f153,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
fof(f3852,plain,
spl0_378,
inference(avatar_split_clause,[],[f152,f3850]) ).
fof(f3850,plain,
( spl0_378
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f152,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
fof(f3848,plain,
spl0_377,
inference(avatar_split_clause,[],[f79,f3846]) ).
fof(f3846,plain,
( spl0_377
<=> ! [X4,X0,X6,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X6,X8,X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| c_HOL_Oord__class_Oless(X4,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f79,axiom,
! [X0,X8,X6,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X6,X8,X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| c_HOL_Oord__class_Oless(X4,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f3844,plain,
spl0_376,
inference(avatar_split_clause,[],[f77,f3842]) ).
fof(f3842,plain,
( spl0_376
<=> ! [X4,X0,X6,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X6,X0)
| ~ c_lessequals(X6,X8,X0)
| c_lessequals(X4,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f77,axiom,
! [X0,X8,X6,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X4,X6,X0)
| ~ c_lessequals(X6,X8,X0)
| c_lessequals(X4,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f3840,plain,
spl0_375,
inference(avatar_split_clause,[],[f75,f3838]) ).
fof(f75,axiom,
! [X0,X8,X6,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X6,X4,X0)
| ~ c_HOL_Oord__class_Oless(X8,X6,X0)
| c_HOL_Oord__class_Oless(X8,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f3836,plain,
spl0_374,
inference(avatar_split_clause,[],[f74,f3834]) ).
fof(f74,axiom,
! [X0,X8,X6,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X8,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X4,X0)
| c_HOL_Oord__class_Oless(X8,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f3832,plain,
spl0_373,
inference(avatar_split_clause,[],[f73,f3830]) ).
fof(f73,axiom,
! [X0,X8,X6,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X6,X4,X0)
| ~ c_lessequals(X8,X6,X0)
| c_lessequals(X8,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f3828,plain,
spl0_372,
inference(avatar_split_clause,[],[f72,f3826]) ).
fof(f3826,plain,
( spl0_372
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(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_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f72,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(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_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
fof(f3824,plain,
spl0_371,
inference(avatar_split_clause,[],[f71,f3822]) ).
fof(f3822,plain,
( spl0_371
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(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_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f71,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(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_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
fof(f3808,plain,
( spl0_370
| ~ spl0_284
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f3408,f3361,f2745,f3806]) ).
fof(f3806,plain,
( spl0_370
<=> ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f3361,plain,
( spl0_345
<=> ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f3408,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_284
| ~ spl0_345 ),
inference(resolution,[],[f3362,f2746]) ).
fof(f3362,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_345 ),
inference(avatar_component_clause,[],[f3361]) ).
fof(f3647,plain,
( spl0_369
| ~ spl0_291
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f3407,f3361,f2776,f3645]) ).
fof(f3645,plain,
( spl0_369
<=> ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f3407,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X0),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_291
| ~ spl0_345 ),
inference(resolution,[],[f3362,f2777]) ).
fof(f3468,plain,
spl0_368,
inference(avatar_split_clause,[],[f1101,f3465]) ).
fof(f3465,plain,
( spl0_368
<=> c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f1101,plain,
c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
inference(forward_demodulation,[],[f509,f868]) ).
fof(f509,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_m2pi__less__pi_0) ).
fof(f3463,plain,
spl0_367,
inference(avatar_split_clause,[],[f821,f3461]) ).
fof(f3461,plain,
( spl0_367
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f821,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oinverse__class_Odivide(X4,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__Numeral1_0) ).
fof(f3459,plain,
( spl0_366
| ~ spl0_280
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f3309,f3256,f2729,f3457]) ).
fof(f3457,plain,
( spl0_366
<=> ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f3309,plain,
( ! [X0] :
( c_lessequals(c_NthRoot_Osqrt(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_280
| ~ spl0_336 ),
inference(resolution,[],[f3257,f2730]) ).
fof(f3455,plain,
spl0_365,
inference(avatar_split_clause,[],[f734,f3453]) ).
fof(f3453,plain,
( spl0_365
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f734,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X2,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self_0) ).
fof(f3451,plain,
spl0_364,
inference(avatar_split_clause,[],[f696,f3448]) ).
fof(f3448,plain,
( spl0_364
<=> c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Oarctan(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f3446,plain,
spl0_363,
inference(avatar_split_clause,[],[f598,f3444]) ).
fof(f3444,plain,
( spl0_363
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f598,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X2,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
fof(f3442,plain,
spl0_362,
inference(avatar_split_clause,[],[f582,f3440]) ).
fof(f3440,plain,
( spl0_362
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0) = c_HOL_Ominus__class_Ominus(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f582,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,X0),X0) = c_HOL_Ominus__class_Ominus(X3,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
fof(f3438,plain,
spl0_361,
inference(avatar_split_clause,[],[f472,f3436]) ).
fof(f472,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X2,X3,X0) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
fof(f3434,plain,
spl0_360,
inference(avatar_split_clause,[],[f402,f3432]) ).
fof(f3432,plain,
( spl0_360
<=> ! [X6,X4,X0] :
( ~ class_Orderings_Oorder(X0)
| X4 = X6
| ~ c_lessequals(X4,X6,X0)
| ~ c_lessequals(X6,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f402,axiom,
! [X0,X6,X4] :
( ~ class_Orderings_Oorder(X0)
| X4 = X6
| ~ c_lessequals(X4,X6,X0)
| ~ c_lessequals(X6,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
fof(f3430,plain,
spl0_359,
inference(avatar_split_clause,[],[f401,f3428]) ).
fof(f3428,plain,
( spl0_359
<=> ! [X6,X4,X0] :
( ~ class_Orderings_Olinorder(X0)
| X4 = X6
| c_HOL_Oord__class_Oless(X4,X6,X0)
| c_HOL_Oord__class_Oless(X6,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f401,axiom,
! [X0,X6,X4] :
( ~ class_Orderings_Olinorder(X0)
| X4 = X6
| c_HOL_Oord__class_Oless(X4,X6,X0)
| c_HOL_Oord__class_Oless(X6,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
fof(f3426,plain,
spl0_358,
inference(avatar_split_clause,[],[f395,f3424]) ).
fof(f3424,plain,
( spl0_358
<=> ! [X6,X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X4 = X6
| c_HOL_Oord__class_Oless(X4,X6,X0)
| c_HOL_Oord__class_Oless(X6,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f395,axiom,
! [X0,X6,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X4 = X6
| c_HOL_Oord__class_Oless(X4,X6,X0)
| c_HOL_Oord__class_Oless(X6,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f3422,plain,
spl0_357,
inference(avatar_split_clause,[],[f323,f3419]) ).
fof(f323,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/sandbox/benchmark/theBenchmark.p',cls_real__mult__is__one_2) ).
fof(f3417,plain,
spl0_356,
inference(avatar_split_clause,[],[f279,f3415]) ).
fof(f3415,plain,
( spl0_356
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f279,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
fof(f3403,plain,
spl0_355,
inference(avatar_split_clause,[],[f270,f3401]) ).
fof(f3401,plain,
( spl0_355
<=> ! [X2,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| X2 = X3
| ~ c_lessequals(X2,X3,X0)
| c_HOL_Oord__class_Oless(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f270,axiom,
! [X2,X3,X0] :
( ~ class_Orderings_Oorder(X0)
| X2 = X3
| ~ c_lessequals(X2,X3,X0)
| c_HOL_Oord__class_Oless(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
fof(f3399,plain,
spl0_354,
inference(avatar_split_clause,[],[f267,f3397]) ).
fof(f3397,plain,
( spl0_354
<=> ! [X6,X4,X0] :
( ~ class_Orderings_Olinorder(X0)
| X4 = X6
| ~ c_lessequals(X4,X6,X0)
| c_HOL_Oord__class_Oless(X4,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f267,axiom,
! [X0,X6,X4] :
( ~ class_Orderings_Olinorder(X0)
| X4 = X6
| ~ c_lessequals(X4,X6,X0)
| c_HOL_Oord__class_Oless(X4,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f3395,plain,
spl0_353,
inference(avatar_split_clause,[],[f253,f3393]) ).
fof(f3393,plain,
( spl0_353
<=> ! [X6,X4,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X4,X6,X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f253,axiom,
! [X0,X6,X4] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X4,X6,X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
fof(f3391,plain,
spl0_352,
inference(avatar_split_clause,[],[f252,f3389]) ).
fof(f3389,plain,
( spl0_352
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X3,X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f252,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X3,X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).
fof(f3387,plain,
spl0_351,
inference(avatar_split_clause,[],[f251,f3385]) ).
fof(f3385,plain,
( spl0_351
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X3,X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f251,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X3,X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
fof(f3383,plain,
spl0_350,
inference(avatar_split_clause,[],[f230,f3381]) ).
fof(f3381,plain,
( spl0_350
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f230,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
fof(f3379,plain,
spl0_349,
inference(avatar_split_clause,[],[f229,f3377]) ).
fof(f3377,plain,
( spl0_349
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f229,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
fof(f3375,plain,
spl0_348,
inference(avatar_split_clause,[],[f228,f3373]) ).
fof(f3373,plain,
( spl0_348
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f228,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
fof(f3371,plain,
spl0_347,
inference(avatar_split_clause,[],[f227,f3369]) ).
fof(f3369,plain,
( spl0_347
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f227,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
fof(f3367,plain,
spl0_346,
inference(avatar_split_clause,[],[f226,f3365]) ).
fof(f3365,plain,
( spl0_346
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f226,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
fof(f3363,plain,
( spl0_345
| ~ spl0_177
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f3306,f3256,f1999,f3361]) ).
fof(f3306,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_177
| ~ spl0_336 ),
inference(resolution,[],[f3257,f2000]) ).
fof(f3359,plain,
spl0_344,
inference(avatar_split_clause,[],[f225,f3357]) ).
fof(f3357,plain,
( spl0_344
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f225,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
fof(f3355,plain,
spl0_343,
inference(avatar_split_clause,[],[f224,f3353]) ).
fof(f3353,plain,
( spl0_343
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f224,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
fof(f3351,plain,
spl0_342,
inference(avatar_split_clause,[],[f223,f3349]) ).
fof(f3349,plain,
( spl0_342
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f223,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
fof(f3347,plain,
spl0_341,
inference(avatar_split_clause,[],[f198,f3345]) ).
fof(f3345,plain,
( spl0_341
<=> ! [X6,X0,X8] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X0),c_HOL_Oplus__class_Oplus(X6,X8,X0),X0) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f198,axiom,
! [X0,X8,X6] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X0),c_HOL_Oplus__class_Oplus(X6,X8,X0),X0) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
fof(f3343,plain,
spl0_340,
inference(avatar_split_clause,[],[f197,f3341]) ).
