TSTP Solution File: SWV602-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV602-1 : 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 : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:03:02 EDT 2024
% Result : Unsatisfiable 13.28s 2.37s
% Output : Refutation 13.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1778
% Syntax : Number of formulae : 3029 (1182 unt; 0 def)
% Number of atoms : 7379 (1111 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 7569 (3219 ~;3424 |; 0 &)
% ( 926 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 980 ( 978 usr; 927 prp; 0-3 aty)
% Number of functors : 32 ( 32 usr; 8 con; 0-3 aty)
% Number of variables : 3814 (3814 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25783,plain,
$false,
inference(avatar_sat_refutation,[],[f1175,f1180,f1185,f1190,f1195,f1200,f1205,f1210,f1215,f1220,f1225,f1230,f1235,f1240,f1245,f1250,f1255,f1260,f1265,f1270,f1275,f1280,f1285,f1290,f1295,f1300,f1305,f1310,f1315,f1320,f1325,f1330,f1335,f1340,f1345,f1350,f1355,f1360,f1365,f1370,f1375,f1380,f1385,f1390,f1395,f1400,f1405,f1410,f1415,f1420,f1425,f1430,f1435,f1440,f1445,f1450,f1455,f1460,f1465,f1470,f1475,f1480,f1485,f1490,f1495,f1500,f1505,f1510,f1515,f1520,f1525,f1530,f1535,f1540,f1545,f1550,f1555,f1560,f1565,f1570,f1575,f1580,f1585,f1590,f1595,f1600,f1605,f1610,f1615,f1620,f1625,f1630,f1635,f1640,f1645,f1650,f1655,f1660,f1665,f1670,f1675,f1680,f1685,f1690,f1695,f1700,f1705,f1710,f1715,f1720,f1725,f1730,f1735,f1740,f1745,f1750,f1755,f1760,f1765,f1770,f1775,f1780,f1785,f1790,f1795,f1800,f1805,f1810,f1815,f1820,f1825,f1830,f1835,f1840,f1845,f1850,f1855,f1860,f1865,f1870,f1875,f1880,f1885,f1890,f1895,f1900,f1905,f1910,f1915,f1920,f1924,f1928,f1932,f1937,f1941,f1946,f1950,f1955,f1962,f1968,f1973,f1978,f1983,f1988,f1992,f1997,f2001,f2005,f2010,f2014,f2018,f2022,f2027,f2032,f2037,f2041,f2050,f2056,f2061,f2067,f2071,f2075,f2079,f2083,f2087,f2091,f2095,f2099,f2104,f2113,f2117,f2121,f2125,f2129,f2133,f2137,f2141,f2145,f2150,f2154,f2158,f2162,f2187,f2191,f2195,f2199,f2203,f2207,f2212,f2216,f2220,f2224,f2228,f2232,f2236,f2240,f2244,f2248,f2252,f2257,f2261,f2265,f2269,f2273,f2277,f2281,f2285,f2289,f2293,f2297,f2302,f2306,f2310,f2315,f2320,f2324,f2412,f2416,f2420,f2424,f2428,f2432,f2436,f2440,f2444,f2448,f2452,f2456,f2460,f2464,f2468,f2472,f2476,f2480,f2484,f2488,f2492,f2496,f2501,f2506,f2511,f2515,f2519,f2523,f2528,f2533,f2538,f2542,f2546,f2550,f2554,f2558,f2562,f2567,f2571,f2575,f2579,f2583,f2587,f2618,f2678,f2772,f2785,f2789,f2793,f2797,f2801,f2805,f2809,f2813,f2817,f2821,f2825,f2829,f2833,f2837,f2841,f2845,f2849,f2853,f2857,f2861,f2865,f2869,f2873,f2877,f2881,f2885,f2889,f2893,f2897,f2901,f2905,f2909,f2913,f2917,f2921,f2925,f2930,f2934,f2938,f2942,f2946,f3002,f3089,f3178,f3182,f3187,f3191,f3195,f3199,f3203,f3207,f3211,f3215,f3219,f3223,f3227,f3232,f3236,f3240,f3244,f3248,f3252,f3257,f3262,f3267,f3271,f3276,f3281,f3285,f3289,f3404,f3444,f3448,f3452,f3456,f3460,f3464,f3468,f3472,f3476,f3480,f3484,f3488,f3492,f3508,f3512,f3516,f3520,f3525,f3531,f3541,f3545,f3549,f3562,f3566,f3570,f3574,f3578,f3582,f3586,f3590,f3594,f3599,f3603,f3669,f3960,f3987,f3991,f3995,f3999,f4003,f4007,f4011,f4015,f4019,f4023,f4027,f4031,f4035,f4039,f4043,f4047,f4051,f4055,f4059,f4063,f4067,f4090,f4094,f4098,f4102,f4106,f4110,f4114,f4118,f4122,f4126,f4135,f4140,f4144,f4148,f4152,f4156,f4160,f4164,f4168,f4172,f4178,f4247,f4251,f4256,f4262,f4266,f4270,f4274,f4278,f4282,f4286,f4290,f4294,f4299,f4304,f4308,f4483,f4875,f5160,f5164,f5168,f5172,f5176,f5180,f5184,f5188,f5192,f5196,f5200,f5204,f5208,f5212,f5216,f5220,f5224,f5228,f5232,f5236,f5240,f5250,f5254,f5258,f5262,f5266,f5270,f5275,f5280,f5284,f5288,f5293,f5297,f5301,f5305,f5310,f5314,f5546,f5663,f5667,f5671,f5675,f5679,f5683,f5687,f5691,f5695,f5699,f5713,f5717,f5721,f5725,f5729,f5733,f5737,f5741,f5745,f5749,f5754,f5758,f5762,f5766,f5771,f6115,f6210,f6214,f6218,f6226,f6231,f6240,f6244,f6248,f6252,f6256,f6260,f6264,f6273,f6277,f6282,f6287,f6291,f6295,f6299,f6303,f6307,f6311,f6320,f6324,f6328,f6332,f6336,f6340,f6344,f6529,f6533,f6537,f6541,f6545,f6549,f6553,f6557,f6561,f6570,f6574,f6578,f6582,f6586,f6590,f6594,f6598,f6602,f6606,f6620,f6624,f6628,f6632,f6636,f6707,f7067,f7085,f7089,f7093,f7097,f7101,f7105,f7109,f7113,f7117,f7121,f7122,f7126,f7130,f7134,f7138,f7142,f7146,f7150,f7154,f7158,f7163,f7171,f7176,f7182,f7599,f7603,f7607,f7611,f7616,f7620,f7624,f7628,f7632,f7636,f7640,f7644,f7648,f7652,f7656,f7665,f7669,f7673,f7677,f7681,f7685,f7689,f7693,f7697,f7701,f7720,f7724,f7728,f7732,f7736,f7740,f7744,f7748,f7752,f7756,f7760,f7764,f7768,f7772,f7776,f7780,f7784,f7788,f7792,f7796,f7800,f7810,f7814,f7818,f7822,f7826,f7830,f7834,f7838,f7842,f7846,f7860,f7864,f7868,f7872,f7876,f7880,f7884,f7888,f7892,f7896,f7897,f7901,f7905,f7909,f7913,f7917,f7921,f7925,f7929,f7933,f7937,f7946,f7951,f8576,f9066,f9374,f9531,f9535,f9539,f9543,f9552,f9568,f9572,f9576,f9580,f9584,f9588,f9592,f9596,f9600,f9604,f9608,f9612,f9616,f9620,f9624,f9628,f9632,f9636,f9640,f9644,f9657,f9661,f9665,f9669,f9673,f9677,f9681,f9685,f9689,f9693,f9701,f9705,f9709,f9713,f9717,f9721,f10772,f11385,f11389,f11393,f11397,f11419,f11423,f11427,f11431,f11435,f11439,f11443,f11447,f11451,f11455,f11459,f11463,f11467,f11471,f11475,f11479,f11483,f11487,f11491,f11495,f11500,f11513,f11519,f11713,f12029,f12033,f12037,f12041,f12045,f12049,f12053,f12057,f12061,f12065,f12069,f12073,f12077,f12081,f12085,f12096,f12100,f12104,f12108,f12642,f12646,f12651,f12656,f12660,f12861,f12865,f12869,f12873,f12877,f12881,f12885,f12889,f12890,f12894,f13093,f13097,f13101,f13105,f13109,f13113,f13117,f13121,f13125,f13129,f13130,f13134,f13138,f13142,f13146,f13150,f13154,f13158,f13162,f13166,f13170,f13739,f13744,f13748,f13752,f13881,f13885,f13889,f13893,f13901,f13905,f13909,f13913,f13917,f13921,f13925,f13929,f13933,f13937,f13955,f13959,f13963,f13967,f13971,f13975,f13979,f13983,f14408,f14807,f14811,f14815,f14819,f14823,f14829,f14873,f14877,f15089,f15093,f15097,f15101,f15105,f15109,f15138,f15142,f15146,f15150,f15154,f15158,f15162,f15166,f15170,f15174,f15175,f15179,f15183,f15187,f15191,f15196,f15226,f15231,f15266,f15276,f15323,f15328,f15332,f15339,f16161,f16433,f16437,f16446,f16450,f16454,f16458,f16462,f16466,f16470,f16474,f16478,f16483,f16489,f16515,f17191,f17196,f17231,f17313,f17319,f17324,f17352,f17357,f17392,f17398,f17490,f17494,f17499,f17572,f17576,f17580,f17585,f17764,f17773,f17778,f17784,f17865,f17869,f17873,f17878,f18084,f18085,f18813,f18817,f18824,f19015,f19019,f19025,f19414,f19418,f19422,f20486,f21123,f21133,f21568,f21623,f21627,f21631,f21879,f21883,f21887,f23235,f23282,f23286,f24012,f24462,f24467,f24535,f24849,f25429,f25434,f25776,f25781,f25782]) ).
fof(f25782,plain,
( spl0_164
| ~ spl0_211
| ~ spl0_324
| ~ spl0_923 ),
inference(avatar_split_clause,[],[f25531,f25426,f3000,f2218,f1985]) ).
fof(f1985,plain,
( spl0_164
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f2218,plain,
( spl0_211
<=> ! [X5,X7] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X7,tc_RealDef_Oreal),X7,tc_RealDef_Oreal) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f3000,plain,
( spl0_324
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f25426,plain,
( spl0_923
<=> 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_923])]) ).
fof(f25531,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ spl0_211
| ~ spl0_324
| ~ spl0_923 ),
inference(forward_demodulation,[],[f25435,f3001]) ).
fof(f3001,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f3000]) ).
fof(f25435,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_211
| ~ spl0_923 ),
inference(superposition,[],[f2219,f25428]) ).
fof(f25428,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_923 ),
inference(avatar_component_clause,[],[f25426]) ).
fof(f2219,plain,
( ! [X7,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X7,tc_RealDef_Oreal),X7,tc_RealDef_Oreal) = X5
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f2218]) ).
fof(f25781,plain,
( spl0_926
| ~ spl0_211
| ~ spl0_324
| ~ spl0_923
| ~ spl0_925 ),
inference(avatar_split_clause,[],[f25777,f25774,f25426,f3000,f2218,f25779]) ).
fof(f25779,plain,
( spl0_926
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X0,tc_nat),tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f25774,plain,
( spl0_925
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X0,tc_nat),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f25777,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X0,tc_nat),tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_211
| ~ spl0_324
| ~ spl0_923
| ~ spl0_925 ),
inference(forward_demodulation,[],[f25775,f25531]) ).
fof(f25775,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X0,tc_nat),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_925 ),
inference(avatar_component_clause,[],[f25774]) ).
fof(f25776,plain,
( spl0_925
| ~ spl0_114
| ~ spl0_160
| ~ spl0_178
| ~ spl0_278
| ~ spl0_667
| ~ spl0_895 ),
inference(avatar_split_clause,[],[f20675,f18082,f7935,f2581,f2053,f1965,f1737,f25774]) ).
fof(f1737,plain,
( spl0_114
<=> class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1965,plain,
( spl0_160
<=> 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_160])]) ).
fof(f2053,plain,
( spl0_178
<=> 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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f2581,plain,
( spl0_278
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f7935,plain,
( spl0_667
<=> ! [X19] : 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(X19,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f18082,plain,
( spl0_895
<=> ! [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_895])]) ).
fof(f20675,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X0,tc_nat),tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_114
| ~ spl0_160
| ~ spl0_178
| ~ spl0_278
| ~ spl0_667
| ~ spl0_895 ),
inference(forward_demodulation,[],[f18658,f18754]) ).
fof(f18754,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_160
| ~ spl0_178
| ~ spl0_278
| ~ spl0_895 ),
inference(forward_demodulation,[],[f18753,f2778]) ).
fof(f2778,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_278 ),
inference(resolution,[],[f2582,f1739]) ).
fof(f1739,plain,
( class_Ring__and__Field_Ofield(tc_RealDef_Oreal)
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1737]) ).
fof(f2582,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f2581]) ).
fof(f18753,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_160
| ~ spl0_178
| ~ spl0_278
| ~ spl0_895 ),
inference(forward_demodulation,[],[f18752,f2055]) ).
fof(f2055,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_178 ),
inference(avatar_component_clause,[],[f2053]) ).
fof(f18752,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_160
| ~ spl0_278
| ~ spl0_895 ),
inference(forward_demodulation,[],[f18557,f2778]) ).
fof(f18557,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_160
| ~ spl0_895 ),
inference(superposition,[],[f18083,f1967]) ).
fof(f1967,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_160 ),
inference(avatar_component_clause,[],[f1965]) ).
fof(f18083,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_895 ),
inference(avatar_component_clause,[],[f18082]) ).
fof(f18658,plain,
( ! [X0] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X0,tc_nat),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_114
| ~ spl0_278
| ~ spl0_667
| ~ spl0_895 ),
inference(forward_demodulation,[],[f18527,f2778]) ).
fof(f18527,plain,
( ! [X0] : c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X0,tc_nat),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_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X0,tc_nat),tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_667
| ~ spl0_895 ),
inference(superposition,[],[f18083,f7936]) ).
fof(f7936,plain,
( ! [X19] : 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(X19,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_667 ),
inference(avatar_component_clause,[],[f7935]) ).
fof(f25434,plain,
( spl0_924
| ~ spl0_114
| ~ spl0_160
| ~ spl0_178
| ~ spl0_278
| ~ spl0_895 ),
inference(avatar_split_clause,[],[f18754,f18082,f2581,f2053,f1965,f1737,f25431]) ).
fof(f25431,plain,
( spl0_924
<=> 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_924])]) ).
fof(f25429,plain,
( spl0_923
| ~ spl0_81
| ~ spl0_160
| ~ spl0_178
| ~ spl0_269
| ~ spl0_891 ),
inference(avatar_split_clause,[],[f18373,f17863,f2544,f2053,f1965,f1572,f25426]) ).
fof(f1572,plain,
( spl0_81
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f2544,plain,
( spl0_269
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f17863,plain,
( spl0_891
<=> ! [X5] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Ocos(X5),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),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f18373,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_160
| ~ spl0_178
| ~ spl0_269
| ~ spl0_891 ),
inference(forward_demodulation,[],[f18372,f2750]) ).
fof(f2750,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_269 ),
inference(resolution,[],[f2545,f1574]) ).
fof(f1574,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal)
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1572]) ).
fof(f2545,plain,
( ! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) )
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f2544]) ).
fof(f18372,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_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_81
| ~ spl0_160
| ~ spl0_178
| ~ spl0_269
| ~ spl0_891 ),
inference(forward_demodulation,[],[f18371,f1967]) ).
fof(f18371,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(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_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)
| ~ spl0_81
| ~ spl0_178
| ~ spl0_269
| ~ spl0_891 ),
inference(forward_demodulation,[],[f18130,f2750]) ).
fof(f18130,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(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_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_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)
| ~ spl0_178
| ~ spl0_891 ),
inference(superposition,[],[f17864,f2055]) ).
fof(f17864,plain,
( ! [X5] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Ocos(X5),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),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_891 ),
inference(avatar_component_clause,[],[f17863]) ).
fof(f24849,plain,
spl0_922,
inference(avatar_split_clause,[],[f1131,f24847]) ).
fof(f24847,plain,
( spl0_922
<=> ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X5)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X6)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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_922])]) ).
fof(f1131,plain,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X5)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X6)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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,[],[f703,f1066,f1066,f1066,f1066,f1066]) ).
fof(f1066,plain,
! [X5] : c_Transcendental_Otan(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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f720,f807]) ).
fof(f807,axiom,
! [X5] : c_Transcendental_Osin(X5) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X5,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__cos__eq_0) ).
fof(f720,axiom,
! [X5] : c_Transcendental_Otan(X5) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Osin(X5),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__def_0) ).
fof(f703,axiom,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X5)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X6)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal))
| c_Transcendental_Otan(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_Transcendental_Otan(X5),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(X5),c_Transcendental_Otan(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__add_0) ).
fof(f24535,plain,
spl0_921,
inference(avatar_split_clause,[],[f1133,f24533]) ).
fof(f24533,plain,
( spl0_921
<=> ! [X6,X5] :
( c_HOL_Oord__class_Oless(X6,X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f1133,plain,
! [X6,X5] :
( c_HOL_Oord__class_Oless(X6,X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f545,f1066,f1066]) ).
fof(f545,axiom,
! [X6,X5] :
( c_HOL_Oord__class_Oless(X6,X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Otan(X6),c_Transcendental_Otan(X5),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(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__monotone_H_1) ).
fof(f24467,plain,
( spl0_920
| ~ spl0_102
| ~ spl0_288
| ~ spl0_919 ),
inference(avatar_split_clause,[],[f24463,f24460,f2803,f1677,f24465]) ).
fof(f24465,plain,
( spl0_920
<=> ! [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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f1677,plain,
( spl0_102
<=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f2803,plain,
( spl0_288
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f24460,plain,
( spl0_919
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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),X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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),X5,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),X5,tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f24463,plain,
( ! [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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal) )
| ~ spl0_102
| ~ spl0_288
| ~ spl0_919 ),
inference(forward_demodulation,[],[f24461,f2973]) ).
fof(f2973,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_288 ),
inference(resolution,[],[f2804,f1679]) ).
fof(f1679,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1677]) ).
fof(f2804,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) )
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f2803]) ).
fof(f24461,plain,
( ! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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),X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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),X5,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),X5,tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_919 ),
inference(avatar_component_clause,[],[f24460]) ).
fof(f24462,plain,
spl0_919,
inference(avatar_split_clause,[],[f1127,f24460]) ).
fof(f1127,plain,
! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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),X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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),X5,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),X5,tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f187,f1066,f807]) ).
fof(f187,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal)
| c_Transcendental_Otan(X5) = 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),X5,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),X5,tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__half_0) ).
fof(f24012,plain,
spl0_918,
inference(avatar_split_clause,[],[f1125,f24010]) ).
fof(f24010,plain,
( spl0_918
<=> ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X5)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X6)
| 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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f1125,plain,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X5)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X6)
| 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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f568,f1066,f1066,f807]) ).
fof(f568,axiom,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X5)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X6)
| c_HOL_Oplus__class_Oplus(c_Transcendental_Otan(X5),c_Transcendental_Otan(X6),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal)),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__tan__eq_0) ).
fof(f23286,plain,
spl0_917,
inference(avatar_split_clause,[],[f1129,f23284]) ).
fof(f23284,plain,
( spl0_917
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X6,X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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_917])]) ).
fof(f1129,plain,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X6,X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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,[],[f543,f1066,f1066]) ).
fof(f543,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X6,X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(X6),c_Transcendental_Otan(X5),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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/sandbox2/benchmark/theBenchmark.p',cls_tan__monotone_0) ).
fof(f23282,plain,
spl0_916,
inference(avatar_split_clause,[],[f1126,f23280]) ).
fof(f23280,plain,
( spl0_916
<=> ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X5)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X6)
| c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal)),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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_916])]) ).
fof(f1126,plain,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X5)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X6)
| c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal)),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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,[],[f702,f1066,f1066]) ).
fof(f702,axiom,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X5)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(X6)
| c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Otan(X5),c_Transcendental_Otan(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal)),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma__tan__add1_0) ).
fof(f23235,plain,
spl0_915,
inference(avatar_split_clause,[],[f1128,f23233]) ).
fof(f23233,plain,
( spl0_915
<=> ! [X6,X5] :
( ~ c_lessequals(X6,X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ c_lessequals(X5,c_HOL_Oinverse__class_Odivide(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_915])]) ).
fof(f1128,plain,
! [X6,X5] :
( ~ c_lessequals(X6,X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ c_lessequals(X5,c_HOL_Oinverse__class_Odivide(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,[],[f730,f807,f807]) ).
fof(f730,axiom,
! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Osin(X6),c_Transcendental_Osin(X5),tc_RealDef_Oreal)
| ~ c_lessequals(X5,c_HOL_Oinverse__class_Odivide(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/sandbox2/benchmark/theBenchmark.p',cls_sin__monotone__2pi_H_0) ).
fof(f21887,plain,
spl0_914,
inference(avatar_split_clause,[],[f1098,f21885]) ).
fof(f21885,plain,
( spl0_914
<=> ! [X6,X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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(X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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_914])]) ).
fof(f1098,plain,
! [X6,X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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(X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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,[],[f717,f807,f807,f807]) ).
fof(f717,axiom,
! [X6,X5] : c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X5),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Osin(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__add_0) ).
fof(f21883,plain,
spl0_913,
inference(avatar_split_clause,[],[f1097,f21881]) ).
fof(f21881,plain,
( spl0_913
<=> ! [X6,X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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(X5,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),X5,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(X5),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f1097,plain,
! [X6,X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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(X5,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),X5,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(X5),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f718,f807,f807,f807]) ).
fof(f718,axiom,
! [X6,X5] : c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(X5,X6,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X6),c_Transcendental_Osin(X5),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X6),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__diff2_0) ).
fof(f21879,plain,
spl0_912,
inference(avatar_split_clause,[],[f1096,f21877]) ).
fof(f21877,plain,
( spl0_912
<=> ! [X6,X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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(X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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_912])]) ).
fof(f1096,plain,
! [X6,X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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(X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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,[],[f719,f807,f807,f807]) ).
fof(f719,axiom,
! [X6,X5] : c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(X5,X6,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X5),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Osin(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__diff_0) ).
fof(f21631,plain,
spl0_911,
inference(avatar_split_clause,[],[f1144,f21629]) ).
fof(f21629,plain,
( spl0_911
<=> ! [X5,X19] : 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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(X19,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(X19,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f1144,plain,
! [X19,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(X19,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(X19,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1088,f901]) ).
fof(f901,axiom,
! [X8,X7] : c_HOL_Otimes__class_Otimes(X7,X8,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X8,X7,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
fof(f1088,plain,
! [X19,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X19,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X19,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f179,f1066,f1066]) ).
fof(f179,axiom,
! [X19,X5] : c_Transcendental_Otan(X5) = c_Transcendental_Otan(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X19,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__periodic__n_0) ).
fof(f21627,plain,
spl0_910,
inference(avatar_split_clause,[],[f1143,f21625]) ).
fof(f21625,plain,
( spl0_910
<=> ! [X5,X19] : 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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X19,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X19,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f1143,plain,
! [X19,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X19,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X19,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1087,f901]) ).
fof(f1087,plain,
! [X19,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X19,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X19,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f182,f1066,f1066]) ).
fof(f182,axiom,
! [X19,X5] : c_Transcendental_Otan(X5) = c_Transcendental_Otan(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X19,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__periodic__nat_0) ).
fof(f21623,plain,
spl0_909,
inference(avatar_split_clause,[],[f1119,f21621]) ).
fof(f21621,plain,
( spl0_909
<=> ! [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),X5,tc_RealDef_Oreal))
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__1(X5),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) = X5
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__2(X5),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) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f1119,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),X5,tc_RealDef_Oreal))
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__1(X5),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) = X5
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__2(X5),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) = X5 ),
inference(definition_unfolding,[],[f725,f807]) ).
fof(f725,axiom,
! [X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Osin(X5)
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__1(X5),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) = X5
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__2(X5),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) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__zero__iff_3) ).
fof(f21568,plain,
spl0_908,
inference(avatar_split_clause,[],[f1158,f21566]) ).
fof(f21566,plain,
( spl0_908
<=> ! [X2,X1,X26] : c_HOL_Ominus__class_Ominus(hAPP(X26,X2),c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X26,X2),hAPP(X26,X1),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(hAPP(X26,X1),c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X26,X2),hAPP(X26,X1),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f1158,plain,
! [X2,X1,X26] : c_HOL_Ominus__class_Ominus(hAPP(X26,X2),c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X26,X2),hAPP(X26,X1),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(hAPP(X26,X1),c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X26,X2),hAPP(X26,X1),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1157,f901]) ).
fof(f1157,plain,
! [X2,X1,X26] : c_HOL_Ominus__class_Ominus(hAPP(X26,X1),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X26,X2),hAPP(X26,X1),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(hAPP(X26,X2),c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X26,X2),hAPP(X26,X1),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f554,f901]) ).
fof(f554,axiom,
! [X2,X1,X26] : c_HOL_Ominus__class_Ominus(hAPP(X26,X1),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X26,X2),hAPP(X26,X1),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(hAPP(X26,X2),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(X26,X2),hAPP(X26,X1),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma__MVT_0) ).
fof(f21133,plain,
spl0_907,
inference(avatar_split_clause,[],[f1105,f21131]) ).
fof(f21131,plain,
( spl0_907
<=> ! [X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal),c_Transcendental_Ocos(X5),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f1105,plain,
! [X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f913,f807,f807]) ).
fof(f913,axiom,
! [X5] : 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),X5,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(X5),tc_RealDef_Oreal),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__double_0) ).
fof(f21123,plain,
spl0_906,
inference(avatar_split_clause,[],[f313,f21121]) ).
fof(f21121,plain,
( spl0_906
<=> ! [X5,X0,X6,X2,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X0),c_HOL_Ominus__class_Ominus(X6,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X0),X2,X0),X0),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X6,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f313,axiom,
! [X2,X0,X1,X6,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X0),c_HOL_Ominus__class_Ominus(X6,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X1,X0),X2,X0),X0),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X6,X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
fof(f20486,plain,
( spl0_905
| ~ spl0_169
| ~ spl0_857 ),
inference(avatar_split_clause,[],[f18968,f16439,f2007,f20483]) ).
fof(f20483,plain,
( spl0_905
<=> c_Transcendental_Opi = c_NthRoot_Osqrt(c_Transcendental_Opi) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f2007,plain,
( spl0_169
<=> 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_169])]) ).
fof(f16439,plain,
( spl0_857
<=> c_Transcendental_Opi = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f18968,plain,
( c_Transcendental_Opi = c_NthRoot_Osqrt(c_Transcendental_Opi)
| ~ spl0_169
| ~ spl0_857 ),
inference(superposition,[],[f2009,f16441]) ).
fof(f16441,plain,
( c_Transcendental_Opi = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ spl0_857 ),
inference(avatar_component_clause,[],[f16439]) ).
fof(f2009,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f2007]) ).
fof(f19422,plain,
spl0_904,
inference(avatar_split_clause,[],[f1101,f19420]) ).
fof(f19420,plain,
( spl0_904
<=> ! [X6,X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),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),X5,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_904])]) ).
fof(f1101,plain,
! [X6,X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),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),X5,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,[],[f183,f807,f807]) ).
fof(f183,axiom,
! [X6,X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X5),c_Transcendental_Osin(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__add_0) ).
fof(f19418,plain,
spl0_903,
inference(avatar_split_clause,[],[f1100,f19416]) ).
fof(f19416,plain,
( spl0_903
<=> ! [X6,X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(X5,X6,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(X5),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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f1100,plain,
! [X6,X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(X5,X6,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(X5),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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f185,f807,f807]) ).
fof(f185,axiom,
! [X6,X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(X5,X6,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X6),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X6),c_Transcendental_Osin(X5),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__diff2_0) ).
fof(f19414,plain,
spl0_902,
inference(avatar_split_clause,[],[f1099,f19412]) ).
fof(f19412,plain,
( spl0_902
<=> ! [X6,X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(X5,X6,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),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),X5,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_902])]) ).
fof(f1099,plain,
! [X6,X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(X5,X6,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),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),X5,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,[],[f186,f807,f807]) ).
fof(f186,axiom,
! [X6,X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(X5,X6,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Ocos(X6),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X5),c_Transcendental_Osin(X6),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__diff_0) ).
fof(f19025,plain,
( spl0_901
| ~ spl0_264
| ~ spl0_846
| ~ spl0_900 ),
inference(avatar_split_clause,[],[f19021,f19017,f15194,f2521,f19023]) ).
fof(f19023,plain,
( spl0_901
<=> ! [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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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(X5),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f2521,plain,
( spl0_264
<=> ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(X5),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f15194,plain,
( spl0_846
<=> ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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(X5,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f19017,plain,
( spl0_900
<=> ! [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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f19021,plain,
( ! [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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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(X5),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_264
| ~ spl0_846
| ~ spl0_900 ),
inference(forward_demodulation,[],[f19020,f15195]) ).
fof(f15195,plain,
( ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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(X5,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_846 ),
inference(avatar_component_clause,[],[f15194]) ).
fof(f19020,plain,
( ! [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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(X5),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_264
| ~ spl0_900 ),
inference(forward_demodulation,[],[f19018,f2522]) ).
fof(f2522,plain,
( ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(X5),tc_RealDef_Oreal)
| ~ spl0_264 ),
inference(avatar_component_clause,[],[f2521]) ).
fof(f19018,plain,
( ! [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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_900 ),
inference(avatar_component_clause,[],[f19017]) ).
fof(f19019,plain,
spl0_900,
inference(avatar_split_clause,[],[f1075,f19017]) ).
fof(f1075,plain,
! [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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f9,f1066,f1066]) ).
fof(f9,axiom,
! [X5] : c_Transcendental_Otan(c_HOL_Oplus__class_Oplus(X5,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Otan(X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__periodic__pi_0) ).
fof(f19015,plain,
spl0_899,
inference(avatar_split_clause,[],[f723,f19013]) ).
fof(f19013,plain,
( spl0_899
<=> ! [X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5)
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__1(X5),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) = X5
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__2(X5),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) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f723,axiom,
! [X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5)
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__1(X5),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) = X5
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__2(X5),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) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__zero__iff_3) ).
fof(f18824,plain,
( spl0_898
| ~ spl0_114
| ~ spl0_473
| ~ spl0_897 ),
inference(avatar_split_clause,[],[f18818,f18815,f5256,f1737,f18822]) ).
fof(f18822,plain,
( spl0_898
<=> ! [X5] :
( ~ 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),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f5256,plain,
( spl0_473
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f18815,plain,
( spl0_897
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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),X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f18818,plain,
( ! [X5] :
( ~ 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),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_114
| ~ spl0_473
| ~ spl0_897 ),
inference(forward_demodulation,[],[f18816,f5536]) ).
fof(f5536,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_473 ),
inference(resolution,[],[f5257,f1739]) ).
fof(f5257,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) )
| ~ spl0_473 ),
inference(avatar_component_clause,[],[f5256]) ).
fof(f18816,plain,
( ! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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),X5,tc_RealDef_Oreal) )
| ~ spl0_897 ),
inference(avatar_component_clause,[],[f18815]) ).
fof(f18817,plain,
spl0_897,
inference(avatar_split_clause,[],[f1120,f18815]) ).
fof(f1120,plain,
! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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),X5,tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f556,f1066]) ).
fof(f556,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Otan(X5),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),X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__less__zero_0) ).
fof(f18813,plain,
spl0_896,
inference(avatar_split_clause,[],[f666,f18811]) ).
fof(f18811,plain,
( spl0_896
<=> ! [X2,X4,X0,X3,X1,X30] :
( ~ class_RealVector_Oreal__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0),X30,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X4,X0),X30,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X3,X0),X30,X0),X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f666,axiom,
! [X2,X3,X0,X1,X4,X30] :
( ~ class_RealVector_Oreal__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0),X30,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X4,X0),X30,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X3,X0),X30,X0),X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).
fof(f18085,plain,
( spl0_567
| ~ spl0_196
| spl0_858 ),
inference(avatar_split_clause,[],[f17008,f16443,f2135,f6704]) ).