fof(f3341,plain,
( spl0_340
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f197,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
fof(f3339,plain,
spl0_339,
inference(avatar_split_clause,[],[f147,f3337]) ).
fof(f3337,plain,
( spl0_339
<=> ! [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_339])]) ).
fof(f147,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/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
fof(f3335,plain,
spl0_338,
inference(avatar_split_clause,[],[f70,f3333]) ).
fof(f3333,plain,
( spl0_338
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f70,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
fof(f3331,plain,
spl0_337,
inference(avatar_split_clause,[],[f69,f3329]) ).
fof(f3329,plain,
( spl0_337
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f69,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
fof(f3258,plain,
( spl0_336
| ~ spl0_297
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f3184,f3076,f2800,f3256]) ).
fof(f3076,plain,
( spl0_313
<=> ! [X13,X14,X15] :
( ~ c_lessequals(X13,X15,tc_RealDef_Oreal)
| ~ c_lessequals(X15,X14,tc_RealDef_Oreal)
| c_lessequals(X13,X14,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f3184,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_297
| ~ spl0_313 ),
inference(resolution,[],[f3077,f2802]) ).
fof(f3077,plain,
( ! [X14,X15,X13] :
( ~ c_lessequals(X15,X14,tc_RealDef_Oreal)
| ~ c_lessequals(X13,X15,tc_RealDef_Oreal)
| c_lessequals(X13,X14,tc_RealDef_Oreal) )
| ~ spl0_313 ),
inference(avatar_component_clause,[],[f3076]) ).
fof(f3172,plain,
spl0_335,
inference(avatar_split_clause,[],[f1122,f3170]) ).
fof(f1122,plain,
! [X18,X19] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X19,X18,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X18,X19,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f249,f255]) ).
fof(f255,axiom,
! [X10,X20] : c_HOL_Ominus__class_Ominus(X10,X20,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Ouminus__class_Ouminus(X20,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__diff__def_0) ).
fof(f249,axiom,
! [X18,X19] :
( c_HOL_Oord__class_Oless(X18,X19,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X19,c_HOL_Ouminus__class_Ouminus(X18,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__gt__zero__less_0) ).
fof(f3168,plain,
spl0_334,
inference(avatar_split_clause,[],[f1121,f3166]) ).
fof(f3166,plain,
( spl0_334
<=> ! [X18,X19] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X19,X18,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X18,X19,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f1121,plain,
! [X18,X19] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X19,X18,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X18,X19,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f250,f255]) ).
fof(f250,axiom,
! [X18,X19] :
( ~ c_HOL_Oord__class_Oless(X18,X19,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X19,c_HOL_Ouminus__class_Ouminus(X18,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__sum__gt__zero_0) ).
fof(f3164,plain,
spl0_333,
inference(avatar_split_clause,[],[f1097,f3161]) ).
fof(f3161,plain,
( spl0_333
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f1097,plain,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f716,f868]) ).
fof(f716,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__two__pi_0) ).
fof(f3159,plain,
spl0_332,
inference(avatar_split_clause,[],[f790,f3157]) ).
fof(f3157,plain,
( spl0_332
<=> ! [X0,X3] :
( ~ 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(X3,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f790,axiom,
! [X3,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(X3,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
fof(f3155,plain,
spl0_331,
inference(avatar_split_clause,[],[f763,f3153]) ).
fof(f3153,plain,
( spl0_331
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X2 = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f763,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X2 = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f3151,plain,
spl0_330,
inference(avatar_split_clause,[],[f762,f3149]) ).
fof(f3149,plain,
( spl0_330
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X2 = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f762,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X2 = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f3147,plain,
spl0_329,
inference(avatar_split_clause,[],[f744,f3145]) ).
fof(f3145,plain,
( spl0_329
<=> ! [X6,X4] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X4,X6,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f744,axiom,
! [X6,X4] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X4,X6,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__mult_0) ).
fof(f3143,plain,
spl0_328,
inference(avatar_split_clause,[],[f742,f3141]) ).
fof(f742,axiom,
! [X6,X4] : c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(X4,X6,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__divide_0) ).
fof(f3139,plain,
spl0_327,
inference(avatar_split_clause,[],[f711,f3136]) ).
fof(f711,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__pi__half_0) ).
fof(f3134,plain,
spl0_326,
inference(avatar_split_clause,[],[f693,f3131]) ).
fof(f3131,plain,
( spl0_326
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f693,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__gt__zero_0) ).
fof(f3129,plain,
( ~ spl0_117
| ~ spl0_325
| ~ spl0_240
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f2980,f2905,f2359,f3126,f1711]) ).
fof(f3126,plain,
( spl0_325
<=> c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f2980,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl0_240
| ~ spl0_311 ),
inference(resolution,[],[f2907,f2360]) ).
fof(f3124,plain,
spl0_324,
inference(avatar_split_clause,[],[f692,f3121]) ).
fof(f3121,plain,
( spl0_324
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f692,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__ge__zero_0) ).
fof(f3119,plain,
spl0_323,
inference(avatar_split_clause,[],[f597,f3117]) ).
fof(f3117,plain,
( spl0_323
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f597,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
fof(f3115,plain,
spl0_322,
inference(avatar_split_clause,[],[f511,f3113]) ).
fof(f3113,plain,
( spl0_322
<=> ! [X6] : c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(X6),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f511,axiom,
! [X6] : c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(X6),c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan_1) ).
fof(f3111,plain,
spl0_321,
inference(avatar_split_clause,[],[f467,f3109]) ).
fof(f3109,plain,
( spl0_321
<=> ! [X4,X17] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X17,X17,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_321])]) ).
fof(f467,axiom,
! [X4,X17] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X17,X17,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__minus__mult__self__le_0) ).
fof(f3107,plain,
spl0_320,
inference(avatar_split_clause,[],[f416,f3105]) ).
fof(f3105,plain,
( spl0_320
<=> ! [X4,X2] :
( X2 = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f416,axiom,
! [X2,X4] :
( X2 = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__minus__iff_0) ).
fof(f3103,plain,
spl0_319,
inference(avatar_split_clause,[],[f405,f3101]) ).
fof(f3101,plain,
( spl0_319
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X2 = X3
| c_HOL_Ouminus__class_Ouminus(X2,X0) != c_HOL_Ouminus__class_Ouminus(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f405,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X2 = X3
| c_HOL_Ouminus__class_Ouminus(X2,X0) != c_HOL_Ouminus__class_Ouminus(X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f3099,plain,
spl0_318,
inference(avatar_split_clause,[],[f332,f3097]) ).
fof(f332,axiom,
! [X6,X4] :
( ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__eq__diff_0) ).
fof(f3095,plain,
spl0_317,
inference(avatar_split_clause,[],[f331,f3093]) ).
fof(f3093,plain,
( spl0_317
<=> ! [X6,X4] :
( c_lessequals(X4,X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f331,axiom,
! [X6,X4] :
( c_lessequals(X4,X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X4,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__eq__diff_1) ).
fof(f3091,plain,
spl0_316,
inference(avatar_split_clause,[],[f311,f3089]) ).
fof(f3089,plain,
( spl0_316
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f311,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/sandbox/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_0) ).
fof(f3087,plain,
spl0_315,
inference(avatar_split_clause,[],[f259,f3085]) ).
fof(f3085,plain,
( spl0_315
<=> ! [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_315])]) ).
fof(f259,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f3082,plain,
spl0_314,
inference(avatar_split_clause,[],[f211,f3080]) ).
fof(f3080,plain,
( spl0_314
<=> ! [X6,X4] :
( c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal) = X6
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f211,axiom,
! [X6,X4] :
( c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal) = X6
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(X4,X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__eq__0__iff_0) ).
fof(f3078,plain,
spl0_313,
inference(avatar_split_clause,[],[f182,f3076]) ).
fof(f182,axiom,
! [X14,X15,X13] :
( ~ c_lessequals(X13,X15,tc_RealDef_Oreal)
| ~ c_lessequals(X15,X14,tc_RealDef_Oreal)
| c_lessequals(X13,X14,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f3048,plain,
( ~ spl0_312
| ~ spl0_119
| ~ spl0_221
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f2975,f2905,f2282,f1721,f3045]) ).
fof(f3045,plain,
( spl0_312
<=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f2975,plain,
( ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_221
| ~ spl0_311 ),
inference(resolution,[],[f2907,f2283]) ).
fof(f2908,plain,
( spl0_311
| spl0_158
| ~ spl0_279
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f2881,f2800,f2725,f1913,f2905]) ).
fof(f2725,plain,
( spl0_279
<=> ! [X6,X4] :
( X4 = X6
| ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f2881,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_279
| ~ spl0_297 ),
inference(resolution,[],[f2726,f2802]) ).
fof(f2726,plain,
( ! [X6,X4] :
( ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| X4 = X6
| c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal) )
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f2725]) ).
fof(f2856,plain,
spl0_310,
inference(avatar_split_clause,[],[f869,f2854]) ).
fof(f2854,plain,
( spl0_310
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f869,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f2852,plain,
spl0_309,
inference(avatar_split_clause,[],[f864,f2850]) ).
fof(f2850,plain,
( spl0_309
<=> ! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f864,axiom,
! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__numeral__1__right_0) ).
fof(f2848,plain,
spl0_308,
inference(avatar_split_clause,[],[f863,f2846]) ).
fof(f2846,plain,
( spl0_308
<=> ! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f863,axiom,
! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X2,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__numeral__1_0) ).
fof(f2844,plain,
spl0_307,
inference(avatar_split_clause,[],[f764,f2842]) ).
fof(f2842,plain,
( spl0_307
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f764,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f2840,plain,
~ spl0_306,
inference(avatar_split_clause,[],[f717,f2837]) ).
fof(f2837,plain,
( spl0_306
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f717,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__neq__zero_0) ).
fof(f2835,plain,
spl0_305,
inference(avatar_split_clause,[],[f605,f2833]) ).
fof(f2833,plain,
( spl0_305
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f605,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f2831,plain,
spl0_304,
inference(avatar_split_clause,[],[f600,f2829]) ).
fof(f2829,plain,
( spl0_304
<=> ! [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_304])]) ).
fof(f600,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/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f2827,plain,
spl0_303,
inference(avatar_split_clause,[],[f596,f2825]) ).
fof(f2825,plain,
( spl0_303
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f596,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f2823,plain,
spl0_302,
inference(avatar_split_clause,[],[f475,f2821]) ).