fof(f6704,plain,
( spl0_567
<=> c_lessequals(c_Transcendental_Opi,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f2135,plain,
( spl0_196
<=> ! [X8,X7] :
( c_lessequals(X7,X8,tc_RealDef_Oreal)
| c_lessequals(X8,X7,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f16443,plain,
( spl0_858
<=> c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f17008,plain,
( c_lessequals(c_Transcendental_Opi,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_196
| spl0_858 ),
inference(resolution,[],[f16445,f2136]) ).
fof(f2136,plain,
( ! [X8,X7] :
( c_lessequals(X7,X8,tc_RealDef_Oreal)
| c_lessequals(X8,X7,tc_RealDef_Oreal) )
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f2135]) ).
fof(f16445,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)
| spl0_858 ),
inference(avatar_component_clause,[],[f16443]) ).
fof(f18084,plain,
spl0_895,
inference(avatar_split_clause,[],[f1152,f18082]) ).
fof(f1152,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,[],[f1095,f1067]) ).
fof(f1067,plain,
! [X5] : c_Transcendental_Ocos(X5) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f808,f807]) ).
fof(f808,axiom,
! [X5] : c_Transcendental_Ocos(X5) = 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),X5,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__sin__eq_0) ).
fof(f1095,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,[],[f546,f1066,f1066]) ).
fof(f546,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/sandbox2/benchmark/theBenchmark.p',cls_tan__inverse_0) ).
fof(f17878,plain,
( spl0_894
| ~ spl0_112
| ~ spl0_381
| ~ spl0_893 ),
inference(avatar_split_clause,[],[f17874,f17871,f3580,f1727,f17876]) ).
fof(f17876,plain,
( spl0_894
<=> ! [X5] : 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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f1727,plain,
( spl0_112
<=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f3580,plain,
( spl0_381
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f17871,plain,
( spl0_893
<=> ! [X5] : 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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f17874,plain,
( ! [X5] : 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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal)
| ~ spl0_112
| ~ spl0_381
| ~ spl0_893 ),
inference(forward_demodulation,[],[f17872,f3939]) ).
fof(f3939,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_381 ),
inference(resolution,[],[f3581,f1729]) ).
fof(f1729,plain,
( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1727]) ).
fof(f3581,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) )
| ~ spl0_381 ),
inference(avatar_component_clause,[],[f3580]) ).
fof(f17872,plain,
( ! [X5] : 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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal)
| ~ spl0_893 ),
inference(avatar_component_clause,[],[f17871]) ).
fof(f17873,plain,
spl0_893,
inference(avatar_split_clause,[],[f1138,f17871]) ).
fof(f1138,plain,
! [X5] : 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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),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(X5,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1076,f709]) ).
fof(f709,axiom,
! [X5] : c_Transcendental_Ocos(X5) = c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__minus_0) ).
fof(f1076,plain,
! [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),c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f104,f1066,f1066]) ).
fof(f104,axiom,
! [X5] : c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(X5),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__minus_0) ).
fof(f17869,plain,
spl0_892,
inference(avatar_split_clause,[],[f1117,f17867]) ).
fof(f17867,plain,
( spl0_892
<=> ! [X5] :
( c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__1(X5),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),X5,tc_RealDef_Oreal))
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__2(X5),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) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f1117,plain,
! [X5] :
( c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__1(X5),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),X5,tc_RealDef_Oreal))
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__2(X5),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) = X5 ),
inference(definition_unfolding,[],[f567,f807]) ).
fof(f567,axiom,
! [X5] :
( c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__1(X5),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Osin(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__2(X5),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) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__zero__iff_1) ).
fof(f17865,plain,
spl0_891,
inference(avatar_split_clause,[],[f1092,f17863]) ).
fof(f1092,plain,
! [X5] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Ocos(X5),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),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f184,f807,f807]) ).
fof(f184,axiom,
! [X5] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X5),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X5),c_Transcendental_Osin(X5),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__cos__squared__add3_0) ).
fof(f17784,plain,
( spl0_890
| ~ spl0_874
| ~ spl0_889 ),
inference(avatar_split_clause,[],[f17779,f17775,f17316,f17781]) ).
fof(f17781,plain,
( spl0_890
<=> 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_890])]) ).
fof(f17316,plain,
( spl0_874
<=> 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_874])]) ).
fof(f17775,plain,
( spl0_889
<=> 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_889])]) ).
fof(f17779,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_874
| ~ spl0_889 ),
inference(forward_demodulation,[],[f17777,f17318]) ).
fof(f17318,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_874 ),
inference(avatar_component_clause,[],[f17316]) ).
fof(f17777,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_889 ),
inference(avatar_component_clause,[],[f17775]) ).
fof(f17778,plain,
spl0_889,
inference(avatar_split_clause,[],[f1091,f17775]) ).
fof(f1091,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,[],[f565,f1066]) ).
fof(f565,axiom,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)) = 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)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__60_0) ).
fof(f17773,plain,
spl0_888,
inference(avatar_split_clause,[],[f593,f17771]) ).
fof(f17771,plain,
( spl0_888
<=> ! [X5,X0,X6,X8,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X6,X0),c_HOL_Oinverse__class_Odivide(X8,X7,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Otimes__class_Otimes(X8,X6,X0),X0),c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f593,axiom,
! [X0,X8,X6,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X6,X0),c_HOL_Oinverse__class_Odivide(X8,X7,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Otimes__class_Otimes(X8,X6,X0),X0),c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).
fof(f17764,plain,
spl0_887,
inference(avatar_split_clause,[],[f578,f17762]) ).
fof(f17762,plain,
( spl0_887
<=> ! [X5,X0,X6,X8,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X5,X6,X0),c_HOL_Oinverse__class_Odivide(X8,X7,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Otimes__class_Otimes(X8,X6,X0),X0),c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f578,axiom,
! [X0,X8,X6,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X5,X6,X0),c_HOL_Oinverse__class_Odivide(X8,X7,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Otimes__class_Otimes(X8,X6,X0),X0),c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
fof(f17585,plain,
( spl0_886
| ~ spl0_121
| ~ spl0_475
| ~ spl0_885 ),
inference(avatar_split_clause,[],[f17581,f17578,f5264,f1772,f17583]) ).
fof(f17583,plain,
( spl0_886
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(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),X5,tc_RealDef_Oreal))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f1772,plain,
( spl0_121
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f5264,plain,
( spl0_475
<=> ! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Otimes__class_Otimes(X7,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X0) = c_HOL_Oplus__class_Oplus(X7,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f17578,plain,
( spl0_885
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,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_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(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),X5,tc_RealDef_Oreal))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f17581,plain,
( ! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(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),X5,tc_RealDef_Oreal))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) )
| ~ spl0_121
| ~ spl0_475
| ~ spl0_885 ),
inference(forward_demodulation,[],[f17579,f5541]) ).
fof(f5541,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_475 ),
inference(resolution,[],[f5265,f1774]) ).
fof(f1774,plain,
( class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1772]) ).
fof(f5265,plain,
( ! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Otimes__class_Otimes(X7,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X0) = c_HOL_Oplus__class_Oplus(X7,X7,X0) )
| ~ spl0_475 ),
inference(avatar_component_clause,[],[f5264]) ).
fof(f17579,plain,
( ! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,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_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(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),X5,tc_RealDef_Oreal))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) )
| ~ spl0_885 ),
inference(avatar_component_clause,[],[f17578]) ).
fof(f17580,plain,
spl0_885,
inference(avatar_split_clause,[],[f1164,f17578]) ).
fof(f1164,plain,
! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,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_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(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),X5,tc_RealDef_Oreal))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1130,f901]) ).
fof(f1130,plain,
! [X5] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(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),X5,tc_RealDef_Oreal))
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,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,[],[f774,f807]) ).
fof(f774,axiom,
! [X5] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Osin(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,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/sandbox2/benchmark/theBenchmark.p',cls_sin__cos__between__zero__two__pi_0) ).
fof(f17576,plain,
spl0_884,
inference(avatar_split_clause,[],[f1122,f17574]) ).
fof(f17574,plain,
( spl0_884
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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_884])]) ).
fof(f1122,plain,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,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),X5,tc_RealDef_Oreal)),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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,[],[f729,f1066]) ).
fof(f729,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Otan(X5),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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/sandbox2/benchmark/theBenchmark.p',cls_tan__gt__zero_0) ).
fof(f17572,plain,
spl0_883,
inference(avatar_split_clause,[],[f1118,f17570]) ).
fof(f17570,plain,
( spl0_883
<=> ! [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),X5,tc_RealDef_Oreal))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__lemma__1__1(X5),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) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f1118,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),X5,tc_RealDef_Oreal))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__lemma__1__1(X5),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) = X5 ),
inference(definition_unfolding,[],[f784,f807]) ).
fof(f784,axiom,
! [X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Osin(X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__lemma__1__1(X5),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) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__zero__lemma_1) ).
fof(f17499,plain,
( spl0_882
| ~ spl0_121
| ~ spl0_475
| ~ spl0_881 ),
inference(avatar_split_clause,[],[f17495,f17492,f5264,f1772,f17497]) ).
fof(f17497,plain,
( spl0_882
<=> ! [X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X5,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(X5,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_882])]) ).
fof(f17492,plain,
( spl0_881
<=> ! [X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X5,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(X5,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_881])]) ).
fof(f17495,plain,
( ! [X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X5,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(X5,c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_121
| ~ spl0_475
| ~ spl0_881 ),
inference(forward_demodulation,[],[f17493,f5541]) ).
fof(f17493,plain,
( ! [X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X5,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(X5,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_881 ),
inference(avatar_component_clause,[],[f17492]) ).
fof(f17494,plain,
spl0_881,
inference(avatar_split_clause,[],[f1147,f17492]) ).
fof(f1147,plain,
! [X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X5,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(X5,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,[],[f1090,f901]) ).
fof(f1090,plain,
! [X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X5,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(X5,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,[],[f796,f807,f807]) ).
fof(f796,axiom,
! [X5] : c_Transcendental_Osin(X5) = c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(X5,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/sandbox2/benchmark/theBenchmark.p',cls_sin__periodic_0) ).
fof(f17490,plain,
spl0_880,
inference(avatar_split_clause,[],[f1116,f17488]) ).
fof(f17488,plain,
( spl0_880
<=> ! [X5] :
( c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__2(X5),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),X5,tc_RealDef_Oreal))
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__1(X5),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) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f1116,plain,
! [X5] :
( c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__2(X5),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),X5,tc_RealDef_Oreal))
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__1(X5),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) = X5 ),
inference(definition_unfolding,[],[f724,f807]) ).
fof(f724,axiom,
! [X5] :
( c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__2(X5),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Osin(X5)
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__1(X5),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) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__zero__iff_2) ).
fof(f17398,plain,
( spl0_879
| ~ spl0_869
| ~ spl0_878 ),
inference(avatar_split_clause,[],[f17393,f17389,f16512,f17395]) ).
fof(f17395,plain,
( spl0_879
<=> c_HOL_Oone__class_Oone(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_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_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f16512,plain,
( spl0_869
<=> 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_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f17389,plain,
( spl0_878
<=> 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_878])]) ).
fof(f17393,plain,
( c_HOL_Oone__class_Oone(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_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_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_869
| ~ spl0_878 ),
inference(forward_demodulation,[],[f17391,f16514]) ).
fof(f16514,plain,
( 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_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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))
| ~ spl0_869 ),
inference(avatar_component_clause,[],[f16512]) ).
fof(f17391,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)
| ~ spl0_878 ),
inference(avatar_component_clause,[],[f17389]) ).
fof(f17392,plain,
spl0_878,
inference(avatar_split_clause,[],[f1086,f17389]) ).
fof(f1086,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,[],[f611,f1066]) ).
fof(f611,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/sandbox2/benchmark/theBenchmark.p',cls_tan__45_0) ).
fof(f17357,plain,
( spl0_877
| ~ spl0_114
| ~ spl0_473
| ~ spl0_876 ),
inference(avatar_split_clause,[],[f17353,f17350,f5256,f1737,f17355]) ).
fof(f17355,plain,
( spl0_877
<=> ! [X5] :
( ~ 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),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,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),X5,tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f17350,plain,
( spl0_876
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,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),X5,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),X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f17353,plain,
( ! [X5] :
( ~ 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),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,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),X5,tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_114
| ~ spl0_473
| ~ spl0_876 ),
inference(forward_demodulation,[],[f17351,f5536]) ).
fof(f17351,plain,
( ! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,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),X5,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),X5,tc_RealDef_Oreal) )
| ~ spl0_876 ),
inference(avatar_component_clause,[],[f17350]) ).
fof(f17352,plain,
spl0_876,
inference(avatar_split_clause,[],[f1121,f17350]) ).
fof(f1121,plain,
! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,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),X5,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),X5,tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f769,f807]) ).
fof(f769,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Osin(X5),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),X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__less__zero_0) ).
fof(f17324,plain,
( spl0_875
| spl0_857
| ~ spl0_298
| ~ spl0_567 ),
inference(avatar_split_clause,[],[f8338,f6704,f2843,f16439,f17321]) ).
fof(f17321,plain,
( spl0_875
<=> c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f2843,plain,
( spl0_298
<=> ! [X6,X5] :
( X5 = X6
| ~ c_lessequals(X5,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f8338,plain,
( c_Transcendental_Opi = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_298
| ~ spl0_567 ),
inference(resolution,[],[f6706,f2844]) ).
fof(f2844,plain,
( ! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_RealDef_Oreal)
| X5 = X6
| c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal) )
| ~ spl0_298 ),
inference(avatar_component_clause,[],[f2843]) ).
fof(f6706,plain,
( c_lessequals(c_Transcendental_Opi,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_567 ),
inference(avatar_component_clause,[],[f6704]) ).
fof(f17319,plain,
( spl0_874
| ~ spl0_762
| ~ spl0_873 ),
inference(avatar_split_clause,[],[f17314,f17310,f12653,f17316]) ).
fof(f12653,plain,
( spl0_762
<=> 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_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) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f17310,plain,
( spl0_873
<=> 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_873])]) ).
fof(f17314,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_762
| ~ spl0_873 ),
inference(forward_demodulation,[],[f17312,f12655]) ).
fof(f12655,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_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)
| ~ spl0_762 ),
inference(avatar_component_clause,[],[f12653]) ).
fof(f17312,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_873 ),
inference(avatar_component_clause,[],[f17310]) ).
fof(f17313,plain,
spl0_873,
inference(avatar_split_clause,[],[f1106,f17310]) ).
fof(f1106,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,[],[f803,f807]) ).
fof(f803,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_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)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__60_0) ).
fof(f17231,plain,
( spl0_872
| ~ spl0_169
| ~ spl0_344
| ~ spl0_871 ),
inference(avatar_split_clause,[],[f17197,f17193,f3250,f2007,f17228]) ).
fof(f17228,plain,
( spl0_872
<=> 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_872])]) ).
fof(f3250,plain,
( spl0_344
<=> ! [X6,X5] : c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(X5,X6,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(X5),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f17193,plain,
( spl0_871
<=> 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_871])]) ).
fof(f17197,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_169
| ~ spl0_344
| ~ spl0_871 ),
inference(forward_demodulation,[],[f17195,f3405]) ).
fof(f3405,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_169
| ~ spl0_344 ),
inference(superposition,[],[f3251,f2009]) ).
fof(f3251,plain,
( ! [X6,X5] : c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(X5,X6,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(X5),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal)
| ~ spl0_344 ),
inference(avatar_component_clause,[],[f3250]) ).
fof(f17195,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_871 ),
inference(avatar_component_clause,[],[f17193]) ).
fof(f17196,plain,
spl0_871,
inference(avatar_split_clause,[],[f1155,f17193]) ).
fof(f1155,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,[],[f1104,f1153]) ).
fof(f1153,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,[],[f1102,f797]) ).
fof(f797,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/sandbox2/benchmark/theBenchmark.p',cls_cos__60_0) ).
fof(f1102,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,[],[f801,f807]) ).
fof(f801,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/sandbox2/benchmark/theBenchmark.p',cls_sin__30_0) ).
fof(f1104,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,[],[f542,f1066]) ).
fof(f542,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/sandbox2/benchmark/theBenchmark.p',cls_tan__30_0) ).
fof(f17191,plain,
spl0_870,
inference(avatar_split_clause,[],[f1124,f17189]) ).
fof(f17189,plain,
( spl0_870
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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_870])]) ).
fof(f1124,plain,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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,[],[f805,f807]) ).
fof(f805,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(X5),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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/sandbox2/benchmark/theBenchmark.p',cls_sin__gt__zero2_0) ).
fof(f16515,plain,
spl0_869,
inference(avatar_split_clause,[],[f1156,f16512]) ).
fof(f1156,plain,
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_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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(forward_demodulation,[],[f1107,f798]) ).
fof(f798,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/sandbox2/benchmark/theBenchmark.p',cls_cos__45_0) ).
fof(f1107,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,[],[f800,f807]) ).
fof(f800,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/sandbox2/benchmark/theBenchmark.p',cls_sin__45_0) ).
fof(f16489,plain,
( spl0_868
| ~ spl0_121
| ~ spl0_175
| ~ spl0_251
| ~ spl0_867 ),
inference(avatar_split_clause,[],[f16484,f16480,f2466,f2034,f1772,f16486]) ).
fof(f16486,plain,
( spl0_868
<=> c_Transcendental_Ocos(c_Transcendental_Opi) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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_868])]) ).
fof(f2034,plain,
( spl0_175
<=> c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Transcendental_Opi) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f2466,plain,
( spl0_251
<=> ! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f16480,plain,
( spl0_867
<=> 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_867])]) ).
fof(f16484,plain,
( c_Transcendental_Ocos(c_Transcendental_Opi) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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_121
| ~ spl0_175
| ~ spl0_251
| ~ spl0_867 ),
inference(forward_demodulation,[],[f16482,f2673]) ).
fof(f2673,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Transcendental_Opi)
| ~ spl0_121
| ~ spl0_175
| ~ spl0_251 ),
inference(forward_demodulation,[],[f2671,f2036]) ).
fof(f2036,plain,
( c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Transcendental_Opi)
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f2034]) ).
fof(f2671,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_RealDef_Oreal)
| ~ spl0_121
| ~ spl0_251 ),
inference(resolution,[],[f2467,f1774]) ).
fof(f2467,plain,
( ! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f2466]) ).
fof(f16482,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_867 ),
inference(avatar_component_clause,[],[f16480]) ).
fof(f16483,plain,
spl0_867,
inference(avatar_split_clause,[],[f1154,f16480]) ).
fof(f1154,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,[],[f1103,f901]) ).
fof(f1103,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,[],[f771,f807]) ).
fof(f771,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/sandbox2/benchmark/theBenchmark.p',cls_sin__3over2__pi_0) ).
fof(f16478,plain,
spl0_866,
inference(avatar_split_clause,[],[f511,f16476]) ).
fof(f16476,plain,
( spl0_866
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f511,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X1 = X2
| X3 = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X4,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
fof(f16474,plain,
spl0_865,
inference(avatar_split_clause,[],[f276,f16472]) ).
fof(f16472,plain,
( spl0_865
<=> ! [X4,X11,X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X11,X0),X3,X0),X4,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f276,axiom,
! [X2,X3,X0,X11,X1,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X11,X0),X3,X0),X4,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
fof(f16470,plain,
spl0_864,
inference(avatar_split_clause,[],[f275,f16468]) ).
fof(f16468,plain,
( spl0_864
<=> ! [X4,X11,X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X11,X0),X3,X0),X4,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f275,axiom,
! [X2,X3,X0,X11,X1,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X11,X0),X3,X0),X4,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
fof(f16466,plain,
spl0_863,
inference(avatar_split_clause,[],[f274,f16464]) ).
fof(f16464,plain,
( spl0_863
<=> ! [X2,X4,X11,X0,X3,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X11,X0),X4,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f274,axiom,
! [X2,X3,X0,X11,X1,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X11,X0),X4,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
fof(f16462,plain,
spl0_862,
inference(avatar_split_clause,[],[f273,f16460]) ).
fof(f16460,plain,
( spl0_862
<=> ! [X2,X4,X11,X0,X3,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X11,X0),X4,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f273,axiom,
! [X2,X3,X0,X11,X1,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X11,X0),X4,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
fof(f16458,plain,
spl0_861,
inference(avatar_split_clause,[],[f153,f16456]) ).
fof(f16456,plain,
( spl0_861
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f153,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).
fof(f16454,plain,
spl0_860,
inference(avatar_split_clause,[],[f40,f16452]) ).
fof(f16452,plain,
( spl0_860
<=> ! [X4,X11,X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X11,X0),X3,X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f40,axiom,
! [X2,X3,X0,X11,X1,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X11,X0),X3,X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
fof(f16450,plain,
spl0_859,
inference(avatar_split_clause,[],[f39,f16448]) ).
fof(f16448,plain,
( spl0_859
<=> ! [X4,X11,X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X11,X0),X3,X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f39,axiom,
! [X2,X3,X0,X11,X1,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X11,X0),X3,X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
fof(f16446,plain,
( spl0_857
| ~ spl0_858
| ~ spl0_302
| ~ spl0_567 ),
inference(avatar_split_clause,[],[f8337,f6704,f2859,f16443,f16439]) ).
fof(f2859,plain,
( spl0_302
<=> ! [X8,X7] :
( X7 = X8
| ~ c_lessequals(X7,X8,tc_RealDef_Oreal)
| ~ c_lessequals(X8,X7,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f8337,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)
| c_Transcendental_Opi = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ spl0_302
| ~ spl0_567 ),
inference(resolution,[],[f6706,f2860]) ).
fof(f2860,plain,
( ! [X8,X7] :
( ~ c_lessequals(X8,X7,tc_RealDef_Oreal)
| ~ c_lessequals(X7,X8,tc_RealDef_Oreal)
| X7 = X8 )
| ~ spl0_302 ),
inference(avatar_component_clause,[],[f2859]) ).
fof(f16437,plain,
spl0_856,
inference(avatar_split_clause,[],[f38,f16435]) ).
fof(f16435,plain,
( spl0_856
<=> ! [X2,X4,X11,X0,X3,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X11,X0),X4,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f38,axiom,
! [X2,X3,X0,X11,X1,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X11,X0),X4,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
fof(f16433,plain,
spl0_855,
inference(avatar_split_clause,[],[f37,f16431]) ).
fof(f16431,plain,
( spl0_855
<=> ! [X2,X4,X11,X0,X3,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X11,X0),X4,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f37,axiom,
! [X2,X3,X0,X11,X1,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X11,X0),X4,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
fof(f16161,plain,
( ~ spl0_671
| spl0_508
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f15525,f11457,f5751,f9371]) ).
fof(f9371,plain,
( spl0_671
<=> c_lessequals(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f5751,plain,
( spl0_508
<=> c_lessequals(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f11457,plain,
( spl0_726
<=> ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f15525,plain,
( ~ c_lessequals(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal)
| spl0_508
| ~ spl0_726 ),
inference(resolution,[],[f11458,f5752]) ).
fof(f5752,plain,
( ~ c_lessequals(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_508 ),
inference(avatar_component_clause,[],[f5751]) ).
fof(f11458,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_726 ),
inference(avatar_component_clause,[],[f11457]) ).
fof(f15339,plain,
( spl0_854
| ~ spl0_93
| ~ spl0_102
| ~ spl0_288
| ~ spl0_543
| ~ spl0_823
| ~ spl0_853 ),
inference(avatar_split_clause,[],[f15335,f15330,f14827,f6527,f2803,f1677,f1632,f15337]) ).
fof(f15337,plain,
( spl0_854
<=> ! [X25] :
( 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(X25,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(X25,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f1632,plain,
( spl0_93
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f6527,plain,
( spl0_543
<=> ! [X0,X1,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X10,c_HOL_Otimes__class_Otimes(X1,X10,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f14827,plain,
( spl0_823
<=> ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f15330,plain,
( spl0_853
<=> ! [X25] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X25,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(X25,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f15335,plain,
( ! [X25] :
( 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(X25,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(X25,tc_nat) )
| ~ spl0_93
| ~ spl0_102
| ~ spl0_288
| ~ spl0_543
| ~ spl0_823
| ~ spl0_853 ),
inference(forward_demodulation,[],[f15334,f2973]) ).
fof(f15334,plain,
( ! [X25] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X25,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(X25,tc_nat) )
| ~ spl0_93
| ~ spl0_543
| ~ spl0_823
| ~ spl0_853 ),
inference(forward_demodulation,[],[f15333,f6637]) ).
fof(f6637,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_93
| ~ spl0_543 ),
inference(resolution,[],[f6528,f1634]) ).
fof(f1634,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1632]) ).
fof(f6528,plain,
( ! [X10,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X10,c_HOL_Otimes__class_Otimes(X1,X10,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X10,X0) )
| ~ spl0_543 ),
inference(avatar_component_clause,[],[f6527]) ).
fof(f15333,plain,
( ! [X25] :
( 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(X25,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(X25,tc_nat) )
| ~ spl0_823
| ~ spl0_853 ),
inference(forward_demodulation,[],[f15331,f14828]) ).
fof(f14828,plain,
( ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal))
| ~ spl0_823 ),
inference(avatar_component_clause,[],[f14827]) ).
fof(f15331,plain,
( ! [X25] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X25,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(X25,tc_nat) )
| ~ spl0_853 ),
inference(avatar_component_clause,[],[f15330]) ).
fof(f15332,plain,
spl0_853,
inference(avatar_split_clause,[],[f1160,f15330]) ).
fof(f1160,plain,
! [X25] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X25,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(X25,tc_nat) ),
inference(forward_demodulation,[],[f1159,f1094]) ).
fof(f1094,plain,
! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f772,f807]) ).
fof(f772,axiom,
! [X5] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X5),tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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/sandbox2/benchmark/theBenchmark.p',cls_minus__sin__cos__eq_0) ).
fof(f1159,plain,
! [X25] :
( 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(X25,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(X25,tc_nat) ),
inference(forward_demodulation,[],[f1109,f1077]) ).
fof(f1077,plain,
! [X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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(X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f713,f807,f807]) ).
fof(f713,axiom,
! [X5] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X5),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__minus_0) ).
fof(f1109,plain,
! [X25] :
( ~ c_Parity_Oeven__odd__class_Oeven(X25,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(X25,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,[],[f783,f807]) ).
fof(f783,axiom,
! [X25] :
( ~ c_Parity_Oeven__odd__class_Oeven(X25,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(X25,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/sandbox2/benchmark/theBenchmark.p',cls_sin__zero__iff_5) ).
fof(f15328,plain,
spl0_852,
inference(avatar_split_clause,[],[f1153,f15325]) ).
fof(f15325,plain,
( spl0_852
<=> 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_852])]) ).
fof(f15323,plain,
spl0_851,
inference(avatar_split_clause,[],[f1108,f15321]) ).
fof(f15321,plain,
( spl0_851
<=> ! [X34] :
( ~ c_Parity_Oeven__odd__class_Oeven(X34,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(X34,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_851])]) ).
fof(f1108,plain,
! [X34] :
( ~ c_Parity_Oeven__odd__class_Oeven(X34,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(X34,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,[],[f810,f807]) ).
fof(f810,axiom,
! [X34] :
( ~ c_Parity_Oeven__odd__class_Oeven(X34,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X34,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/sandbox2/benchmark/theBenchmark.p',cls_sin__zero__iff_4) ).
fof(f15276,plain,
( spl0_850
| ~ spl0_794
| ~ spl0_849 ),
inference(avatar_split_clause,[],[f15267,f15264,f13746,f15274]) ).
fof(f15274,plain,
( spl0_850
<=> ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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(X5,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f13746,plain,
( spl0_794
<=> ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f15264,plain,
( spl0_849
<=> ! [X5] : 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),X5,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(X5,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f15267,plain,
( ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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(X5,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_794
| ~ spl0_849 ),
inference(forward_demodulation,[],[f15265,f13747]) ).
fof(f13747,plain,
( ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_794 ),
inference(avatar_component_clause,[],[f13746]) ).
fof(f15265,plain,
( ! [X5] : 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),X5,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(X5,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_849 ),
inference(avatar_component_clause,[],[f15264]) ).
fof(f15266,plain,
spl0_849,
inference(avatar_split_clause,[],[f1083,f15264]) ).
fof(f1083,plain,
! [X5] : 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),X5,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(X5,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f710,f807,f807]) ).
fof(f710,axiom,
! [X5] : c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(X5,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X5),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__periodic__pi__diff_0) ).
fof(f15231,plain,
( spl0_848
| ~ spl0_794
| ~ spl0_847 ),
inference(avatar_split_clause,[],[f15227,f15224,f13746,f15229]) ).
fof(f15229,plain,
( spl0_848
<=> ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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,X5,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f15224,plain,
( spl0_847
<=> ! [X5] : 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),X5,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,X5,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f15227,plain,
( ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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,X5,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_794
| ~ spl0_847 ),
inference(forward_demodulation,[],[f15225,f13747]) ).
fof(f15225,plain,
( ! [X5] : 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),X5,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,X5,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_847 ),
inference(avatar_component_clause,[],[f15224]) ).
fof(f15226,plain,
spl0_847,
inference(avatar_split_clause,[],[f1082,f15224]) ).
fof(f1082,plain,
! [X5] : 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),X5,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,X5,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f711,f807,f807]) ).
fof(f711,axiom,
! [X5] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X5),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,X5,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__periodic__pi2_0) ).
fof(f15196,plain,
( spl0_846
| ~ spl0_794
| ~ spl0_845 ),
inference(avatar_split_clause,[],[f15192,f15189,f13746,f15194]) ).
fof(f15189,plain,
( spl0_845
<=> ! [X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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(X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f15192,plain,
( ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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(X5,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_794
| ~ spl0_845 ),
inference(forward_demodulation,[],[f15190,f13747]) ).
fof(f15190,plain,
( ! [X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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(X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_845 ),
inference(avatar_component_clause,[],[f15189]) ).
fof(f15191,plain,
spl0_845,
inference(avatar_split_clause,[],[f1081,f15189]) ).
fof(f1081,plain,
! [X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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(X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f712,f807,f807]) ).
fof(f712,axiom,
! [X5] : c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X5),tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(X5,c_Transcendental_Opi,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__periodic__pi_0) ).
fof(f15187,plain,
spl0_844,
inference(avatar_split_clause,[],[f768,f15185]) ).
fof(f15185,plain,
( spl0_844
<=> ! [X5] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(X5),tc_RealDef_Oreal)
| ~ c_lessequals(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f768,axiom,
! [X5] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(X5),tc_RealDef_Oreal)
| ~ c_lessequals(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__ge__zero_0) ).
fof(f15183,plain,
spl0_843,
inference(avatar_split_clause,[],[f767,f15181]) ).
fof(f15181,plain,
( spl0_843
<=> ! [X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(X5),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f767,axiom,
! [X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(X5),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__gt__zero__pi_0) ).
fof(f15179,plain,
spl0_842,
inference(avatar_split_clause,[],[f660,f15177]) ).
fof(f15177,plain,
( spl0_842
<=> ! [X5,X0,X6,X8,X7] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X8,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X7,X0),c_HOL_Oinverse__class_Odivide(X6,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f660,axiom,
! [X0,X8,X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X8,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X7,X0),c_HOL_Oinverse__class_Odivide(X6,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less2_0) ).
fof(f15175,plain,
( spl0_158
| ~ spl0_162
| ~ spl0_302
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f6609,f5751,f2859,f1975,f1952]) ).
fof(f1952,plain,
( spl0_158
<=> c_Transcendental_Opi = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1975,plain,
( spl0_162
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f6609,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)
| c_Transcendental_Opi = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ spl0_302
| ~ spl0_508 ),
inference(resolution,[],[f5753,f2860]) ).
fof(f5753,plain,
( c_lessequals(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_508 ),
inference(avatar_component_clause,[],[f5751]) ).
fof(f15174,plain,
spl0_841,
inference(avatar_split_clause,[],[f653,f15172]) ).
fof(f15172,plain,
( spl0_841
<=> ! [X5,X0,X6,X8,X7] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X8,X7,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X7,X0),c_HOL_Oinverse__class_Odivide(X6,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f653,axiom,
! [X0,X8,X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X8,X7,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X7,X0),c_HOL_Oinverse__class_Odivide(X6,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less_0) ).
fof(f15170,plain,
spl0_840,
inference(avatar_split_clause,[],[f648,f15168]) ).
fof(f15168,plain,
( spl0_840
<=> ! [X5,X0,X6,X8,X7] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X8,X7,X0)
| ~ c_lessequals(X5,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X7,X0),c_HOL_Oinverse__class_Odivide(X6,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f648,axiom,
! [X0,X8,X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X8,X7,X0)
| ~ c_lessequals(X5,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X7,X0),c_HOL_Oinverse__class_Odivide(X6,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__le_0) ).