fof(f2821,plain,
( spl0_302
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X3,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f475,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X3,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f2819,plain,
spl0_301,
inference(avatar_split_clause,[],[f461,f2817]) ).
fof(f2817,plain,
( spl0_301
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f461,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).
fof(f2815,plain,
spl0_300,
inference(avatar_split_clause,[],[f460,f2813]) ).
fof(f2813,plain,
( spl0_300
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f460,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
fof(f2811,plain,
spl0_299,
inference(avatar_split_clause,[],[f459,f2809]) ).
fof(f2809,plain,
( spl0_299
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f459,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
fof(f2807,plain,
spl0_298,
inference(avatar_split_clause,[],[f431,f2805]) ).
fof(f2805,plain,
( spl0_298
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X0),X3,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f431,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X0),X3,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f2803,plain,
( spl0_297
| ~ spl0_166
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f2757,f2712,f1946,f2800]) ).
fof(f1946,plain,
( spl0_166
<=> ! [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_166])]) ).
fof(f2757,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_166
| ~ spl0_276 ),
inference(superposition,[],[f1947,f2714]) ).
fof(f1947,plain,
( ! [X4] : c_lessequals(c_Transcendental_Ocos(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1946]) ).
fof(f2798,plain,
spl0_296,
inference(avatar_split_clause,[],[f403,f2796]) ).
fof(f2796,plain,
( spl0_296
<=> ! [X8,X7] :
( X7 = X8
| ~ c_lessequals(X8,X7,tc_RealDef_Oreal)
| ~ c_lessequals(X7,X8,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f403,axiom,
! [X8,X7] :
( X7 = X8
| ~ c_lessequals(X8,X7,tc_RealDef_Oreal)
| ~ c_lessequals(X7,X8,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f2794,plain,
spl0_295,
inference(avatar_split_clause,[],[f355,f2792]) ).
fof(f355,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/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__1__iff_0) ).
fof(f2790,plain,
spl0_294,
inference(avatar_split_clause,[],[f354,f2788]) ).
fof(f2788,plain,
( spl0_294
<=> ! [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_294])]) ).
fof(f354,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/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__1__iff_1) ).
fof(f2786,plain,
spl0_293,
inference(avatar_split_clause,[],[f352,f2784]) ).
fof(f2784,plain,
( spl0_293
<=> ! [X6] :
( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f352,axiom,
! [X6] :
( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__1__iff_0) ).
fof(f2782,plain,
spl0_292,
inference(avatar_split_clause,[],[f351,f2780]) ).
fof(f351,axiom,
! [X6] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__1__iff_1) ).
fof(f2778,plain,
spl0_291,
inference(avatar_split_clause,[],[f350,f2776]) ).
fof(f350,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/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__1__iff_0) ).
fof(f2774,plain,
spl0_290,
inference(avatar_split_clause,[],[f349,f2772]) ).
fof(f2772,plain,
( spl0_290
<=> ! [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_290])]) ).
fof(f349,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/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__1__iff_1) ).
fof(f2770,plain,
spl0_289,
inference(avatar_split_clause,[],[f348,f2768]) ).
fof(f2768,plain,
( spl0_289
<=> ! [X6] :
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f348,axiom,
! [X6] :
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__1__iff_0) ).
fof(f2766,plain,
spl0_288,
inference(avatar_split_clause,[],[f347,f2764]) ).
fof(f347,axiom,
! [X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__1__iff_1) ).
fof(f2762,plain,
spl0_287,
inference(avatar_split_clause,[],[f343,f2760]) ).
fof(f2760,plain,
( spl0_287
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f343,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/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__zero_0) ).
fof(f2755,plain,
spl0_286,
inference(avatar_split_clause,[],[f342,f2753]) ).
fof(f342,axiom,
! [X6] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__0__iff_0) ).
fof(f2751,plain,
spl0_285,
inference(avatar_split_clause,[],[f340,f2749]) ).
fof(f2749,plain,
( spl0_285
<=> ! [X4] :
( ~ 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_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f340,axiom,
! [X4] :
( ~ 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_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__zero_0) ).
fof(f2747,plain,
spl0_284,
inference(avatar_split_clause,[],[f339,f2745]) ).
fof(f339,axiom,
! [X6] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__0__iff_0) ).
fof(f2743,plain,
spl0_283,
inference(avatar_split_clause,[],[f336,f2741]) ).
fof(f2741,plain,
( spl0_283
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f336,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/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_0) ).
fof(f2739,plain,
spl0_282,
inference(avatar_split_clause,[],[f335,f2737]) ).
fof(f335,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/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_1) ).
fof(f2735,plain,
spl0_281,
inference(avatar_split_clause,[],[f334,f2733]) ).
fof(f2733,plain,
( spl0_281
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f334,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/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_0) ).
fof(f2731,plain,
spl0_280,
inference(avatar_split_clause,[],[f333,f2729]) ).
fof(f333,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/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_1) ).
fof(f2727,plain,
spl0_279,
inference(avatar_split_clause,[],[f271,f2725]) ).
fof(f271,axiom,
! [X6,X4] :
( X4 = X6
| ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_2) ).
fof(f2723,plain,
spl0_278,
inference(avatar_split_clause,[],[f255,f2721]) ).
fof(f2721,plain,
( spl0_278
<=> ! [X20,X10] : c_HOL_Ominus__class_Ominus(X10,X20,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Ouminus__class_Ouminus(X20,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f2719,plain,
spl0_277,
inference(avatar_split_clause,[],[f217,f2717]) ).
fof(f2717,plain,
( spl0_277
<=> ! [X6,X4,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X4,X6,X0) = c_HOL_Oplus__class_Oplus(X6,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f217,axiom,
! [X0,X6,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X4,X6,X0) = c_HOL_Oplus__class_Oplus(X6,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
fof(f2715,plain,
( spl0_276
| ~ spl0_253
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2702,f2691,f2416,f2712]) ).
fof(f2416,plain,
( spl0_253
<=> ! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X2
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f2702,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal))
| ~ spl0_253
| ~ spl0_273 ),
inference(trivial_inequality_removal,[],[f2699]) ).
fof(f2699,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal))
| ~ spl0_253
| ~ spl0_273 ),
inference(superposition,[],[f2417,f2693]) ).
fof(f2417,plain,
( ! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(X2,X3)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X2 )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f2416]) ).
fof(f2710,plain,
spl0_275,
inference(avatar_split_clause,[],[f216,f2708]) ).
fof(f216,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,X3,X0) = c_HOL_Oplus__class_Oplus(X3,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f2706,plain,
spl0_274,
inference(avatar_split_clause,[],[f151,f2704]) ).
fof(f2704,plain,
( spl0_274
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f151,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
fof(f2694,plain,
( spl0_273
| ~ spl0_220
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2689,f2685,f2195,f2691]) ).
fof(f2685,plain,
( spl0_272
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f2689,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)))
| ~ spl0_220
| ~ spl0_272 ),
inference(forward_demodulation,[],[f2687,f2196]) ).
fof(f2687,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)))
| ~ spl0_272 ),
inference(avatar_component_clause,[],[f2685]) ).
fof(f2688,plain,
spl0_272,
inference(avatar_split_clause,[],[f1032,f2685]) ).
fof(f1032,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal))),
inference(definition_unfolding,[],[f880,f786]) ).
fof(f880,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2672,plain,
( spl0_271
| ~ spl0_26
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2215,f2113,f1256,f2670]) ).
fof(f2670,plain,
( spl0_271
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f1256,plain,
( spl0_26
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f2113,plain,
( spl0_200
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f2215,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_26
| ~ spl0_200 ),
inference(resolution,[],[f2114,f1258]) ).
fof(f1258,plain,
( class_OrderedGroup_Omonoid__add(tc_nat)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f1256]) ).
fof(f2114,plain,
( ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 )
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f2113]) ).
fof(f2640,plain,
( spl0_270
| ~ spl0_142
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2214,f2104,f1836,f2637]) ).
fof(f2637,plain,
( spl0_270
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f1836,plain,
( spl0_142
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f2104,plain,
( spl0_198
<=> ! [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_198])]) ).
fof(f2214,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_142
| ~ spl0_198 ),
inference(resolution,[],[f2105,f1838]) ).
fof(f1838,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1836]) ).
fof(f2105,plain,
( ! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f2104]) ).
fof(f2504,plain,
( spl0_269
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2489,f2294,f2502]) ).
fof(f2502,plain,
( spl0_269
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f2294,plain,
( spl0_224
<=> ! [X6,X4,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X6,X0)
| c_lessequals(X6,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f2489,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_224 ),
inference(factoring,[],[f2295]) ).
fof(f2295,plain,
( ! [X0,X6,X4] :
( c_lessequals(X6,X4,X0)
| c_lessequals(X4,X6,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f2294]) ).
fof(f2480,plain,
spl0_268,
inference(avatar_split_clause,[],[f874,f2478]) ).
fof(f2478,plain,
( spl0_268
<=> ! [X6,X0] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f874,axiom,
! [X0,X6] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
fof(f2476,plain,
spl0_267,
inference(avatar_split_clause,[],[f871,f2474]) ).
fof(f871,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
fof(f2472,plain,
( spl0_266
| ~ spl0_86
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2211,f2100,f1556,f2469]) ).
fof(f1556,plain,
( spl0_86
<=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f2100,plain,
( spl0_197
<=> ! [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_197])]) ).
fof(f2211,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_86
| ~ spl0_197 ),
inference(resolution,[],[f2101,f1558]) ).
fof(f1558,plain,
( class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal)
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f1556]) ).
fof(f2101,plain,
( ! [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) )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f2100]) ).
fof(f2467,plain,
spl0_265,
inference(avatar_split_clause,[],[f859,f2465]) ).
fof(f2465,plain,
( spl0_265
<=> ! [X5,X12] :
( X5 = X12
| c_RealDef_Oreal(X5,tc_nat) != c_RealDef_Oreal(X12,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f859,axiom,
! [X5,X12] :
( X5 = X12
| c_RealDef_Oreal(X5,tc_nat) != c_RealDef_Oreal(X12,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__inject_0) ).
fof(f2463,plain,
spl0_264,
inference(avatar_split_clause,[],[f841,f2461]) ).
fof(f2461,plain,
( spl0_264
<=> ! [X38,X41,X40,X39] :
( X39 = X41
| c_Complex_Ocomplex_OComplex(X38,X39) != c_Complex_Ocomplex_OComplex(X40,X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f841,axiom,
! [X40,X38,X41,X39] :
( X39 = X41
| c_Complex_Ocomplex_OComplex(X38,X39) != c_Complex_Ocomplex_OComplex(X40,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex_Oinject_1) ).