fof(f15166,plain,
spl0_839,
inference(avatar_split_clause,[],[f582,f15164]) ).
fof(f15164,plain,
( spl0_839
<=> ! [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_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f582,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_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).
fof(f15162,plain,
spl0_838,
inference(avatar_split_clause,[],[f581,f15160]) ).
fof(f15160,plain,
( spl0_838
<=> ! [X0,X3,X2,X1] :
( ~ 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_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f581,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(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).
fof(f15158,plain,
spl0_837,
inference(avatar_split_clause,[],[f580,f15156]) ).
fof(f15156,plain,
( spl0_837
<=> ! [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_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f580,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_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).
fof(f15154,plain,
spl0_836,
inference(avatar_split_clause,[],[f579,f15152]) ).
fof(f15152,plain,
( spl0_836
<=> ! [X0,X3,X2,X1] :
( ~ 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_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f579,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(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).
fof(f15150,plain,
spl0_835,
inference(avatar_split_clause,[],[f571,f15148]) ).
fof(f15148,plain,
( spl0_835
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f571,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).
fof(f15146,plain,
spl0_834,
inference(avatar_split_clause,[],[f570,f15144]) ).
fof(f15144,plain,
( spl0_834
<=> ! [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),X1,X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f570,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),X1,X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).
fof(f15142,plain,
spl0_833,
inference(avatar_split_clause,[],[f498,f15140]) ).
fof(f15140,plain,
( spl0_833
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,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_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f498,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,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_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
fof(f15138,plain,
spl0_832,
inference(avatar_split_clause,[],[f490,f15136]) ).
fof(f15136,plain,
( spl0_832
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f490,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
fof(f15109,plain,
spl0_831,
inference(avatar_split_clause,[],[f486,f15107]) ).
fof(f15107,plain,
( spl0_831
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),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,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f486,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),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,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
fof(f15105,plain,
spl0_830,
inference(avatar_split_clause,[],[f485,f15103]) ).
fof(f15103,plain,
( spl0_830
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f485,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
fof(f15101,plain,
spl0_829,
inference(avatar_split_clause,[],[f332,f15099]) ).
fof(f15099,plain,
( spl0_829
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f332,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
fof(f15097,plain,
spl0_828,
inference(avatar_split_clause,[],[f331,f15095]) ).
fof(f15095,plain,
( spl0_828
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X4,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(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f331,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X4,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(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
fof(f15093,plain,
spl0_827,
inference(avatar_split_clause,[],[f161,f15091]) ).
fof(f15091,plain,
( spl0_827
<=> ! [X0,X3,X2,X1] :
( ~ 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_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f161,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(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).
fof(f15089,plain,
spl0_826,
inference(avatar_split_clause,[],[f160,f15087]) ).
fof(f15087,plain,
( spl0_826
<=> ! [X0,X3,X2,X1] :
( ~ 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_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f160,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(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).
fof(f14877,plain,
spl0_825,
inference(avatar_split_clause,[],[f1139,f14875]) ).
fof(f14875,plain,
( spl0_825
<=> ! [X19] : 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(X19,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X19,tc_nat),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f1139,plain,
! [X19] : 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(X19,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X19,tc_nat),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1078,f901]) ).
fof(f1078,plain,
! [X19] : 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(X19,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X19,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f773,f1066]) ).
fof(f773,axiom,
! [X19] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Otan(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X19,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__npi_0) ).
fof(f14873,plain,
spl0_824,
inference(avatar_split_clause,[],[f1123,f14871]) ).
fof(f14871,plain,
( spl0_824
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,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_824])]) ).
fof(f1123,plain,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f789,f807]) ).
fof(f789,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(X5),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__gt__zero_0) ).
fof(f14829,plain,
( spl0_823
| ~ spl0_112
| ~ spl0_381
| ~ spl0_794
| ~ spl0_822 ),
inference(avatar_split_clause,[],[f14825,f14821,f13746,f3580,f1727,f14827]) ).
fof(f14821,plain,
( spl0_822
<=> ! [X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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(X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f14825,plain,
( ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal))
| ~ spl0_112
| ~ spl0_381
| ~ spl0_794
| ~ spl0_822 ),
inference(forward_demodulation,[],[f14824,f3939]) ).
fof(f14824,plain,
( ! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oinverse__class_Odivide(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(X5,tc_RealDef_Oreal),tc_RealDef_Oreal))
| ~ spl0_794
| ~ spl0_822 ),
inference(forward_demodulation,[],[f14822,f13747]) ).
fof(f14822,plain,
( ! [X5] : c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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(X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_822 ),
inference(avatar_component_clause,[],[f14821]) ).
fof(f14823,plain,
spl0_822,
inference(avatar_split_clause,[],[f1077,f14821]) ).
fof(f14819,plain,
spl0_821,
inference(avatar_split_clause,[],[f595,f14817]) ).
fof(f14817,plain,
( spl0_821
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,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(X1,X2,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f595,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,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(X1,X2,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).
fof(f14815,plain,
spl0_820,
inference(avatar_split_clause,[],[f594,f14813]) ).
fof(f14813,plain,
( spl0_820
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f594,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).
fof(f14811,plain,
spl0_819,
inference(avatar_split_clause,[],[f152,f14809]) ).
fof(f14809,plain,
( spl0_819
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f152,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X3,X1,X0),c_HOL_Oinverse__class_Odivide(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).
fof(f14807,plain,
spl0_818,
inference(avatar_split_clause,[],[f51,f14805]) ).
fof(f14805,plain,
( spl0_818
<=> ! [X2,X4,X11,X0,X3,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X11,X0),X4,X0) = X3
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f51,axiom,
! [X2,X3,X0,X11,X1,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X11,X0),X4,X0) = X3
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),X3,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
fof(f14408,plain,
( spl0_450
| ~ spl0_190
| ~ spl0_535 ),
inference(avatar_split_clause,[],[f9845,f6313,f2111,f5157]) ).
fof(f5157,plain,
( spl0_450
<=> c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f2111,plain,
( spl0_190
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| c_lessequals(X5,X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f6313,plain,
( spl0_535
<=> c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f9845,plain,
( c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_190
| ~ spl0_535 ),
inference(resolution,[],[f6315,f2112]) ).
fof(f2112,plain,
( ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| c_lessequals(X5,X6,tc_RealDef_Oreal) )
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f2111]) ).
fof(f6315,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_535 ),
inference(avatar_component_clause,[],[f6313]) ).
fof(f13983,plain,
spl0_817,
inference(avatar_split_clause,[],[f813,f13981]) ).
fof(f13981,plain,
( spl0_817
<=> ! [X5,X0,X6,X8,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Otimes__class_Otimes(X8,X6,X0) != c_HOL_Otimes__class_Otimes(X5,X7,X0)
| c_HOL_Oinverse__class_Odivide(X5,X6,X0) = c_HOL_Oinverse__class_Odivide(X8,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f813,axiom,
! [X0,X8,X6,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Otimes__class_Otimes(X8,X6,X0) != c_HOL_Otimes__class_Otimes(X5,X7,X0)
| c_HOL_Oinverse__class_Odivide(X5,X6,X0) = c_HOL_Oinverse__class_Odivide(X8,X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
fof(f13979,plain,
spl0_816,
inference(avatar_split_clause,[],[f812,f13977]) ).
fof(f13977,plain,
( spl0_816
<=> ! [X5,X0,X6,X8,X7] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Oinverse__class_Odivide(X5,X6,X0) != c_HOL_Oinverse__class_Odivide(X8,X7,X0)
| c_HOL_Otimes__class_Otimes(X8,X6,X0) = c_HOL_Otimes__class_Otimes(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f812,axiom,
! [X0,X8,X6,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Ozero__class_Ozero(X0) = X7
| c_HOL_Oinverse__class_Odivide(X5,X6,X0) != c_HOL_Oinverse__class_Odivide(X8,X7,X0)
| c_HOL_Otimes__class_Otimes(X8,X6,X0) = c_HOL_Otimes__class_Otimes(X5,X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
fof(f13975,plain,
spl0_815,
inference(avatar_split_clause,[],[f592,f13973]) ).
fof(f13973,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_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f592,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_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).
fof(f13971,plain,
spl0_814,
inference(avatar_split_clause,[],[f591,f13969]) ).
fof(f13969,plain,
( spl0_814
<=> ! [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),X3,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f591,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),X3,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).
fof(f13967,plain,
spl0_813,
inference(avatar_split_clause,[],[f590,f13965]) ).
fof(f13965,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(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(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f590,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(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(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).
fof(f13963,plain,
spl0_812,
inference(avatar_split_clause,[],[f589,f13961]) ).
fof(f13961,plain,
( spl0_812
<=> ! [X0,X3,X2,X1] :
( ~ 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(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f589,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(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(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).
fof(f13959,plain,
spl0_811,
inference(avatar_split_clause,[],[f588,f13957]) ).
fof(f13957,plain,
( spl0_811
<=> ! [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(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f588,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(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).
fof(f13955,plain,
spl0_810,
inference(avatar_split_clause,[],[f587,f13953]) ).
fof(f13953,plain,
( spl0_810
<=> ! [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_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f587,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_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).
fof(f13937,plain,
spl0_809,
inference(avatar_split_clause,[],[f586,f13935]) ).
fof(f13935,plain,
( spl0_809
<=> ! [X0,X3,X2,X1] :
( ~ 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_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f586,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(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_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).
fof(f13933,plain,
spl0_808,
inference(avatar_split_clause,[],[f585,f13931]) ).
fof(f13931,plain,
( spl0_808
<=> ! [X0,X3,X2,X1] :
( ~ 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),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f585,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(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),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).
fof(f13929,plain,
spl0_807,
inference(avatar_split_clause,[],[f351,f13927]) ).
fof(f13927,plain,
( spl0_807
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Osemiring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_Int_Onumber__class_Onumber__of(X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X9,X0),X0),c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X9,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f351,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Osemiring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_Int_Onumber__class_Onumber__of(X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X9,X0),X0),c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X9,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__distrib__number__of_0) ).
fof(f13925,plain,
spl0_806,
inference(avatar_split_clause,[],[f350,f13923]) ).
fof(f13923,plain,
( spl0_806
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_Int_Onumber__class_Onumber__of(X9,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X9,X0),X0),c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X9,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f350,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_Int_Onumber__class_Onumber__of(X9,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X9,X0),X0),c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X9,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).
fof(f13921,plain,
spl0_805,
inference(avatar_split_clause,[],[f349,f13919]) ).
fof(f13919,plain,
( spl0_805
<=> ! [X3,X0,X9,X2] :
( ~ class_Ring__and__Field_Oring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X9,X0),c_HOL_Ominus__class_Ominus(X2,X3,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X9,X0),X2,X0),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X9,X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f349,axiom,
! [X2,X3,X0,X9] :
( ~ class_Ring__and__Field_Oring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X9,X0),c_HOL_Ominus__class_Ominus(X2,X3,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X9,X0),X2,X0),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X9,X0),X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).
fof(f13917,plain,
spl0_804,
inference(avatar_split_clause,[],[f348,f13915]) ).
fof(f13915,plain,
( spl0_804
<=> ! [X3,X0,X9,X2] :
( ~ class_Ring__and__Field_Osemiring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X9,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X9,X0),X2,X0),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X9,X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f348,axiom,
! [X2,X3,X0,X9] :
( ~ class_Ring__and__Field_Osemiring(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X9,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X9,X0),X2,X0),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X9,X0),X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__distrib__number__of_0) ).
fof(f13913,plain,
spl0_803,
inference(avatar_split_clause,[],[f169,f13911]) ).
fof(f13911,plain,
( spl0_803
<=> ! [X0,X3,X2,X1] :
( ~ 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_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f169,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(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).
fof(f13909,plain,
spl0_802,
inference(avatar_split_clause,[],[f168,f13907]) ).
fof(f13907,plain,
( spl0_802
<=> ! [X0,X3,X2,X1] :
( ~ 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_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f168,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(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).
fof(f13905,plain,
spl0_801,
inference(avatar_split_clause,[],[f167,f13903]) ).
fof(f13903,plain,
( spl0_801
<=> ! [X0,X3,X2,X1] :
( ~ 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_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f167,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(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).
fof(f13901,plain,
spl0_800,
inference(avatar_split_clause,[],[f166,f13899]) ).
fof(f13899,plain,
( spl0_800
<=> ! [X0,X3,X2,X1] :
( ~ 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_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f166,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(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).
fof(f13893,plain,
spl0_799,
inference(avatar_split_clause,[],[f165,f13891]) ).
fof(f13891,plain,
( spl0_799
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f165,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).
fof(f13889,plain,
spl0_798,
inference(avatar_split_clause,[],[f164,f13887]) ).
fof(f13887,plain,
( spl0_798
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f164,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).
fof(f13885,plain,
spl0_797,
inference(avatar_split_clause,[],[f163,f13883]) ).
fof(f13883,plain,
( spl0_797
<=> ! [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),X1,X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f163,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),X1,X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).
fof(f13881,plain,
spl0_796,
inference(avatar_split_clause,[],[f162,f13879]) ).
fof(f13879,plain,
( spl0_796
<=> ! [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),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f162,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),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).
fof(f13752,plain,
spl0_795,
inference(avatar_split_clause,[],[f1150,f13750]) ).
fof(f13750,plain,
( spl0_795
<=> ! [X19] : 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(X19,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f1150,plain,
! [X19] : 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(X19,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f1093,f901]) ).
fof(f1093,plain,
! [X19] : 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(X19,tc_nat),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f822,f807]) ).
fof(f822,axiom,
! [X19] : 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(X19,tc_nat),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__2npi_0) ).
fof(f13748,plain,
spl0_794,
inference(avatar_split_clause,[],[f1094,f13746]) ).
fof(f13744,plain,
spl0_793,
inference(avatar_split_clause,[],[f566,f13742]) ).
fof(f13742,plain,
( spl0_793
<=> ! [X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__1(X5),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__2(X5),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) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f566,axiom,
! [X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__1(X5),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__2(X5),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) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__zero__iff_1) ).
fof(f13739,plain,
( ~ spl0_162
| spl0_448
| ~ spl0_670 ),
inference(avatar_split_clause,[],[f13465,f9064,f4872,f1975]) ).
fof(f4872,plain,
( spl0_448
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f9064,plain,
( spl0_670
<=> ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f13465,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)
| spl0_448
| ~ spl0_670 ),
inference(resolution,[],[f9065,f4874]) ).
fof(f4874,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| spl0_448 ),
inference(avatar_component_clause,[],[f4872]) ).
fof(f9065,plain,
( ! [X0] :
( c_lessequals(X0,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_670 ),
inference(avatar_component_clause,[],[f9064]) ).
fof(f13170,plain,
spl0_792,
inference(avatar_split_clause,[],[f1111,f13168]) ).
fof(f13168,plain,
( spl0_792
<=> ! [X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(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_Osko__Transcendental__Xlemma__tan__total__1__1(X6),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(X6)),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f1111,plain,
! [X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(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_Osko__Transcendental__Xlemma__tan__total__1__1(X6),tc_RealDef_Oreal)),c_Transcendental_Ocos(c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(X6)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f260,f1066]) ).
fof(f260,axiom,
! [X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X6,c_Transcendental_Otan(c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(X6)),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma__tan__total_2) ).
fof(f13166,plain,
spl0_791,
inference(avatar_split_clause,[],[f818,f13164]) ).
fof(f13164,plain,
( spl0_791
<=> ! [X6,X5,X7] :
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X5,tc_RealDef_Oreal) != c_HOL_Oinverse__class_Odivide(X6,X7,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),X7,tc_RealDef_Oreal),tc_RealDef_Oreal) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f818,axiom,
! [X6,X7,X5] :
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),X5,tc_RealDef_Oreal) != c_HOL_Oinverse__class_Odivide(X6,X7,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),X7,tc_RealDef_Oreal),tc_RealDef_Oreal) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__2__times__iff_1) ).
fof(f13162,plain,
spl0_790,
inference(avatar_split_clause,[],[f816,f13160]) ).