fof(f2459,plain,
spl0_263,
inference(avatar_split_clause,[],[f840,f2457]) ).
fof(f2457,plain,
( spl0_263
<=> ! [X38,X41,X40,X39] :
( X38 = X40
| c_Complex_Ocomplex_OComplex(X38,X39) != c_Complex_Ocomplex_OComplex(X40,X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f840,axiom,
! [X40,X38,X41,X39] :
( X38 = X40
| c_Complex_Ocomplex_OComplex(X38,X39) != c_Complex_Ocomplex_OComplex(X40,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex_Oinject_0) ).
fof(f2455,plain,
spl0_262,
inference(avatar_split_clause,[],[f807,f2453]) ).
fof(f2453,plain,
( spl0_262
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f807,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f2451,plain,
spl0_261,
inference(avatar_split_clause,[],[f805,f2449]) ).
fof(f2449,plain,
( spl0_261
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f805,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
fof(f2447,plain,
spl0_260,
inference(avatar_split_clause,[],[f803,f2445]) ).
fof(f2445,plain,
( spl0_260
<=> ! [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_260])]) ).
fof(f803,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/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
fof(f2443,plain,
spl0_259,
inference(avatar_split_clause,[],[f802,f2441]) ).
fof(f2441,plain,
( spl0_259
<=> ! [X4,X0] :
( ~ 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),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f802,axiom,
! [X0,X4] :
( ~ 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),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
fof(f2439,plain,
spl0_258,
inference(avatar_split_clause,[],[f801,f2437]) ).
fof(f2437,plain,
( spl0_258
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(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_258])]) ).
fof(f801,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f2435,plain,
spl0_257,
inference(avatar_split_clause,[],[f800,f2433]) ).
fof(f2433,plain,
( spl0_257
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f800,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f2431,plain,
spl0_256,
inference(avatar_split_clause,[],[f799,f2429]) ).
fof(f799,axiom,
! [X3,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),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f2427,plain,
( spl0_255
| ~ spl0_43
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2210,f2100,f1341,f2424]) ).
fof(f2424,plain,
( spl0_255
<=> c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f1341,plain,
( spl0_43
<=> class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f2210,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint)
| ~ spl0_43
| ~ spl0_197 ),
inference(resolution,[],[f2101,f1343]) ).
fof(f1343,plain,
( class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f1341]) ).
fof(f2422,plain,
spl0_254,
inference(avatar_split_clause,[],[f798,f2420]) ).
fof(f2420,plain,
( spl0_254
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f798,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f2418,plain,
spl0_253,
inference(avatar_split_clause,[],[f730,f2416]) ).
fof(f730,axiom,
! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X2
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Complex__eq__0_0) ).
fof(f2414,plain,
spl0_252,
inference(avatar_split_clause,[],[f729,f2412]) ).
fof(f729,axiom,
! [X2,X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Complex__eq__0_1) ).
fof(f2410,plain,
spl0_251,
inference(avatar_split_clause,[],[f687,f2407]) ).
fof(f2407,plain,
( spl0_251
<=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f687,axiom,
c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__two__gt__one_0) ).
fof(f2405,plain,
spl0_250,
inference(avatar_split_clause,[],[f684,f2402]) ).
fof(f2402,plain,
( spl0_250
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f684,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__two__ge__zero_0) ).
fof(f2400,plain,
spl0_249,
inference(avatar_split_clause,[],[f683,f2397]) ).
fof(f2397,plain,
( spl0_249
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f683,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__two__gt__zero_0) ).
fof(f2395,plain,
spl0_248,
inference(avatar_split_clause,[],[f681,f2392]) ).
fof(f681,axiom,
c_lessequals(c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__two__le__zero_0) ).
fof(f2390,plain,
spl0_247,
inference(avatar_split_clause,[],[f680,f2387]) ).
fof(f2387,plain,
( spl0_247
<=> c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f680,axiom,
c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__two__less__zero_0) ).
fof(f2385,plain,
spl0_246,
inference(avatar_split_clause,[],[f675,f2383]) ).
fof(f675,axiom,
! [X4] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X4,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(X4),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__periodic__pi_0) ).
fof(f2381,plain,
spl0_245,
inference(avatar_split_clause,[],[f471,f2379]) ).
fof(f2379,plain,
( spl0_245
<=> ! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f471,axiom,
! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_1) ).
fof(f2377,plain,
( spl0_244
| ~ spl0_142
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2209,f2096,f1836,f2375]) ).
fof(f2375,plain,
( spl0_244
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f2096,plain,
( spl0_196
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f2209,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_142
| ~ spl0_196 ),
inference(resolution,[],[f2097,f1838]) ).
fof(f2097,plain,
( ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = X2 )
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f2096]) ).
fof(f2373,plain,
spl0_243,
inference(avatar_split_clause,[],[f470,f2371]) ).
fof(f2371,plain,
( spl0_243
<=> ! [X6,X4] :
( c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f470,axiom,
! [X6,X4] :
( c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_0) ).
fof(f2369,plain,
spl0_242,
inference(avatar_split_clause,[],[f450,f2367]) ).
fof(f2367,plain,
( spl0_242
<=> ! [X6,X4,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X6,X4,X0)
| c_HOL_Oord__class_Oless(X4,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f450,axiom,
! [X0,X6,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X6,X4,X0)
| c_HOL_Oord__class_Oless(X4,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
fof(f2365,plain,
spl0_241,
inference(avatar_split_clause,[],[f449,f2363]) ).
fof(f2363,plain,
( spl0_241
<=> ! [X6,X4,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X6,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f449,axiom,
! [X0,X6,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X6,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
fof(f2361,plain,
spl0_240,
inference(avatar_split_clause,[],[f445,f2359]) ).
fof(f445,axiom,
! [X0,X6,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X6,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f2357,plain,
spl0_239,
inference(avatar_split_clause,[],[f418,f2355]) ).
fof(f2355,plain,
( spl0_239
<=> ! [X6,X4] :
( ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Oarctan(X4),c_Transcendental_Oarctan(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f418,axiom,
! [X6,X4] :
( ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Oarctan(X4),c_Transcendental_Oarctan(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan__monotone_H_0) ).
fof(f2353,plain,
spl0_238,
inference(avatar_split_clause,[],[f382,f2351]) ).
fof(f2351,plain,
( spl0_238
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f382,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f2349,plain,
spl0_237,
inference(avatar_split_clause,[],[f337,f2347]) ).
fof(f2347,plain,
( spl0_237
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f337,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/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__not__eq__zero_0) ).
fof(f2345,plain,
~ spl0_236,
inference(avatar_split_clause,[],[f309,f2342]) ).
fof(f2342,plain,
( spl0_236
<=> 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) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f309,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/sandbox/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_1) ).
fof(f2340,plain,
spl0_235,
inference(avatar_split_clause,[],[f295,f2338]) ).
fof(f2338,plain,
( spl0_235
<=> ! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f295,axiom,
! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X2,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__numeral__0_0) ).
fof(f2336,plain,
spl0_234,
inference(avatar_split_clause,[],[f294,f2334]) ).
fof(f2334,plain,
( spl0_234
<=> ! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f294,axiom,
! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__numeral__0__right_0) ).
fof(f2332,plain,
( spl0_233
| ~ spl0_112
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2208,f2096,f1686,f2330]) ).
fof(f2208,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_112
| ~ spl0_196 ),
inference(resolution,[],[f2097,f1688]) ).
fof(f2328,plain,
spl0_232,
inference(avatar_split_clause,[],[f237,f2326]) ).
fof(f2326,plain,
( spl0_232
<=> ! [X6,X4] :
( ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f237,axiom,
! [X6,X4] :
( ~ c_lessequals(X4,X6,tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_1) ).
fof(f2324,plain,
spl0_231,
inference(avatar_split_clause,[],[f236,f2322]) ).
fof(f2322,plain,
( spl0_231
<=> ! [X6,X4] :
( c_lessequals(X4,X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f236,axiom,
! [X6,X4] :
( c_lessequals(X4,X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_0) ).
fof(f2320,plain,
spl0_230,
inference(avatar_split_clause,[],[f231,f2318]) ).
fof(f2318,plain,
( spl0_230
<=> ! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(X4),c_Transcendental_Oarctan(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f231,axiom,
! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(X4),c_Transcendental_Oarctan(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan__monotone_0) ).
fof(f2316,plain,
spl0_229,
inference(avatar_split_clause,[],[f201,f2314]) ).
fof(f2314,plain,
( spl0_229
<=> ! [X6,X4,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| c_lessequals(X4,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f201,axiom,
! [X0,X6,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| c_lessequals(X4,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f2312,plain,
spl0_228,
inference(avatar_split_clause,[],[f199,f2310]) ).
fof(f2310,plain,
( spl0_228
<=> ! [X6,X4,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| c_lessequals(X4,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f199,axiom,
! [X0,X6,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| c_lessequals(X4,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f2308,plain,
spl0_227,
inference(avatar_split_clause,[],[f99,f2306]) ).
fof(f2306,plain,
( spl0_227
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f99,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f2304,plain,
spl0_226,
inference(avatar_split_clause,[],[f87,f2302]) ).
fof(f2302,plain,
( spl0_226
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f87,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
fof(f2300,plain,
spl0_225,
inference(avatar_split_clause,[],[f65,f2298]) ).
fof(f2298,plain,
( spl0_225
<=> ! [X6,X4,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f65,axiom,
! [X0,X6,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f2296,plain,
spl0_224,
inference(avatar_split_clause,[],[f64,f2294]) ).
fof(f64,axiom,
! [X0,X6,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X6,X0)
| c_lessequals(X6,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f2292,plain,
spl0_223,
inference(avatar_split_clause,[],[f62,f2290]) ).
fof(f2290,plain,
( spl0_223
<=> ! [X6,X4,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f62,axiom,
! [X0,X6,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f2288,plain,
( spl0_222
| ~ spl0_65
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f2207,f2096,f1451,f2286]) ).
fof(f2286,plain,
( spl0_222
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f1451,plain,
( spl0_65
<=> class_OrderedGroup_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f2207,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_65
| ~ spl0_196 ),
inference(resolution,[],[f2097,f1453]) ).
fof(f1453,plain,
( class_OrderedGroup_Ogroup__add(tc_Int_Oint)
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1451]) ).
fof(f2284,plain,
spl0_221,
inference(avatar_split_clause,[],[f61,f2282]) ).
fof(f61,axiom,
! [X2,X3,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f2197,plain,
spl0_220,
inference(avatar_split_clause,[],[f868,f2195]) ).
fof(f2193,plain,
spl0_219,
inference(avatar_split_clause,[],[f778,f2191]) ).
fof(f2191,plain,
( spl0_219
<=> ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f778,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/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__eq__0__iff_0) ).
fof(f2189,plain,
spl0_218,
inference(avatar_split_clause,[],[f773,f2187]) ).
fof(f2187,plain,
( spl0_218
<=> ! [X4] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X4
| c_NthRoot_Osqrt(X4) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f773,axiom,
! [X4] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X4
| c_NthRoot_Osqrt(X4) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__eq__1__iff_0) ).
fof(f2185,plain,
spl0_217,
inference(avatar_split_clause,[],[f768,f2183]) ).
fof(f2183,plain,
( spl0_217
<=> ! [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_217])]) ).
fof(f768,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/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f2181,plain,
spl0_216,
inference(avatar_split_clause,[],[f767,f2179]) ).
fof(f767,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
fof(f2177,plain,
spl0_215,
inference(avatar_split_clause,[],[f766,f2175]) ).
fof(f766,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f2173,plain,
spl0_214,
inference(avatar_split_clause,[],[f760,f2171]) ).
fof(f2171,plain,
( spl0_214
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f760,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
fof(f2169,plain,
spl0_213,
inference(avatar_split_clause,[],[f759,f2167]) ).
fof(f2167,plain,
( spl0_213
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f759,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X2,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
fof(f2165,plain,
spl0_212,
inference(avatar_split_clause,[],[f758,f2163]) ).
fof(f2163,plain,
( spl0_212
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f758,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X2,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
fof(f2161,plain,
spl0_211,
inference(avatar_split_clause,[],[f757,f2159]) ).
fof(f2159,plain,
( spl0_211
<=> ! [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_211])]) ).
fof(f757,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
fof(f2157,plain,
( spl0_210
| ~ spl0_148
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f2060,f2037,f1866,f2154]) ).
fof(f2154,plain,
( spl0_210
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1866,plain,
( spl0_148
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f2037,plain,
( spl0_186
<=> ! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f2060,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Complex_Ocomplex)
| ~ spl0_148
| ~ spl0_186 ),
inference(resolution,[],[f2038,f1868]) ).
fof(f1868,plain,
( class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1866]) ).
fof(f2038,plain,
( ! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0) )
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f2037]) ).
fof(f2152,plain,
spl0_209,
inference(avatar_split_clause,[],[f756,f2150]) ).
fof(f2150,plain,
( spl0_209
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f756,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(f2148,plain,
spl0_208,
inference(avatar_split_clause,[],[f750,f2146]) ).
fof(f2146,plain,
( spl0_208
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f750,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).
fof(f2144,plain,
spl0_207,
inference(avatar_split_clause,[],[f725,f2142]) ).
fof(f2142,plain,
( spl0_207
<=> ! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f725,axiom,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_numeral__1__eq__1_0) ).
fof(f2140,plain,
~ spl0_206,
inference(avatar_split_clause,[],[f718,f2137]) ).
fof(f2137,plain,
( spl0_206
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f718,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__two__neq__zero_0) ).
fof(f2135,plain,
spl0_205,
inference(avatar_split_clause,[],[f609,f2133]) ).
fof(f2133,plain,
( spl0_205
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f609,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f2131,plain,
spl0_204,
inference(avatar_split_clause,[],[f608,f2129]) ).
fof(f2129,plain,
( spl0_204
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f608,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f2127,plain,
spl0_203,
inference(avatar_split_clause,[],[f607,f2125]) ).
fof(f2125,plain,
( spl0_203
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f607,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f2123,plain,
spl0_202,
inference(avatar_split_clause,[],[f604,f2121]) ).
fof(f2121,plain,
( spl0_202
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f604,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f2119,plain,
spl0_201,
inference(avatar_split_clause,[],[f603,f2117]) ).
fof(f603,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f2115,plain,
spl0_200,
inference(avatar_split_clause,[],[f602,f2113]) ).
fof(f602,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f2111,plain,
( spl0_199
| ~ spl0_121
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f2059,f2037,f1731,f2108]) ).
fof(f2108,plain,
( spl0_199
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f2059,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_RealDef_Oreal)
| ~ spl0_121
| ~ spl0_186 ),
inference(resolution,[],[f2038,f1733]) ).
fof(f2106,plain,
spl0_198,
inference(avatar_split_clause,[],[f595,f2104]) ).
fof(f595,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/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
fof(f2102,plain,
spl0_197,
inference(avatar_split_clause,[],[f593,f2100]) ).
fof(f593,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/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
fof(f2098,plain,
spl0_196,
inference(avatar_split_clause,[],[f581,f2096]) ).
fof(f581,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
fof(f2094,plain,
spl0_195,
inference(avatar_split_clause,[],[f575,f2091]) ).
fof(f2091,plain,
( spl0_195
<=> c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f575,axiom,
c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__less__4_0) ).
fof(f2089,plain,
spl0_194,
inference(avatar_split_clause,[],[f476,f2087]) ).
fof(f476,axiom,
! [X8,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X8,tc_RealDef_Oreal),X8,tc_RealDef_Oreal) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__eq_H_1) ).
fof(f2085,plain,
spl0_193,
inference(avatar_split_clause,[],[f462,f2083]) ).
fof(f462,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__eq__0__iff_1) ).
fof(f2081,plain,
spl0_192,
inference(avatar_split_clause,[],[f432,f2079]) ).
fof(f432,axiom,
! [X8,X6] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X6,X8,tc_RealDef_Oreal),X8,tc_RealDef_Oreal) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__eq_H_0) ).
fof(f2077,plain,
spl0_191,
inference(avatar_split_clause,[],[f430,f2075]) ).
fof(f2075,plain,
( spl0_191
<=> ! [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_191])]) ).
fof(f430,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/sandbox/benchmark/theBenchmark.p',cls_arctan__minus_0) ).
fof(f2073,plain,
spl0_190,
inference(avatar_split_clause,[],[f219,f2071]) ).
fof(f2071,plain,
( spl0_190
<=> ! [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_190])]) ).
fof(f219,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/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__minus_0) ).
fof(f2068,plain,
( spl0_189
| ~ spl0_72
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f2058,f2037,f1486,f2065]) ).
fof(f2065,plain,
( spl0_189
<=> c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1486,plain,
( spl0_72
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f2058,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint)
| ~ spl0_72
| ~ spl0_186 ),
inference(resolution,[],[f2038,f1488]) ).
fof(f1488,plain,
( class_Int_Onumber__ring(tc_Int_Oint)
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f1486]) ).
fof(f2047,plain,
spl0_188,
inference(avatar_split_clause,[],[f866,f2045]) ).
fof(f2045,plain,
( spl0_188
<=> ! [X32,X14] :
( X14 = X32
| c_Int_OBit1(X32) != c_Int_OBit1(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f866,axiom,
! [X14,X32] :
( X14 = X32
| c_Int_OBit1(X32) != c_Int_OBit1(X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I51_J_0) ).
fof(f2043,plain,
spl0_187,
inference(avatar_split_clause,[],[f820,f2041]) ).
fof(f2041,plain,
( spl0_187
<=> ! [X32,X14] :
( X14 = X32
| c_Int_OBit0(X14) != c_Int_OBit0(X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f820,axiom,
! [X14,X32] :
( X14 = X32
| c_Int_OBit0(X14) != c_Int_OBit0(X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I48_J_0) ).
fof(f2039,plain,
spl0_186,
inference(avatar_split_clause,[],[f791,f2037]) ).
fof(f791,axiom,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__arith_I112_J_0) ).
fof(f2035,plain,
spl0_185,
inference(avatar_split_clause,[],[f774,f2033]) ).
fof(f2033,plain,
( spl0_185
<=> ! [X6,X4] :
( X4 = X6
| c_NthRoot_Osqrt(X4) != c_NthRoot_Osqrt(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f774,axiom,
! [X6,X4] :
( X4 = X6
| c_NthRoot_Osqrt(X4) != c_NthRoot_Osqrt(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__eq__iff_0) ).
fof(f2031,plain,
spl0_184,
inference(avatar_split_clause,[],[f728,f2028]) ).
fof(f2028,plain,
( spl0_184
<=> c_Complex_Ocomplex_OComplex(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f728,axiom,
c_Complex_Ocomplex_OComplex(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__zero__def_0) ).
fof(f2026,plain,
spl0_183,
inference(avatar_split_clause,[],[f574,f2023]) ).
fof(f2023,plain,
( spl0_183
<=> c_lessequals(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f574,axiom,
c_lessequals(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__ge__two_0) ).
fof(f2021,plain,
spl0_182,
inference(avatar_split_clause,[],[f200,f2019]) ).
fof(f200,axiom,
! [X6,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X6,tc_RealDef_Oreal)
| c_lessequals(X4,X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_0) ).
fof(f2017,plain,
spl0_181,
inference(avatar_split_clause,[],[f115,f2015]) ).
fof(f2015,plain,
( spl0_181
<=> ! [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_181])]) ).
fof(f115,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f2013,plain,
spl0_180,
inference(avatar_split_clause,[],[f114,f2011]) ).
fof(f2011,plain,
( spl0_180
<=> ! [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_180])]) ).
fof(f114,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f2009,plain,
spl0_179,
inference(avatar_split_clause,[],[f113,f2007]) ).
fof(f2007,plain,
( spl0_179
<=> ! [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_179])]) ).
fof(f113,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f2005,plain,
spl0_178,
inference(avatar_split_clause,[],[f112,f2003]) ).
fof(f2003,plain,
( spl0_178
<=> ! [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_178])]) ).
fof(f112,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/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f2001,plain,
spl0_177,
inference(avatar_split_clause,[],[f63,f1999]) ).
fof(f63,axiom,
! [X8,X7] :
( c_lessequals(X8,X7,tc_RealDef_Oreal)
| c_lessequals(X7,X8,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
fof(f1995,plain,
spl0_176,
inference(avatar_split_clause,[],[f865,f1993]) ).
fof(f1993,plain,
( spl0_176
<=> ! [X32] :
( c_Int_OPls = X32
| c_Int_OPls != c_Int_OBit0(X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f865,axiom,
! [X32] :
( c_Int_OPls = X32
| c_Int_OPls != c_Int_OBit0(X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I38_J_0) ).
fof(f1991,plain,
spl0_175,
inference(avatar_split_clause,[],[f770,f1989]) ).