fof(f13160,plain,
( spl0_790
<=> ! [X0,X8,X3,X2] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_Int_Onumber__class_Onumber__of(X8,X0) != c_HOL_Oinverse__class_Odivide(X2,X3,X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X8,X0),X3,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f816,axiom,
! [X2,X3,X0,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_Int_Onumber__class_Onumber__of(X8,X0) != c_HOL_Oinverse__class_Odivide(X2,X3,X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X8,X0),X3,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_0) ).
fof(f13158,plain,
spl0_789,
inference(avatar_split_clause,[],[f782,f13156]) ).
fof(f13156,plain,
( spl0_789
<=> ! [X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1(X5),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) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f782,axiom,
! [X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1(X5),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) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__zero__lemma_1) ).
fof(f13154,plain,
spl0_788,
inference(avatar_split_clause,[],[f726,f13152]) ).
fof(f13152,plain,
( spl0_788
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,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),X5,tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f726,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,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),X5,tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__double__less__one_0) ).
fof(f13150,plain,
spl0_787,
inference(avatar_split_clause,[],[f664,f13148]) ).
fof(f13148,plain,
( spl0_787
<=> ! [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),X1,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_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f664,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),X1,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_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).
fof(f13146,plain,
spl0_786,
inference(avatar_split_clause,[],[f663,f13144]) ).
fof(f13144,plain,
( spl0_786
<=> ! [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),X1,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_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f663,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),X1,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_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).
fof(f13142,plain,
spl0_785,
inference(avatar_split_clause,[],[f662,f13140]) ).
fof(f13140,plain,
( spl0_785
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_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_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f662,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_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_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
fof(f13138,plain,
spl0_784,
inference(avatar_split_clause,[],[f661,f13136]) ).
fof(f13136,plain,
( spl0_784
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_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_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f661,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_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_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
fof(f13134,plain,
spl0_783,
inference(avatar_split_clause,[],[f639,f13132]) ).
fof(f13132,plain,
( spl0_783
<=> ! [X11,X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X11,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f639,axiom,
! [X2,X3,X0,X11,X1] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X11,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
fof(f13130,plain,
( spl0_450
| ~ spl0_487
| ~ spl0_627 ),
inference(avatar_split_clause,[],[f11415,f7758,f5544,f5157]) ).
fof(f5544,plain,
( spl0_487
<=> ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f7758,plain,
( spl0_627
<=> ! [X0] :
( c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f11415,plain,
( c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_487
| ~ spl0_627 ),
inference(duplicate_literal_removal,[],[f11402]) ).
fof(f11402,plain,
( c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_487
| ~ spl0_627 ),
inference(resolution,[],[f7759,f5545]) ).
fof(f5545,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_487 ),
inference(avatar_component_clause,[],[f5544]) ).
fof(f7759,plain,
( ! [X0] :
( c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),X0,tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_627 ),
inference(avatar_component_clause,[],[f7758]) ).
fof(f13129,plain,
spl0_782,
inference(avatar_split_clause,[],[f584,f13127]) ).
fof(f13127,plain,
( spl0_782
<=> ! [X5,X0,X6,X7] :
( ~ 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(X5,c_HOL_Otimes__class_Otimes(X7,X6,X0),X0),X6,X0) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f584,axiom,
! [X0,X6,X7,X5] :
( ~ 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(X5,c_HOL_Otimes__class_Otimes(X7,X6,X0),X0),X6,X0) = c_HOL_Oplus__class_Oplus(X7,c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
fof(f13125,plain,
spl0_781,
inference(avatar_split_clause,[],[f583,f13123]) ).
fof(f13123,plain,
( spl0_781
<=> ! [X5,X0,X6,X7] :
( ~ 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(X5,X6,X0),X7,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X7,X6,X0),X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f583,axiom,
! [X0,X6,X7,X5] :
( ~ 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(X5,X6,X0),X7,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X7,X6,X0),X0),X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
fof(f13121,plain,
spl0_780,
inference(avatar_split_clause,[],[f564,f13119]) ).
fof(f13119,plain,
( spl0_780
<=> ! [X2,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X1,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(X2,X1,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f564,axiom,
! [X2,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X1,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(X2,X1,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__average__minus__second_0) ).
fof(f13117,plain,
spl0_779,
inference(avatar_split_clause,[],[f563,f13115]) ).
fof(f13115,plain,
( spl0_779
<=> ! [X2,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,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),X1,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X1,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_779])]) ).
fof(f563,axiom,
! [X2,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,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),X1,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X1,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/sandbox2/benchmark/theBenchmark.p',cls_real__average__minus__first_0) ).
fof(f13113,plain,
spl0_778,
inference(avatar_split_clause,[],[f404,f13111]) ).
fof(f13111,plain,
( spl0_778
<=> ! [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_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f404,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_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
fof(f13109,plain,
spl0_777,
inference(avatar_split_clause,[],[f403,f13107]) ).
fof(f13107,plain,
( spl0_777
<=> ! [X0,X3,X2,X1] :
( ~ 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(X1,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(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f403,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(X3,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),X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
fof(f13105,plain,
spl0_776,
inference(avatar_split_clause,[],[f402,f13103]) ).
fof(f13103,plain,
( spl0_776
<=> ! [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),X1,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),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f402,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(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),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
fof(f13101,plain,
spl0_775,
inference(avatar_split_clause,[],[f401,f13099]) ).
fof(f13099,plain,
( spl0_775
<=> ! [X2,X0,X1,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),X1,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),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f401,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(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
fof(f13097,plain,
spl0_774,
inference(avatar_split_clause,[],[f317,f13095]) ).
fof(f13095,plain,
( spl0_774
<=> ! [X5,X17,X4,X0,X3] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) = X17
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X17,X3,X0),X0) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X17,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f317,axiom,
! [X3,X0,X4,X17,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) = X17
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X17,X3,X0),X0) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X17,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(f13093,plain,
spl0_773,
inference(avatar_split_clause,[],[f279,f13091]) ).
fof(f13091,plain,
( spl0_773
<=> ! [X2,X4,X11,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X11,X0),X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f279,axiom,
! [X2,X0,X11,X1,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X11,X0),X4,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X11,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X11,X0),X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
fof(f12894,plain,
spl0_772,
inference(avatar_split_clause,[],[f1113,f12892]) ).
fof(f12892,plain,
( spl0_772
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f1113,plain,
! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f614,f807]) ).
fof(f614,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__gt__zero__pi_0) ).
fof(f12890,plain,
( spl0_481
| ~ spl0_190
| ~ spl0_596 ),
inference(avatar_split_clause,[],[f8801,f7613,f2111,f5290]) ).
fof(f5290,plain,
( spl0_481
<=> c_lessequals(c_Transcendental_Opi,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f7613,plain,
( spl0_596
<=> c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f8801,plain,
( c_lessequals(c_Transcendental_Opi,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_190
| ~ spl0_596 ),
inference(resolution,[],[f7614,f2112]) ).
fof(f7614,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_596 ),
inference(avatar_component_clause,[],[f7613]) ).
fof(f12889,plain,
spl0_771,
inference(avatar_split_clause,[],[f1112,f12887]) ).
fof(f12887,plain,
( spl0_771
<=> ! [X5] :
( ~ c_lessequals(X5,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f1112,plain,
! [X5] :
( ~ c_lessequals(X5,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,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),X5,tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f613,f807]) ).
fof(f613,axiom,
! [X5] :
( ~ c_lessequals(X5,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__ge__zero_0) ).
fof(f12885,plain,
spl0_770,
inference(avatar_split_clause,[],[f1067,f12883]) ).
fof(f12883,plain,
( spl0_770
<=> ! [X5] : c_Transcendental_Ocos(X5) = c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(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),X5,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f12881,plain,
spl0_769,
inference(avatar_split_clause,[],[f875,f12879]) ).
fof(f12879,plain,
( spl0_769
<=> ! [X5,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(X5,X6,X0),c_HOL_Oinverse__class_Odivide(X7,X8,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Otimes__class_Otimes(X6,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f875,axiom,
! [X0,X8,X6,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X5,X6,X0),c_HOL_Oinverse__class_Odivide(X7,X8,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Otimes__class_Otimes(X6,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
fof(f12877,plain,
spl0_768,
inference(avatar_split_clause,[],[f722,f12875]) ).
fof(f12875,plain,
( spl0_768
<=> ! [X10] : 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_RealDef_Oreal(c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X10,tc_nat)),tc_nat),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_768])]) ).
fof(f722,axiom,
! [X10] : 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_RealDef_Oreal(c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X10,tc_nat)),tc_nat),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/sandbox2/benchmark/theBenchmark.p',cls_cos__pi__eq__zero_0) ).
fof(f12873,plain,
spl0_767,
inference(avatar_split_clause,[],[f721,f12871]) ).
fof(f12871,plain,
( spl0_767
<=> ! [X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__2(X5),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5)
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__1(X5),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) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f721,axiom,
! [X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__2(X5),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5)
| c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__1(X5),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) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__zero__iff_2) ).
fof(f12869,plain,
spl0_766,
inference(avatar_split_clause,[],[f637,f12867]) ).
fof(f12867,plain,
( spl0_766
<=> ! [X5,X0,X6,X7] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f637,axiom,
! [X0,X6,X7,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
fof(f12865,plain,
spl0_765,
inference(avatar_split_clause,[],[f560,f12863]) ).
fof(f12863,plain,
( spl0_765
<=> ! [X6,X5] :
( ~ c_lessequals(X5,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(X5,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_765])]) ).
fof(f560,axiom,
! [X6,X5] :
( ~ c_lessequals(X5,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(X5,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/sandbox2/benchmark/theBenchmark.p',cls_real__le__add__half__cancel_1) ).
fof(f12861,plain,
spl0_764,
inference(avatar_split_clause,[],[f559,f12859]) ).
fof(f12859,plain,
( spl0_764
<=> ! [X6,X5] :
( c_lessequals(X5,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(X5,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_764])]) ).
fof(f559,axiom,
! [X6,X5] :
( c_lessequals(X5,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(X5,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/sandbox2/benchmark/theBenchmark.p',cls_real__le__add__half__cancel_0) ).
fof(f12660,plain,
spl0_763,
inference(avatar_split_clause,[],[f1114,f12658]) ).
fof(f12658,plain,
( spl0_763
<=> ! [X5] :
( c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__lemma__1__1(X5),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),X5,tc_RealDef_Oreal))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f1114,plain,
! [X5] :
( c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__lemma__1__1(X5),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),X5,tc_RealDef_Oreal))
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) ),
inference(definition_unfolding,[],[f290,f807]) ).
fof(f290,axiom,
! [X5] :
( c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__lemma__1__1(X5),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Osin(X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__zero__lemma_0) ).
fof(f12656,plain,
spl0_762,
inference(avatar_split_clause,[],[f799,f12653]) ).
fof(f799,axiom,
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_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/sandbox2/benchmark/theBenchmark.p',cls_cos__30_0) ).
fof(f12651,plain,
spl0_761,
inference(avatar_split_clause,[],[f798,f12648]) ).
fof(f12648,plain,
( spl0_761
<=> 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) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f12646,plain,
spl0_760,
inference(avatar_split_clause,[],[f488,f12644]) ).
fof(f12644,plain,
( spl0_760
<=> ! [X6,X0,X5] :
( ~ 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),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X5,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f488,axiom,
! [X0,X6,X5] :
( ~ 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),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X5,X0),X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
fof(f12642,plain,
spl0_759,
inference(avatar_split_clause,[],[f487,f12640]) ).
fof(f12640,plain,
( spl0_759
<=> ! [X6,X0,X5] :
( ~ 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),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X6,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f487,axiom,
! [X0,X6,X5] :
( ~ 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),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X6,X0),X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
fof(f12108,plain,
spl0_758,
inference(avatar_split_clause,[],[f1115,f12106]) ).
fof(f12106,plain,
( spl0_758
<=> ! [X5] :
( c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__1(X5),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__2(X5),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),X5,tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f1115,plain,
! [X5] :
( c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__1(X5),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__2(X5),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),X5,tc_RealDef_Oreal)) ),
inference(definition_unfolding,[],[f417,f807]) ).
fof(f417,axiom,
! [X5] :
( c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__1(X5),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xsin__zero__iff__1__2(X5),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Osin(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__zero__iff_0) ).
fof(f12104,plain,
spl0_757,
inference(avatar_split_clause,[],[f910,f12102]) ).
fof(f12102,plain,
( spl0_757
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f910,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) = X3
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
fof(f12100,plain,
spl0_756,
inference(avatar_split_clause,[],[f909,f12098]) ).
fof(f12098,plain,
( spl0_756
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f909,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) = X3
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
fof(f12096,plain,
spl0_755,
inference(avatar_split_clause,[],[f884,f12094]) ).
fof(f12094,plain,
( spl0_755
<=> ! [X38,X0,X36,X39,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X39,X0),c_HOL_Otimes__class_Otimes(X37,X38,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X37,X0),c_HOL_Otimes__class_Otimes(X39,X38,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f884,axiom,
! [X38,X39,X0,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X39,X0),c_HOL_Otimes__class_Otimes(X37,X38,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X37,X0),c_HOL_Otimes__class_Otimes(X39,X38,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f12085,plain,
spl0_754,
inference(avatar_split_clause,[],[f853,f12083]) ).
fof(f12083,plain,
( spl0_754
<=> ! [X6,X7] : c_HOL_Oinverse__class_Odivide(X6,X7,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),X7,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f853,axiom,
! [X6,X7] : c_HOL_Oinverse__class_Odivide(X6,X7,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),X7,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__2__times__iff_0) ).
fof(f12081,plain,
spl0_753,
inference(avatar_split_clause,[],[f786,f12079]) ).
fof(f12079,plain,
( spl0_753
<=> ! [X0,X17] :
( ~ 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),X17,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X17,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_753])]) ).
fof(f786,axiom,
! [X0,X17] :
( ~ 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),X17,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_half__gt__zero_0) ).
fof(f12077,plain,
spl0_752,
inference(avatar_split_clause,[],[f785,f12075]) ).
fof(f12075,plain,
( spl0_752
<=> ! [X0,X17] :
( ~ 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),X17,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X17,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_752])]) ).
fof(f785,axiom,
! [X0,X17] :
( ~ 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),X17,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X17,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_half__gt__zero__iff_0) ).
fof(f12073,plain,
spl0_751,
inference(avatar_split_clause,[],[f608,f12071]) ).
fof(f12071,plain,
( spl0_751
<=> ! [X19] : c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X19,tc_nat),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_RealDef_Oreal(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),X19,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f608,axiom,
! [X19] : c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X19,tc_nat),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_RealDef_Oreal(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),X19,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fact__lemma_0) ).
fof(f12069,plain,
spl0_750,
inference(avatar_split_clause,[],[f574,f12067]) ).
fof(f12067,plain,
( spl0_750
<=> ! [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),X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f574,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),X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).
fof(f12065,plain,
spl0_749,
inference(avatar_split_clause,[],[f572,f12063]) ).
fof(f12063,plain,
( spl0_749
<=> ! [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),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f572,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),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).
fof(f12061,plain,
spl0_748,
inference(avatar_split_clause,[],[f424,f12059]) ).
fof(f12059,plain,
( spl0_748
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f424,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
fof(f12057,plain,
spl0_747,
inference(avatar_split_clause,[],[f399,f12055]) ).
fof(f12055,plain,
( spl0_747
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Oinverse__class_Odivide(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f399,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),c_HOL_Oinverse__class_Odivide(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
fof(f12053,plain,
spl0_746,
inference(avatar_split_clause,[],[f398,f12051]) ).
fof(f12051,plain,
( spl0_746
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f398,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X3,X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
fof(f12049,plain,
spl0_745,
inference(avatar_split_clause,[],[f270,f12047]) ).
fof(f12047,plain,
( spl0_745
<=> ! [X5,X0,X6] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f270,axiom,
! [X0,X6,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
fof(f12045,plain,
( ~ spl0_119
| spl0_744
| ~ spl0_410
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f5383,f5157,f4088,f12043,f1762]) ).
fof(f1762,plain,
( spl0_119
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f12043,plain,
( spl0_744
<=> ! [X0] :
( ~ c_lessequals(c_Transcendental_Opi,X0,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f4088,plain,
( spl0_410
<=> ! [X6,X0,X5,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X6,X5,X0)
| ~ c_lessequals(X7,X6,X0)
| c_lessequals(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f5383,plain,
( ! [X0] :
( ~ c_lessequals(c_Transcendental_Opi,X0,tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_410
| ~ spl0_450 ),
inference(resolution,[],[f5158,f4089]) ).