fof(f1989,plain,
( spl0_175
<=> ! [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_175])]) ).
fof(f770,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f1987,plain,
spl0_174,
inference(avatar_split_clause,[],[f745,f1985]) ).
fof(f745,axiom,
! [X8] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X8,tc_RealDef_Oreal) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__1_0) ).
fof(f1983,plain,
spl0_173,
inference(avatar_split_clause,[],[f676,f1981]) ).
fof(f1981,plain,
( spl0_173
<=> ! [X4] : c_Transcendental_Ocos(X4) = c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(X4,tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1979,plain,
spl0_172,
inference(avatar_split_clause,[],[f325,f1977]) ).
fof(f1977,plain,
( spl0_172
<=> ! [X5] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X5,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f325,axiom,
! [X5] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X5,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__real__of__nat__less__zero_0) ).
fof(f1975,plain,
spl0_171,
inference(avatar_split_clause,[],[f324,f1973]) ).
fof(f1973,plain,
( spl0_171
<=> ! [X5] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f324,axiom,
! [X5] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X5,tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__ge__zero_0) ).
fof(f1968,plain,
spl0_170,
inference(avatar_split_clause,[],[f779,f1965]) ).
fof(f779,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__one_0) ).
fof(f1963,plain,
spl0_169,
inference(avatar_split_clause,[],[f776,f1960]) ).
fof(f1958,plain,
spl0_168,
inference(avatar_split_clause,[],[f775,f1955]) ).
fof(f1955,plain,
( spl0_168
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f775,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__zero_0) ).
fof(f1953,plain,
spl0_167,
inference(avatar_split_clause,[],[f394,f1950]) ).
fof(f1950,plain,
( spl0_167
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Oarctan(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f394,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Oarctan(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan__zero__zero_0) ).
fof(f1948,plain,
spl0_166,
inference(avatar_split_clause,[],[f345,f1946]) ).
fof(f345,axiom,
! [X4] : c_lessequals(c_Transcendental_Ocos(X4),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__le__one_0) ).
fof(f1944,plain,
spl0_165,
inference(avatar_split_clause,[],[f330,f1942]) ).
fof(f1942,plain,
( spl0_165
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(c_Transcendental_Oarctan(X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f330,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(c_Transcendental_Oarctan(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__arctan__not__zero_0) ).
fof(f1940,plain,
spl0_164,
inference(avatar_split_clause,[],[f208,f1938]) ).
fof(f1938,plain,
( spl0_164
<=> ! [X4,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f208,axiom,
! [X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1936,plain,
spl0_163,
inference(avatar_split_clause,[],[f207,f1934]) ).
fof(f1934,plain,
( spl0_163
<=> ! [X4,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f207,axiom,
! [X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1932,plain,
spl0_162,
inference(avatar_split_clause,[],[f205,f1930]) ).
fof(f1930,plain,
( spl0_162
<=> ! [X4,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f205,axiom,
! [X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1928,plain,
spl0_161,
inference(avatar_split_clause,[],[f184,f1926]) ).
fof(f1926,plain,
( spl0_161
<=> ! [X4,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f184,axiom,
! [X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X4,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1924,plain,
spl0_160,
inference(avatar_split_clause,[],[f183,f1922]) ).
fof(f1922,plain,
( spl0_160
<=> ! [X4,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f183,axiom,
! [X0,X4] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X4,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1920,plain,
spl0_159,
inference(avatar_split_clause,[],[f877,f1918]) ).
fof(f1918,plain,
( spl0_159
<=> ! [X32,X14] : c_Int_OBit1(X32) != c_Int_OBit0(X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f877,axiom,
! [X14,X32] : c_Int_OBit1(X32) != c_Int_OBit0(X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I49_J_0) ).
fof(f1916,plain,
~ spl0_158,
inference(avatar_split_clause,[],[f777,f1913]) ).
fof(f777,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
fof(f1911,plain,
spl0_157,
inference(avatar_split_clause,[],[f329,f1908]) ).
fof(f1908,plain,
( spl0_157
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f329,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__gt__zero_0) ).
fof(f1906,plain,
spl0_156,
inference(avatar_split_clause,[],[f328,f1903]) ).
fof(f1903,plain,
( spl0_156
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f328,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__ge__zero_0) ).
fof(f1901,plain,
~ spl0_155,
inference(avatar_split_clause,[],[f326,f1898]) ).
fof(f1898,plain,
( spl0_155
<=> c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f326,axiom,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__not__less__zero_0) ).
fof(f1896,plain,
spl0_154,
inference(avatar_split_clause,[],[f818,f1894]) ).
fof(f1894,plain,
( spl0_154
<=> ! [X14] : c_Int_OPls != c_Int_OBit1(X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f818,axiom,
! [X14] : c_Int_OPls != c_Int_OBit1(X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I46_J_0) ).
fof(f1892,plain,
spl0_153,
inference(avatar_split_clause,[],[f795,f1889]) ).
fof(f1889,plain,
( spl0_153
<=> c_Int_OPls = c_Int_OBit0(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f795,axiom,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Bit0__Pls_0) ).
fof(f1887,plain,
~ spl0_152,
inference(avatar_split_clause,[],[f741,f1884]) ).
fof(f1884,plain,
( spl0_152
<=> c_Transcendental_Opi = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f741,axiom,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__neq__zero_0) ).
fof(f1882,plain,
spl0_151,
inference(avatar_split_clause,[],[f206,f1880]) ).
fof(f1880,plain,
( spl0_151
<=> ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f206,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_1) ).
fof(f1878,plain,
spl0_150,
inference(avatar_split_clause,[],[f181,f1876]) ).
fof(f1876,plain,
( spl0_150
<=> ! [X7] : c_lessequals(X7,X7,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f181,axiom,
! [X7] : c_lessequals(X7,X7,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
fof(f1874,plain,
spl0_149,
inference(avatar_split_clause,[],[f1029,f1871]) ).
fof(f1871,plain,
( spl0_149
<=> class_Int_Onumber(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1029,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).
fof(f1869,plain,
spl0_148,
inference(avatar_split_clause,[],[f1028,f1866]) ).
fof(f1028,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f1864,plain,
spl0_147,
inference(avatar_split_clause,[],[f1027,f1861]) ).
fof(f1861,plain,
( spl0_147
<=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1027,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(f1859,plain,
spl0_146,
inference(avatar_split_clause,[],[f1026,f1856]) ).
fof(f1856,plain,
( spl0_146
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1026,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f1854,plain,
spl0_145,
inference(avatar_split_clause,[],[f1025,f1851]) ).
fof(f1851,plain,
( spl0_145
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1025,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(f1849,plain,
spl0_144,
inference(avatar_split_clause,[],[f1024,f1846]) ).
fof(f1846,plain,
( spl0_144
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1024,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f1844,plain,
spl0_143,
inference(avatar_split_clause,[],[f1023,f1841]) ).
fof(f1841,plain,
( spl0_143
<=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1023,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(f1839,plain,
spl0_142,
inference(avatar_split_clause,[],[f1022,f1836]) ).
fof(f1022,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(f1834,plain,
spl0_141,
inference(avatar_split_clause,[],[f1021,f1831]) ).
fof(f1831,plain,
( spl0_141
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1021,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(f1829,plain,
spl0_140,
inference(avatar_split_clause,[],[f1020,f1826]) ).
fof(f1826,plain,
( spl0_140
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1020,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(f1824,plain,
spl0_139,
inference(avatar_split_clause,[],[f1019,f1821]) ).
fof(f1821,plain,
( spl0_139
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1019,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f1819,plain,
spl0_138,
inference(avatar_split_clause,[],[f1018,f1816]) ).
fof(f1816,plain,
( spl0_138
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1018,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
fof(f1814,plain,
spl0_137,
inference(avatar_split_clause,[],[f1017,f1811]) ).
fof(f1811,plain,
( spl0_137
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1017,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f1809,plain,
spl0_136,
inference(avatar_split_clause,[],[f1016,f1806]) ).
fof(f1806,plain,
( spl0_136
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1016,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
fof(f1804,plain,
spl0_135,
inference(avatar_split_clause,[],[f1015,f1801]) ).
fof(f1801,plain,
( spl0_135
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1015,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f1799,plain,
spl0_134,
inference(avatar_split_clause,[],[f1014,f1796]) ).
fof(f1796,plain,
( spl0_134
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1014,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f1794,plain,
spl0_133,
inference(avatar_split_clause,[],[f1013,f1791]) ).
fof(f1791,plain,
( spl0_133
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1013,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
fof(f1789,plain,
spl0_132,
inference(avatar_split_clause,[],[f1012,f1786]) ).
fof(f1786,plain,
( spl0_132
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1012,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(f1784,plain,
spl0_131,
inference(avatar_split_clause,[],[f1011,f1781]) ).
fof(f1781,plain,
( spl0_131
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1011,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1779,plain,
spl0_130,
inference(avatar_split_clause,[],[f1010,f1776]) ).
fof(f1776,plain,
( spl0_130
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1010,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f1774,plain,
spl0_129,
inference(avatar_split_clause,[],[f1009,f1771]) ).
fof(f1771,plain,
( spl0_129
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1009,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1769,plain,
spl0_128,
inference(avatar_split_clause,[],[f1008,f1766]) ).
fof(f1766,plain,
( spl0_128
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1008,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1764,plain,
spl0_127,
inference(avatar_split_clause,[],[f1007,f1761]) ).
fof(f1761,plain,
( spl0_127
<=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1007,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
fof(f1759,plain,
spl0_126,
inference(avatar_split_clause,[],[f1006,f1756]) ).
fof(f1756,plain,
( spl0_126
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1006,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
fof(f1754,plain,
spl0_125,
inference(avatar_split_clause,[],[f1005,f1751]) ).
fof(f1751,plain,
( spl0_125
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1005,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1749,plain,
spl0_124,
inference(avatar_split_clause,[],[f1004,f1746]) ).
fof(f1746,plain,
( spl0_124
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1004,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1744,plain,
spl0_123,
inference(avatar_split_clause,[],[f1003,f1741]) ).
fof(f1741,plain,
( spl0_123
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1003,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1739,plain,
spl0_122,
inference(avatar_split_clause,[],[f1002,f1736]) ).
fof(f1736,plain,
( spl0_122
<=> class_Int_Onumber(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1002,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber) ).
fof(f1734,plain,
spl0_121,
inference(avatar_split_clause,[],[f1001,f1731]) ).
fof(f1001,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f1729,plain,
spl0_120,
inference(avatar_split_clause,[],[f1000,f1726]) ).