fof(f4089,plain,
( ! [X0,X6,X7,X5] :
( ~ c_lessequals(X7,X6,X0)
| ~ c_lessequals(X6,X5,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X7,X5,X0) )
| ~ spl0_410 ),
inference(avatar_component_clause,[],[f4088]) ).
fof(f5158,plain,
( c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_450 ),
inference(avatar_component_clause,[],[f5157]) ).
fof(f12041,plain,
spl0_743,
inference(avatar_split_clause,[],[f269,f12039]) ).
fof(f12039,plain,
( spl0_743
<=> ! [X6,X0,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f269,axiom,
! [X0,X6,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
fof(f12037,plain,
spl0_742,
inference(avatar_split_clause,[],[f156,f12035]) ).
fof(f12035,plain,
( spl0_742
<=> ! [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),X3,X0)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f156,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),X3,X0)
| ~ c_lessequals(X1,c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).
fof(f12033,plain,
spl0_741,
inference(avatar_split_clause,[],[f154,f12031]) ).
fof(f12031,plain,
( spl0_741
<=> ! [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),X3,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f154,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),X3,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X1,X0)
| c_lessequals(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).
fof(f12029,plain,
spl0_740,
inference(avatar_split_clause,[],[f92,f12027]) ).
fof(f12027,plain,
( spl0_740
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f92,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f11713,plain,
( spl0_739
| ~ spl0_332
| ~ spl0_567 ),
inference(avatar_split_clause,[],[f8336,f6704,f3201,f11711]) ).
fof(f11711,plain,
( spl0_739
<=> ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f3201,plain,
( spl0_332
<=> ! [X22,X20,X21] :
( ~ c_lessequals(X21,X22,tc_RealDef_Oreal)
| ~ c_lessequals(X22,X20,tc_RealDef_Oreal)
| c_lessequals(X21,X20,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f8336,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_332
| ~ spl0_567 ),
inference(resolution,[],[f6706,f3202]) ).
fof(f3202,plain,
( ! [X21,X22,X20] :
( ~ c_lessequals(X22,X20,tc_RealDef_Oreal)
| ~ c_lessequals(X21,X22,tc_RealDef_Oreal)
| c_lessequals(X21,X20,tc_RealDef_Oreal) )
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f3201]) ).
fof(f11519,plain,
( spl0_738
| ~ spl0_121
| ~ spl0_475
| ~ spl0_737 ),
inference(avatar_split_clause,[],[f11514,f11510,f5264,f1772,f11516]) ).
fof(f11516,plain,
( spl0_738
<=> 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_738])]) ).
fof(f11510,plain,
( spl0_737
<=> 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_737])]) ).
fof(f11514,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_475
| ~ spl0_737 ),
inference(forward_demodulation,[],[f11512,f5541]) ).
fof(f11512,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_737 ),
inference(avatar_component_clause,[],[f11510]) ).
fof(f11513,plain,
spl0_737,
inference(avatar_split_clause,[],[f1142,f11510]) ).
fof(f1142,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,[],[f1085,f901]) ).
fof(f1085,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,[],[f894,f807]) ).
fof(f894,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/sandbox2/benchmark/theBenchmark.p',cls_sin__two__pi_0) ).
fof(f11500,plain,
spl0_736,
inference(avatar_split_clause,[],[f1084,f11497]) ).
fof(f11497,plain,
( spl0_736
<=> 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_736])]) ).
fof(f1084,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,[],[f802,f807]) ).
fof(f802,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/sandbox2/benchmark/theBenchmark.p',cls_sin__pi__half_0) ).
fof(f11495,plain,
spl0_735,
inference(avatar_split_clause,[],[f804,f11493]) ).
fof(f11493,plain,
( spl0_735
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(X5),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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_735])]) ).
fof(f804,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(X5),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(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/sandbox2/benchmark/theBenchmark.p',cls_cos__gt__zero_0) ).
fof(f11491,plain,
spl0_734,
inference(avatar_split_clause,[],[f517,f11489]) ).
fof(f11489,plain,
( spl0_734
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f517,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
fof(f11487,plain,
spl0_733,
inference(avatar_split_clause,[],[f516,f11485]) ).
fof(f11485,plain,
( spl0_733
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f516,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).
fof(f11483,plain,
spl0_732,
inference(avatar_split_clause,[],[f515,f11481]) ).
fof(f11481,plain,
( spl0_732
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f515,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
fof(f11479,plain,
spl0_731,
inference(avatar_split_clause,[],[f414,f11477]) ).
fof(f11477,plain,
( spl0_731
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f414,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
fof(f11475,plain,
spl0_730,
inference(avatar_split_clause,[],[f413,f11473]) ).
fof(f11473,plain,
( spl0_730
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f413,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
fof(f11471,plain,
spl0_729,
inference(avatar_split_clause,[],[f412,f11469]) ).
fof(f11469,plain,
( spl0_729
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f412,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
fof(f11467,plain,
spl0_728,
inference(avatar_split_clause,[],[f397,f11465]) ).
fof(f11465,plain,
( spl0_728
<=> ! [X2,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),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f397,axiom,
! [X2,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),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
fof(f11463,plain,
spl0_727,
inference(avatar_split_clause,[],[f396,f11461]) ).
fof(f11461,plain,
( spl0_727
<=> ! [X2,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),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f396,axiom,
! [X2,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),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
fof(f11459,plain,
( spl0_726
| ~ spl0_332
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f6608,f5751,f3201,f11457]) ).
fof(f6608,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_332
| ~ spl0_508 ),
inference(resolution,[],[f5753,f3202]) ).
fof(f11455,plain,
spl0_725,
inference(avatar_split_clause,[],[f395,f11453]) ).
fof(f11453,plain,
( spl0_725
<=> ! [X2,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(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f395,axiom,
! [X2,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(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
fof(f11451,plain,
spl0_724,
inference(avatar_split_clause,[],[f394,f11449]) ).
fof(f11449,plain,
( spl0_724
<=> ! [X2,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_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f394,axiom,
! [X2,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_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
fof(f11447,plain,
spl0_723,
inference(avatar_split_clause,[],[f393,f11445]) ).
fof(f11445,plain,
( spl0_723
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f393,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
fof(f11443,plain,
spl0_722,
inference(avatar_split_clause,[],[f392,f11441]) ).
fof(f11441,plain,
( spl0_722
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f392,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
fof(f11439,plain,
spl0_721,
inference(avatar_split_clause,[],[f387,f11437]) ).
fof(f11437,plain,
( spl0_721
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f387,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
fof(f11435,plain,
spl0_720,
inference(avatar_split_clause,[],[f386,f11433]) ).
fof(f11433,plain,
( spl0_720
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f386,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
fof(f11431,plain,
spl0_719,
inference(avatar_split_clause,[],[f385,f11429]) ).
fof(f11429,plain,
( spl0_719
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f385,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
fof(f11427,plain,
spl0_718,
inference(avatar_split_clause,[],[f384,f11425]) ).
fof(f11425,plain,
( spl0_718
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f384,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
fof(f11423,plain,
spl0_717,
inference(avatar_split_clause,[],[f383,f11421]) ).
fof(f11421,plain,
( spl0_717
<=> ! [X2,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),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f383,axiom,
! [X2,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),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
fof(f11419,plain,
spl0_716,
inference(avatar_split_clause,[],[f382,f11417]) ).
fof(f11417,plain,
( spl0_716
<=> ! [X2,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_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f382,axiom,
! [X2,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_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
fof(f11397,plain,
spl0_715,
inference(avatar_split_clause,[],[f381,f11395]) ).
fof(f11395,plain,
( spl0_715
<=> ! [X2,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_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f381,axiom,
! [X2,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_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
fof(f11393,plain,
spl0_714,
inference(avatar_split_clause,[],[f380,f11391]) ).
fof(f11391,plain,
( spl0_714
<=> ! [X2,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(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f380,axiom,
! [X2,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(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
fof(f11389,plain,
spl0_713,
inference(avatar_split_clause,[],[f334,f11387]) ).
fof(f11387,plain,
( spl0_713
<=> ! [X2,X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__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),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f334,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__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),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
fof(f11385,plain,
spl0_712,
inference(avatar_split_clause,[],[f333,f11383]) ).
fof(f11383,plain,
( spl0_712
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__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),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f333,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__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),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
fof(f10772,plain,
( spl0_487
| ~ spl0_332
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f5380,f5157,f3201,f5544]) ).
fof(f5380,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal) )
| ~ spl0_332
| ~ spl0_450 ),
inference(resolution,[],[f5158,f3202]) ).
fof(f9721,plain,
spl0_711,
inference(avatar_split_clause,[],[f891,f9719]) ).
fof(f9719,plain,
( spl0_711
<=> ! [X2,X0,X8] :
( ~ 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(X8,X0)
| c_Int_Onumber__class_Onumber__of(X8,X0) != c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f891,axiom,
! [X2,X0,X8] :
( ~ 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(X8,X0)
| c_Int_Onumber__class_Onumber__of(X8,X0) != c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_1) ).
fof(f9717,plain,
spl0_710,
inference(avatar_split_clause,[],[f705,f9715]) ).
fof(f9715,plain,
( spl0_710
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X6,X5,tc_RealDef_Oreal)
| ~ c_lessequals(X5,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(X5),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f705,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X6,X5,tc_RealDef_Oreal)
| ~ c_lessequals(X5,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(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__monotone__minus__pi__0_0) ).
fof(f9713,plain,
spl0_709,
inference(avatar_split_clause,[],[f577,f9711]) ).
fof(f9711,plain,
( spl0_709
<=> ! [X5,X0,X6,X7] :
( ~ 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(X7,X6,X0),X5,X0)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f577,axiom,
! [X0,X6,X7,X5] :
( ~ 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(X7,X6,X0),X5,X0)
| c_HOL_Oord__class_Oless(X7,c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
fof(f9709,plain,
spl0_708,
inference(avatar_split_clause,[],[f576,f9707]) ).
fof(f9707,plain,
( spl0_708
<=> ! [X5,X0,X6,X7] :
( ~ 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(X5,c_HOL_Otimes__class_Otimes(X7,X6,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f576,axiom,
! [X0,X6,X7,X5] :
( ~ 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(X5,c_HOL_Otimes__class_Otimes(X7,X6,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).
fof(f9705,plain,
spl0_707,
inference(avatar_split_clause,[],[f504,f9703]) ).
fof(f9703,plain,
( spl0_707
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f504,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
fof(f9701,plain,
spl0_706,
inference(avatar_split_clause,[],[f503,f9699]) ).
fof(f9699,plain,
( spl0_706
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f503,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
fof(f9693,plain,
spl0_705,
inference(avatar_split_clause,[],[f502,f9691]) ).
fof(f9691,plain,
( spl0_705
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f502,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
fof(f9689,plain,
spl0_704,
inference(avatar_split_clause,[],[f501,f9687]) ).
fof(f9687,plain,
( spl0_704
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f501,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
fof(f9685,plain,
spl0_703,
inference(avatar_split_clause,[],[f500,f9683]) ).
fof(f9683,plain,
( spl0_703
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f500,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
fof(f9681,plain,
spl0_702,
inference(avatar_split_clause,[],[f499,f9679]) ).
fof(f9679,plain,
( spl0_702
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f499,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
fof(f9677,plain,
spl0_701,
inference(avatar_split_clause,[],[f496,f9675]) ).
fof(f9675,plain,
( spl0_701
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f496,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
fof(f9673,plain,
spl0_700,
inference(avatar_split_clause,[],[f495,f9671]) ).
fof(f9671,plain,
( spl0_700
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f495,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
fof(f9669,plain,
spl0_699,
inference(avatar_split_clause,[],[f494,f9667]) ).
fof(f9667,plain,
( spl0_699
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f494,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
fof(f9665,plain,
spl0_698,
inference(avatar_split_clause,[],[f493,f9663]) ).
fof(f9663,plain,
( spl0_698
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f493,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
fof(f9661,plain,
spl0_697,
inference(avatar_split_clause,[],[f411,f9659]) ).
fof(f9659,plain,
( spl0_697
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f411,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
fof(f9657,plain,
spl0_696,
inference(avatar_split_clause,[],[f410,f9655]) ).
fof(f9655,plain,
( spl0_696
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f410,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X3,X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
fof(f9644,plain,
spl0_695,
inference(avatar_split_clause,[],[f347,f9642]) ).
fof(f9642,plain,
( spl0_695
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f347,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
fof(f9640,plain,
spl0_694,
inference(avatar_split_clause,[],[f346,f9638]) ).
fof(f9638,plain,
( spl0_694
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f346,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
fof(f9636,plain,
spl0_693,
inference(avatar_split_clause,[],[f345,f9634]) ).
fof(f9634,plain,
( spl0_693
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f345,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
fof(f9632,plain,
spl0_692,
inference(avatar_split_clause,[],[f344,f9630]) ).
fof(f9630,plain,
( spl0_692
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f344,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
fof(f9628,plain,
spl0_691,
inference(avatar_split_clause,[],[f316,f9626]) ).
fof(f9626,plain,
( spl0_691
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f316,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
fof(f9624,plain,
spl0_690,
inference(avatar_split_clause,[],[f315,f9622]) ).
fof(f9622,plain,
( spl0_690
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f315,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
fof(f9620,plain,
spl0_689,
inference(avatar_split_clause,[],[f233,f9618]) ).
fof(f9618,plain,
( spl0_689
<=> ! [X5] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f233,axiom,
! [X5] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X5,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__squared__diff__one__factored_0) ).
fof(f9616,plain,
spl0_688,
inference(avatar_split_clause,[],[f214,f9614]) ).
fof(f9614,plain,
( spl0_688
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f214,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
fof(f9612,plain,
spl0_687,
inference(avatar_split_clause,[],[f213,f9610]) ).
fof(f9610,plain,
( spl0_687
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f213,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
fof(f9608,plain,
spl0_686,
inference(avatar_split_clause,[],[f212,f9606]) ).
fof(f9606,plain,
( spl0_686
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f212,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
fof(f9604,plain,
spl0_685,
inference(avatar_split_clause,[],[f200,f9602]) ).
fof(f9602,plain,
( spl0_685
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f200,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
fof(f9600,plain,
spl0_684,
inference(avatar_split_clause,[],[f198,f9598]) ).
fof(f9598,plain,
( spl0_684
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f198,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
fof(f9596,plain,
spl0_683,
inference(avatar_split_clause,[],[f197,f9594]) ).
fof(f9594,plain,
( spl0_683
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f197,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
fof(f9592,plain,
spl0_682,
inference(avatar_split_clause,[],[f196,f9590]) ).
fof(f9590,plain,
( spl0_682
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f196,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
fof(f9588,plain,
spl0_681,
inference(avatar_split_clause,[],[f194,f9586]) ).
fof(f9586,plain,
( spl0_681
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f194,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
fof(f9584,plain,
spl0_680,
inference(avatar_split_clause,[],[f193,f9582]) ).
fof(f9582,plain,
( spl0_680
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f193,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
fof(f9580,plain,
spl0_679,
inference(avatar_split_clause,[],[f190,f9578]) ).
fof(f9578,plain,
( spl0_679
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f190,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
fof(f9576,plain,
spl0_678,
inference(avatar_split_clause,[],[f189,f9574]) ).
fof(f9574,plain,
( spl0_678
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f189,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
fof(f9572,plain,
spl0_677,
inference(avatar_split_clause,[],[f188,f9570]) ).
fof(f9570,plain,
( spl0_677
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f188,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
fof(f9568,plain,
spl0_676,
inference(avatar_split_clause,[],[f180,f9566]) ).
fof(f9566,plain,
( spl0_676
<=> ! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_RealDef_Oreal)
| ~ c_lessequals(X5,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(X5),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f180,axiom,
! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_RealDef_Oreal)
| ~ c_lessequals(X5,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(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__monotone__minus__pi__0_H_0) ).
fof(f9552,plain,
( ~ spl0_152
| spl0_671 ),
inference(avatar_contradiction_clause,[],[f9544]) ).
fof(f9544,plain,
( $false
| ~ spl0_152
| spl0_671 ),
inference(resolution,[],[f9373,f1927]) ).
fof(f1927,plain,
( ! [X8] : c_lessequals(X8,X8,tc_RealDef_Oreal)
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f1926]) ).