fof(f1726,plain,
( spl0_120
<=> class_Int_Oring__char__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1000,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Oring__char__0) ).
fof(f1724,plain,
spl0_119,
inference(avatar_split_clause,[],[f999,f1721]) ).
fof(f999,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
fof(f1719,plain,
spl0_118,
inference(avatar_split_clause,[],[f998,f1716]) ).
fof(f1716,plain,
( spl0_118
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f998,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f1714,plain,
spl0_117,
inference(avatar_split_clause,[],[f997,f1711]) ).
fof(f997,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f1709,plain,
spl0_116,
inference(avatar_split_clause,[],[f996,f1706]) ).
fof(f1706,plain,
( spl0_116
<=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f996,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
fof(f1704,plain,
spl0_115,
inference(avatar_split_clause,[],[f995,f1701]) ).
fof(f1701,plain,
( spl0_115
<=> class_Ring__and__Field_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f995,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
fof(f1699,plain,
spl0_114,
inference(avatar_split_clause,[],[f994,f1696]) ).
fof(f994,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
fof(f1694,plain,
spl0_113,
inference(avatar_split_clause,[],[f993,f1691]) ).
fof(f1691,plain,
( spl0_113
<=> class_RealVector_Oreal__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f993,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__field) ).
fof(f1689,plain,
spl0_112,
inference(avatar_split_clause,[],[f992,f1686]) ).
fof(f992,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f1684,plain,
spl0_111,
inference(avatar_split_clause,[],[f991,f1681]) ).
fof(f991,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
fof(f1679,plain,
spl0_110,
inference(avatar_split_clause,[],[f990,f1676]) ).
fof(f1676,plain,
( spl0_110
<=> class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f990,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
fof(f1674,plain,
spl0_109,
inference(avatar_split_clause,[],[f989,f1671]) ).
fof(f1671,plain,
( spl0_109
<=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f989,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
fof(f1669,plain,
spl0_108,
inference(avatar_split_clause,[],[f988,f1666]) ).
fof(f1666,plain,
( spl0_108
<=> class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f988,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) ).
fof(f1664,plain,
spl0_107,
inference(avatar_split_clause,[],[f987,f1661]) ).
fof(f1661,plain,
( spl0_107
<=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f987,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
fof(f1659,plain,
spl0_106,
inference(avatar_split_clause,[],[f986,f1656]) ).
fof(f1656,plain,
( spl0_106
<=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f986,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
fof(f1654,plain,
spl0_105,
inference(avatar_split_clause,[],[f985,f1651]) ).
fof(f1651,plain,
( spl0_105
<=> class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f985,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).
fof(f1649,plain,
spl0_104,
inference(avatar_split_clause,[],[f984,f1646]) ).
fof(f1646,plain,
( spl0_104
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f984,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
fof(f1644,plain,
spl0_103,
inference(avatar_split_clause,[],[f983,f1641]) ).
fof(f1641,plain,
( spl0_103
<=> class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f983,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).
fof(f1639,plain,
spl0_102,
inference(avatar_split_clause,[],[f982,f1636]) ).
fof(f982,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
fof(f1634,plain,
spl0_101,
inference(avatar_split_clause,[],[f981,f1631]) ).
fof(f981,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(f1629,plain,
spl0_100,
inference(avatar_split_clause,[],[f980,f1626]) ).
fof(f1626,plain,
( spl0_100
<=> class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f980,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
fof(f1624,plain,
spl0_99,
inference(avatar_split_clause,[],[f979,f1621]) ).
fof(f1621,plain,
( spl0_99
<=> class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f979,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
fof(f1619,plain,
spl0_98,
inference(avatar_split_clause,[],[f978,f1616]) ).
fof(f1616,plain,
( spl0_98
<=> class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f978,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) ).
fof(f1614,plain,
spl0_97,
inference(avatar_split_clause,[],[f977,f1611]) ).
fof(f1611,plain,
( spl0_97
<=> class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f977,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
fof(f1609,plain,
spl0_96,
inference(avatar_split_clause,[],[f976,f1606]) ).
fof(f1606,plain,
( spl0_96
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f976,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1604,plain,
spl0_95,
inference(avatar_split_clause,[],[f975,f1601]) ).
fof(f1601,plain,
( spl0_95
<=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f975,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
fof(f1599,plain,
spl0_94,
inference(avatar_split_clause,[],[f974,f1596]) ).
fof(f1596,plain,
( spl0_94
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f974,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f1594,plain,
spl0_93,
inference(avatar_split_clause,[],[f973,f1591]) ).
fof(f973,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1589,plain,
spl0_92,
inference(avatar_split_clause,[],[f972,f1586]) ).
fof(f1586,plain,
( spl0_92
<=> class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f972,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
fof(f1584,plain,
spl0_91,
inference(avatar_split_clause,[],[f971,f1581]) ).
fof(f1581,plain,
( spl0_91
<=> class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f971,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
fof(f1579,plain,
spl0_90,
inference(avatar_split_clause,[],[f970,f1576]) ).
fof(f1576,plain,
( spl0_90
<=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f970,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).
fof(f1574,plain,
spl0_89,
inference(avatar_split_clause,[],[f969,f1571]) ).
fof(f1571,plain,
( spl0_89
<=> class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f969,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).
fof(f1569,plain,
spl0_88,
inference(avatar_split_clause,[],[f968,f1566]) ).
fof(f1566,plain,
( spl0_88
<=> class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f968,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) ).
fof(f1564,plain,
spl0_87,
inference(avatar_split_clause,[],[f967,f1561]) ).
fof(f1561,plain,
( spl0_87
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f967,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1559,plain,
spl0_86,
inference(avatar_split_clause,[],[f966,f1556]) ).
fof(f966,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
fof(f1554,plain,
spl0_85,
inference(avatar_split_clause,[],[f965,f1551]) ).
fof(f1551,plain,
( spl0_85
<=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f965,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
fof(f1549,plain,
spl0_84,
inference(avatar_split_clause,[],[f964,f1546]) ).
fof(f1546,plain,
( spl0_84
<=> class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f964,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
fof(f1544,plain,
spl0_83,
inference(avatar_split_clause,[],[f963,f1541]) ).
fof(f1541,plain,
( spl0_83
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f963,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
fof(f1539,plain,
spl0_82,
inference(avatar_split_clause,[],[f962,f1536]) ).
fof(f1536,plain,
( spl0_82
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f962,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1534,plain,
spl0_81,
inference(avatar_split_clause,[],[f961,f1531]) ).
fof(f961,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1529,plain,
spl0_80,
inference(avatar_split_clause,[],[f960,f1526]) ).
fof(f1526,plain,
( spl0_80
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f960,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1524,plain,
spl0_79,
inference(avatar_split_clause,[],[f959,f1521]) ).
fof(f1521,plain,
( spl0_79
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f959,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1519,plain,
spl0_78,
inference(avatar_split_clause,[],[f958,f1516]) ).
fof(f1516,plain,
( spl0_78
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f958,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1514,plain,
spl0_77,
inference(avatar_split_clause,[],[f957,f1511]) ).
fof(f1511,plain,
( spl0_77
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f957,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1509,plain,
spl0_76,
inference(avatar_split_clause,[],[f956,f1506]) ).
fof(f1506,plain,
( spl0_76
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f956,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1504,plain,
spl0_75,
inference(avatar_split_clause,[],[f955,f1501]) ).
fof(f1501,plain,
( spl0_75
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f955,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1499,plain,
spl0_74,
inference(avatar_split_clause,[],[f954,f1496]) ).
fof(f1496,plain,
( spl0_74
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f954,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1494,plain,
spl0_73,
inference(avatar_split_clause,[],[f953,f1491]) ).
fof(f1491,plain,
( spl0_73
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f953,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
fof(f1489,plain,
spl0_72,
inference(avatar_split_clause,[],[f952,f1486]) ).
fof(f952,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
fof(f1484,plain,
spl0_71,
inference(avatar_split_clause,[],[f951,f1481]) ).
fof(f1481,plain,
( spl0_71
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f951,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
fof(f1479,plain,
spl0_70,
inference(avatar_split_clause,[],[f950,f1476]) ).
fof(f1476,plain,
( spl0_70
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f950,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
fof(f1474,plain,
spl0_69,
inference(avatar_split_clause,[],[f949,f1471]) ).
fof(f1471,plain,
( spl0_69
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f949,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
fof(f1469,plain,
spl0_68,
inference(avatar_split_clause,[],[f948,f1466]) ).
fof(f1466,plain,
( spl0_68
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f948,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
fof(f1464,plain,
spl0_67,
inference(avatar_split_clause,[],[f947,f1461]) ).
fof(f1461,plain,
( spl0_67
<=> class_Ring__and__Field_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f947,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
fof(f1459,plain,
spl0_66,
inference(avatar_split_clause,[],[f946,f1456]) ).
fof(f1456,plain,
( spl0_66
<=> class_Ring__and__Field_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f946,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).
fof(f1454,plain,
spl0_65,
inference(avatar_split_clause,[],[f945,f1451]) ).
fof(f945,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
fof(f1449,plain,
spl0_64,
inference(avatar_split_clause,[],[f944,f1446]) ).
fof(f1446,plain,
( spl0_64
<=> class_OrderedGroup_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f944,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
fof(f1444,plain,
spl0_63,
inference(avatar_split_clause,[],[f943,f1441]) ).
fof(f1441,plain,
( spl0_63
<=> class_Ring__and__Field_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f943,axiom,
class_Ring__and__Field_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).
fof(f1439,plain,
spl0_62,
inference(avatar_split_clause,[],[f942,f1436]) ).
fof(f1436,plain,
( spl0_62
<=> class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f942,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
fof(f1434,plain,
spl0_61,
inference(avatar_split_clause,[],[f941,f1431]) ).
fof(f1431,plain,
( spl0_61
<=> class_Ring__and__Field_Omult__mono(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f941,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).
fof(f1429,plain,
spl0_60,
inference(avatar_split_clause,[],[f940,f1426]) ).
fof(f1426,plain,
( spl0_60
<=> class_Ring__and__Field_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f940,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
fof(f1424,plain,
spl0_59,
inference(avatar_split_clause,[],[f939,f1421]) ).
fof(f1421,plain,
( spl0_59
<=> class_OrderedGroup_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f939,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
fof(f1419,plain,
spl0_58,
inference(avatar_split_clause,[],[f938,f1416]) ).
fof(f1416,plain,
( spl0_58
<=> class_Ring__and__Field_Omult__mono1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f938,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).
fof(f1414,plain,
spl0_57,
inference(avatar_split_clause,[],[f937,f1411]) ).
fof(f1411,plain,
( spl0_57
<=> class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f937,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
fof(f1409,plain,
spl0_56,
inference(avatar_split_clause,[],[f936,f1406]) ).
fof(f1406,plain,
( spl0_56
<=> class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f936,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
fof(f1404,plain,
spl0_55,
inference(avatar_split_clause,[],[f935,f1401]) ).
fof(f1401,plain,
( spl0_55
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f935,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
fof(f1399,plain,
spl0_54,
inference(avatar_split_clause,[],[f934,f1396]) ).
fof(f1396,plain,
( spl0_54
<=> class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f934,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) ).
fof(f1394,plain,
spl0_53,
inference(avatar_split_clause,[],[f933,f1391]) ).
fof(f1391,plain,
( spl0_53
<=> class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f933,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).
fof(f1389,plain,
spl0_52,
inference(avatar_split_clause,[],[f932,f1386]) ).
fof(f1386,plain,
( spl0_52
<=> class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f932,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
fof(f1384,plain,
spl0_51,
inference(avatar_split_clause,[],[f931,f1381]) ).
fof(f1381,plain,
( spl0_51
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f931,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1379,plain,
spl0_50,
inference(avatar_split_clause,[],[f930,f1376]) ).
fof(f1376,plain,
( spl0_50
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f930,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).
fof(f1374,plain,
spl0_49,
inference(avatar_split_clause,[],[f929,f1371]) ).
fof(f1371,plain,
( spl0_49
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f929,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1369,plain,
spl0_48,
inference(avatar_split_clause,[],[f928,f1366]) ).
fof(f1366,plain,
( spl0_48
<=> class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f928,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
fof(f1364,plain,
spl0_47,
inference(avatar_split_clause,[],[f927,f1361]) ).
fof(f1361,plain,
( spl0_47
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f927,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
fof(f1359,plain,
spl0_46,
inference(avatar_split_clause,[],[f926,f1356]) ).
fof(f1356,plain,
( spl0_46
<=> class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f926,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).
fof(f1354,plain,
spl0_45,
inference(avatar_split_clause,[],[f925,f1351]) ).
fof(f1351,plain,
( spl0_45
<=> class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f925,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).
fof(f1349,plain,
spl0_44,
inference(avatar_split_clause,[],[f924,f1346]) ).
fof(f1346,plain,
( spl0_44
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f924,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1344,plain,
spl0_43,
inference(avatar_split_clause,[],[f923,f1341]) ).
fof(f923,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) ).
fof(f1339,plain,
spl0_42,
inference(avatar_split_clause,[],[f922,f1336]) ).
fof(f1336,plain,
( spl0_42
<=> class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f922,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
fof(f1334,plain,
spl0_41,
inference(avatar_split_clause,[],[f921,f1331]) ).
fof(f1331,plain,
( spl0_41
<=> class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f921,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
fof(f1329,plain,
spl0_40,
inference(avatar_split_clause,[],[f920,f1326]) ).
fof(f1326,plain,
( spl0_40
<=> class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f920,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).
fof(f1324,plain,
spl0_39,
inference(avatar_split_clause,[],[f919,f1321]) ).
fof(f1321,plain,
( spl0_39
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f919,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1319,plain,
spl0_38,
inference(avatar_split_clause,[],[f918,f1316]) ).
fof(f1316,plain,
( spl0_38
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f918,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1314,plain,
spl0_37,
inference(avatar_split_clause,[],[f917,f1311]) ).
fof(f1311,plain,
( spl0_37
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f917,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1309,plain,
spl0_36,
inference(avatar_split_clause,[],[f916,f1306]) ).
fof(f1306,plain,
( spl0_36
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f916,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1304,plain,
spl0_35,
inference(avatar_split_clause,[],[f915,f1301]) ).
fof(f1301,plain,
( spl0_35
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f915,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1299,plain,
spl0_34,
inference(avatar_split_clause,[],[f914,f1296]) ).
fof(f1296,plain,
( spl0_34
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f914,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1294,plain,
spl0_33,
inference(avatar_split_clause,[],[f913,f1291]) ).
fof(f1291,plain,
( spl0_33
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f913,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1289,plain,
spl0_32,
inference(avatar_split_clause,[],[f912,f1286]) ).
fof(f1286,plain,
( spl0_32
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f912,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1284,plain,
spl0_31,
inference(avatar_split_clause,[],[f911,f1281]) ).
fof(f1281,plain,
( spl0_31
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f911,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1279,plain,
spl0_30,
inference(avatar_split_clause,[],[f910,f1276]) ).
fof(f1276,plain,
( spl0_30
<=> class_Int_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f910,axiom,
class_Int_Onumber(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
fof(f1274,plain,
spl0_29,
inference(avatar_split_clause,[],[f909,f1271]) ).
fof(f1271,plain,
( spl0_29
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f909,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1269,plain,
spl0_28,
inference(avatar_split_clause,[],[f908,f1266]) ).
fof(f1266,plain,
( spl0_28
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f908,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1264,plain,
spl0_27,
inference(avatar_split_clause,[],[f907,f1261]) ).
fof(f1261,plain,
( spl0_27
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f907,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1259,plain,
spl0_26,
inference(avatar_split_clause,[],[f906,f1256]) ).
fof(f906,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f1254,plain,
spl0_25,
inference(avatar_split_clause,[],[f905,f1251]) ).
fof(f1251,plain,
( spl0_25
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f905,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f1249,plain,
spl0_24,
inference(avatar_split_clause,[],[f904,f1246]) ).
fof(f1246,plain,
( spl0_24
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f904,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f1244,plain,
spl0_23,
inference(avatar_split_clause,[],[f903,f1241]) ).
fof(f1241,plain,
( spl0_23
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f903,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f1239,plain,
spl0_22,
inference(avatar_split_clause,[],[f902,f1236]) ).
fof(f1236,plain,
( spl0_22
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f902,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f1234,plain,
spl0_21,
inference(avatar_split_clause,[],[f901,f1231]) ).
fof(f1231,plain,
( spl0_21
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f901,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f1229,plain,
spl0_20,
inference(avatar_split_clause,[],[f900,f1226]) ).
fof(f1226,plain,
( spl0_20
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f900,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f1224,plain,
spl0_19,
inference(avatar_split_clause,[],[f899,f1221]) ).
fof(f1221,plain,
( spl0_19
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f899,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1219,plain,
spl0_18,
inference(avatar_split_clause,[],[f898,f1216]) ).
fof(f1216,plain,
( spl0_18
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f898,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f1214,plain,
spl0_17,
inference(avatar_split_clause,[],[f897,f1211]) ).
fof(f1211,plain,
( spl0_17
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f897,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1209,plain,
spl0_16,
inference(avatar_split_clause,[],[f896,f1206]) ).
fof(f1206,plain,
( spl0_16
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f896,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1204,plain,
spl0_15,
inference(avatar_split_clause,[],[f895,f1201]) ).
fof(f1201,plain,
( spl0_15
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f895,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f1199,plain,
spl0_14,
inference(avatar_split_clause,[],[f894,f1196]) ).
fof(f1196,plain,
( spl0_14
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f894,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1194,plain,
spl0_13,
inference(avatar_split_clause,[],[f893,f1191]) ).
fof(f1191,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f893,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f1189,plain,
spl0_12,
inference(avatar_split_clause,[],[f892,f1186]) ).
fof(f1186,plain,
( spl0_12
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f892,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f1184,plain,
spl0_11,
inference(avatar_split_clause,[],[f891,f1181]) ).
fof(f1181,plain,
( spl0_11
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f891,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f1179,plain,
spl0_10,
inference(avatar_split_clause,[],[f890,f1176]) ).
fof(f1176,plain,
( spl0_10
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f890,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f1174,plain,
spl0_9,
inference(avatar_split_clause,[],[f889,f1171]) ).
fof(f1171,plain,
( spl0_9
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f889,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1169,plain,
spl0_8,
inference(avatar_split_clause,[],[f888,f1166]) ).
fof(f1166,plain,
( spl0_8
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f888,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1164,plain,
spl0_7,
inference(avatar_split_clause,[],[f887,f1161]) ).
fof(f1161,plain,
( spl0_7
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f887,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1159,plain,
spl0_6,
inference(avatar_split_clause,[],[f886,f1156]) ).
fof(f1156,plain,
( spl0_6
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f886,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1154,plain,
spl0_5,
inference(avatar_split_clause,[],[f885,f1151]) ).
fof(f1151,plain,
( spl0_5
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f885,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1149,plain,
spl0_4,
inference(avatar_split_clause,[],[f884,f1146]) ).
fof(f1146,plain,
( spl0_4
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f884,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1144,plain,
spl0_3,
inference(avatar_split_clause,[],[f883,f1141]) ).
fof(f1141,plain,
( spl0_3
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f883,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1139,plain,
spl0_2,
inference(avatar_split_clause,[],[f882,f1136]) ).
fof(f1136,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f882,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1134,plain,
spl0_1,
inference(avatar_split_clause,[],[f881,f1131]) ).
fof(f1131,plain,
( spl0_1
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f881,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV601-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 21:13:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (14420)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (14423)WARNING: value z3 for option sas not known
% 0.21/0.43 % (14426)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.43 % (14421)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.43 % (14422)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.43 % (14423)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.43 % (14424)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.43 % (14425)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.43 % (14427)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 1.45/0.60 TRYING [1]
% 1.45/0.61 TRYING [2]
% 3.54/0.89 TRYING [3]
% 3.83/0.93 TRYING [1]
% 3.85/0.99 TRYING [2]
% 8.00/1.59 TRYING [1]
% 8.00/1.61 TRYING [2]
% 8.00/1.61 % (14425)First to succeed.
% 8.67/1.63 % (14425)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14420"
% 8.67/1.64 % (14425)Refutation found. Thanks to Tanya!
% 8.67/1.64 % SZS status Unsatisfiable for theBenchmark
% 8.67/1.64 % SZS output start Proof for theBenchmark
% See solution above
% 8.67/1.65 % (14425)------------------------------
% 8.67/1.65 % (14425)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 8.67/1.65 % (14425)Termination reason: Refutation
% 8.67/1.65
% 8.67/1.65 % (14425)Memory used [KB]: 14638
% 8.67/1.65 % (14425)Time elapsed: 1.207 s
% 8.67/1.65 % (14425)Instructions burned: 3710 (million)
% 8.67/1.65 % (14420)Success in time 1.271 s
%------------------------------------------------------------------------------