fof(f1926,plain,
( spl0_152
<=> ! [X8] : c_lessequals(X8,X8,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f9373,plain,
( ~ c_lessequals(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal)
| spl0_671 ),
inference(avatar_component_clause,[],[f9371]) ).
fof(f9543,plain,
spl0_675,
inference(avatar_split_clause,[],[f159,f9541]) ).
fof(f9541,plain,
( spl0_675
<=> ! [X5,X0,X6,X7] :
( ~ 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(X7,X6,X0),X5,X0)
| c_lessequals(X7,c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f159,axiom,
! [X0,X6,X7,X5] :
( ~ 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(X7,X6,X0),X5,X0)
| c_lessequals(X7,c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).
fof(f9539,plain,
spl0_674,
inference(avatar_split_clause,[],[f158,f9537]) ).
fof(f9537,plain,
( spl0_674
<=> ! [X5,X0,X6,X7] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_lessequals(X5,c_HOL_Otimes__class_Otimes(X7,X6,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f158,axiom,
! [X0,X6,X7,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_lessequals(X5,c_HOL_Otimes__class_Otimes(X7,X6,X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).
fof(f9535,plain,
spl0_673,
inference(avatar_split_clause,[],[f94,f9533]) ).
fof(f9533,plain,
( spl0_673
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f94,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
fof(f9531,plain,
spl0_672,
inference(avatar_split_clause,[],[f93,f9529]) ).
fof(f9529,plain,
( spl0_672
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f93,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
fof(f9374,plain,
( ~ spl0_671
| spl0_481
| ~ spl0_536 ),
inference(avatar_split_clause,[],[f9073,f6317,f5290,f9371]) ).
fof(f6317,plain,
( spl0_536
<=> c_Transcendental_Opi = c_Transcendental_Ocos(c_Transcendental_Opi) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f9073,plain,
( ~ c_lessequals(c_Transcendental_Opi,c_Transcendental_Opi,tc_RealDef_Oreal)
| spl0_481
| ~ spl0_536 ),
inference(forward_demodulation,[],[f5291,f6319]) ).
fof(f6319,plain,
( c_Transcendental_Opi = c_Transcendental_Ocos(c_Transcendental_Opi)
| ~ spl0_536 ),
inference(avatar_component_clause,[],[f6317]) ).
fof(f5291,plain,
( ~ c_lessequals(c_Transcendental_Opi,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| spl0_481 ),
inference(avatar_component_clause,[],[f5290]) ).
fof(f9066,plain,
( spl0_670
| ~ spl0_332
| ~ spl0_481 ),
inference(avatar_split_clause,[],[f5701,f5290,f3201,f9064]) ).
fof(f5701,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(X0,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal) )
| ~ spl0_332
| ~ spl0_481 ),
inference(resolution,[],[f5292,f3202]) ).
fof(f5292,plain,
( c_lessequals(c_Transcendental_Opi,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_481 ),
inference(avatar_component_clause,[],[f5290]) ).
fof(f8576,plain,
( ~ spl0_118
| spl0_450
| ~ spl0_249
| spl0_596 ),
inference(avatar_split_clause,[],[f7661,f7613,f2458,f5157,f1757]) ).
fof(f1757,plain,
( spl0_118
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f2458,plain,
( spl0_249
<=> ! [X5,X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X6,X5,X0)
| c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f7661,plain,
( c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ spl0_249
| spl0_596 ),
inference(resolution,[],[f7615,f2459]) ).
fof(f2459,plain,
( ! [X0,X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,X0)
| c_lessequals(X6,X5,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2458]) ).
fof(f7615,plain,
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| spl0_596 ),
inference(avatar_component_clause,[],[f7613]) ).
fof(f7951,plain,
spl0_669,
inference(avatar_split_clause,[],[f1135,f7948]) ).
fof(f7948,plain,
( spl0_669
<=> 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_669])]) ).
fof(f1135,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,[],[f1071,f553]) ).
fof(f553,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__zero_0) ).
fof(f1071,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,[],[f677,f1066]) ).
fof(f677,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Otan(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__zero_0) ).
fof(f7946,plain,
spl0_668,
inference(avatar_split_clause,[],[f1110,f7944]) ).
fof(f7944,plain,
( spl0_668
<=> ! [X5] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(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),X5,tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f1110,plain,
! [X5] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(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),X5,tc_RealDef_Oreal)) ),
inference(definition_unfolding,[],[f715,f807]) ).
fof(f715,axiom,
! [X5] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__one__sin__zero_0) ).
fof(f7937,plain,
spl0_667,
inference(avatar_split_clause,[],[f1079,f7935]) ).
fof(f1079,plain,
! [X19] : 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(X19,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f869,f807]) ).
fof(f869,axiom,
! [X19] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(X19,tc_nat),tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__npi2_0) ).
fof(f7933,plain,
spl0_666,
inference(avatar_split_clause,[],[f809,f7931]) ).
fof(f7931,plain,
( spl0_666
<=> ! [X34] :
( c_Parity_Oeven__odd__class_Oeven(X34,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X34,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_666])]) ).
fof(f809,axiom,
! [X34] :
( c_Parity_Oeven__odd__class_Oeven(X34,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X34,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/sandbox2/benchmark/theBenchmark.p',cls_cos__zero__iff_4) ).
fof(f7929,plain,
spl0_665,
inference(avatar_split_clause,[],[f778,f7927]) ).
fof(f7927,plain,
( spl0_665
<=> ! [X5] : c_HOL_Oinverse__class_Odivide(X5,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(X5,c_HOL_Oinverse__class_Odivide(X5,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_665])]) ).
fof(f778,axiom,
! [X5] : c_HOL_Oinverse__class_Odivide(X5,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(X5,c_HOL_Oinverse__class_Odivide(X5,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/sandbox2/benchmark/theBenchmark.p',cls_real__minus__half__eq_0) ).
fof(f7925,plain,
spl0_664,
inference(avatar_split_clause,[],[f777,f7923]) ).
fof(f7923,plain,
( spl0_664
<=> ! [X5] : c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,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(X5,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f777,axiom,
! [X5] : c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,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(X5,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__of__halves_0) ).
fof(f7921,plain,
spl0_663,
inference(avatar_split_clause,[],[f689,f7919]) ).
fof(f7919,plain,
( spl0_663
<=> ! [X5,X0,X6,X28] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,X6,X0),X28,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X28,X0),c_HOL_Oinverse__class_Odivide(X6,X28,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f689,axiom,
! [X28,X0,X6,X5] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,X6,X0),X28,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X28,X0),c_HOL_Oinverse__class_Odivide(X6,X28,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
fof(f7917,plain,
spl0_662,
inference(avatar_split_clause,[],[f688,f7915]) ).
fof(f7915,plain,
( spl0_662
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X3,X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f688,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X3,X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
fof(f7913,plain,
spl0_661,
inference(avatar_split_clause,[],[f685,f7911]) ).
fof(f7911,plain,
( spl0_661
<=> ! [X5,X0,X6,X28] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X5,X6,X0),X28,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X5,X28,X0),c_HOL_Oinverse__class_Odivide(X6,X28,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f685,axiom,
! [X28,X0,X6,X5] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X5,X6,X0),X28,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X5,X28,X0),c_HOL_Oinverse__class_Odivide(X6,X28,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
fof(f7909,plain,
spl0_660,
inference(avatar_split_clause,[],[f684,f7907]) ).
fof(f7907,plain,
( spl0_660
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X3,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X3,X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f684,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X3,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X3,X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
fof(f7905,plain,
spl0_659,
inference(avatar_split_clause,[],[f655,f7903]) ).
fof(f7903,plain,
( spl0_659
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f655,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).
fof(f7901,plain,
spl0_658,
inference(avatar_split_clause,[],[f654,f7899]) ).
fof(f7899,plain,
( spl0_658
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X5,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(X5,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f654,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X5,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(X5,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
fof(f7897,plain,
( spl0_450
| ~ spl0_190
| ~ spl0_535 ),
inference(avatar_split_clause,[],[f7068,f6313,f2111,f5157]) ).
fof(f7068,plain,
( c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_190
| ~ spl0_535 ),
inference(resolution,[],[f6315,f2112]) ).
fof(f7896,plain,
spl0_657,
inference(avatar_split_clause,[],[f652,f7894]) ).
fof(f7894,plain,
( spl0_657
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,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(X5,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f652,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,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(X5,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
fof(f7892,plain,
spl0_656,
inference(avatar_split_clause,[],[f651,f7890]) ).
fof(f7890,plain,
( spl0_656
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X5,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(X5,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f651,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X5,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(X5,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
fof(f7888,plain,
spl0_655,
inference(avatar_split_clause,[],[f643,f7886]) ).
fof(f7886,plain,
( spl0_655
<=> ! [X5,X0,X6,X28] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X6,X0),X28,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X28,X0),c_HOL_Otimes__class_Otimes(X6,X28,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f643,axiom,
! [X28,X0,X6,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X6,X0),X28,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X28,X0),c_HOL_Otimes__class_Otimes(X6,X28,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
fof(f7884,plain,
spl0_654,
inference(avatar_split_clause,[],[f640,f7882]) ).
fof(f7882,plain,
( spl0_654
<=> ! [X5,X0,X6,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Ominus__class_Ominus(X5,X6,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X25,X5,X0),c_HOL_Otimes__class_Otimes(X25,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f640,axiom,
! [X0,X6,X5,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Ominus__class_Ominus(X5,X6,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X25,X5,X0),c_HOL_Otimes__class_Otimes(X25,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
fof(f7880,plain,
spl0_653,
inference(avatar_split_clause,[],[f627,f7878]) ).
fof(f7878,plain,
( spl0_653
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f627,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f7876,plain,
spl0_652,
inference(avatar_split_clause,[],[f626,f7874]) ).
fof(f7874,plain,
( spl0_652
<=> ! [X5,X0,X6,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X5,X0),c_HOL_Otimes__class_Otimes(X25,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f626,axiom,
! [X0,X6,X5,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X25,X5,X0),c_HOL_Otimes__class_Otimes(X25,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
fof(f7872,plain,
spl0_651,
inference(avatar_split_clause,[],[f624,f7870]) ).
fof(f7870,plain,
( spl0_651
<=> ! [X5,X0,X6,X28] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X6,X0),X28,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X28,X0),c_HOL_Otimes__class_Otimes(X6,X28,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f624,axiom,
! [X28,X0,X6,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X6,X0),X28,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X28,X0),c_HOL_Otimes__class_Otimes(X6,X28,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
fof(f7868,plain,
spl0_650,
inference(avatar_split_clause,[],[f622,f7866]) ).
fof(f7866,plain,
( spl0_650
<=> ! [X6,X0,X5,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f622,axiom,
! [X0,X6,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
fof(f7864,plain,
spl0_649,
inference(avatar_split_clause,[],[f621,f7862]) ).
fof(f7862,plain,
( spl0_649
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f621,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
fof(f7860,plain,
spl0_648,
inference(avatar_split_clause,[],[f519,f7858]) ).
fof(f7858,plain,
( spl0_648
<=> ! [X6,X0,X5] :
( ~ 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),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f519,axiom,
! [X0,X6,X5] :
( ~ 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),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X5,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
fof(f7846,plain,
spl0_647,
inference(avatar_split_clause,[],[f518,f7844]) ).
fof(f7844,plain,
( spl0_647
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X5,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(X5,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f518,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X5,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(X5,X6,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
fof(f7842,plain,
spl0_646,
inference(avatar_split_clause,[],[f513,f7840]) ).
fof(f7840,plain,
( spl0_646
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f513,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X1,X0),c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
fof(f7838,plain,
spl0_645,
inference(avatar_split_clause,[],[f512,f7836]) ).
fof(f7836,plain,
( spl0_645
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f512,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
fof(f7834,plain,
spl0_644,
inference(avatar_split_clause,[],[f508,f7832]) ).
fof(f7832,plain,
( spl0_644
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f508,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
fof(f7830,plain,
spl0_643,
inference(avatar_split_clause,[],[f507,f7828]) ).
fof(f7828,plain,
( spl0_643
<=> ! [X6,X0,X5] :
( ~ 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(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f507,axiom,
! [X0,X6,X5] :
( ~ 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(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
fof(f7826,plain,
spl0_642,
inference(avatar_split_clause,[],[f506,f7824]) ).
fof(f7824,plain,
( spl0_642
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f506,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
fof(f7822,plain,
spl0_641,
inference(avatar_split_clause,[],[f505,f7820]) ).
fof(f7820,plain,
( spl0_641
<=> ! [X6,X0,X5] :
( ~ 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(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f505,axiom,
! [X0,X6,X5] :
( ~ 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(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
fof(f7818,plain,
spl0_640,
inference(avatar_split_clause,[],[f491,f7816]) ).
fof(f7816,plain,
( spl0_640
<=> ! [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_640])]) ).
fof(f491,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
fof(f7814,plain,
spl0_639,
inference(avatar_split_clause,[],[f489,f7812]) ).
fof(f7812,plain,
( spl0_639
<=> ! [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_639])]) ).
fof(f489,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
fof(f7810,plain,
spl0_638,
inference(avatar_split_clause,[],[f449,f7808]) ).
fof(f7808,plain,
( spl0_638
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f449,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
fof(f7800,plain,
spl0_637,
inference(avatar_split_clause,[],[f448,f7798]) ).
fof(f7798,plain,
( spl0_637
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f448,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
fof(f7796,plain,
spl0_636,
inference(avatar_split_clause,[],[f441,f7794]) ).
fof(f7794,plain,
( spl0_636
<=> ! [X0,X19,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X10,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X19,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X10,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f441,axiom,
! [X10,X0,X19] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X10,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X19,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X10,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
fof(f7792,plain,
spl0_635,
inference(avatar_split_clause,[],[f423,f7790]) ).
fof(f7790,plain,
( spl0_635
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f423,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f7788,plain,
spl0_634,
inference(avatar_split_clause,[],[f406,f7786]) ).
fof(f7786,plain,
( spl0_634
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,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(X5,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f406,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X5,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(X5,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
fof(f7784,plain,
spl0_633,
inference(avatar_split_clause,[],[f405,f7782]) ).
fof(f7782,plain,
( spl0_633
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X5,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(X5,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f405,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X5,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(X5,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
fof(f7780,plain,
spl0_632,
inference(avatar_split_clause,[],[f339,f7778]) ).
fof(f7778,plain,
( spl0_632
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f339,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
fof(f7776,plain,
spl0_631,
inference(avatar_split_clause,[],[f338,f7774]) ).
fof(f7774,plain,
( spl0_631
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f338,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
fof(f7772,plain,
spl0_630,
inference(avatar_split_clause,[],[f337,f7770]) ).
fof(f7770,plain,
( spl0_630
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f337,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
fof(f7768,plain,
spl0_629,
inference(avatar_split_clause,[],[f336,f7766]) ).
fof(f7766,plain,
( spl0_629
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f336,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
fof(f7764,plain,
spl0_628,
inference(avatar_split_clause,[],[f330,f7762]) ).
fof(f7762,plain,
( spl0_628
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f330,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
fof(f7760,plain,
( spl0_627
| ~ spl0_196
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f7703,f5544,f2135,f7758]) ).
fof(f7703,plain,
( ! [X0] :
( c_lessequals(X0,c_Transcendental_Opi,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_196
| ~ spl0_487 ),
inference(resolution,[],[f5545,f2136]) ).
fof(f7756,plain,
spl0_626,
inference(avatar_split_clause,[],[f329,f7754]) ).
fof(f7754,plain,
( spl0_626
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f329,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
fof(f7752,plain,
spl0_625,
inference(avatar_split_clause,[],[f328,f7750]) ).
fof(f7750,plain,
( spl0_625
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f328,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
fof(f7748,plain,
spl0_624,
inference(avatar_split_clause,[],[f327,f7746]) ).
fof(f7746,plain,
( spl0_624
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f327,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
fof(f7744,plain,
spl0_623,
inference(avatar_split_clause,[],[f326,f7742]) ).
fof(f7742,plain,
( spl0_623
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f326,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
fof(f7740,plain,
spl0_622,
inference(avatar_split_clause,[],[f325,f7738]) ).
fof(f7738,plain,
( spl0_622
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f325,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
fof(f7736,plain,
spl0_621,
inference(avatar_split_clause,[],[f324,f7734]) ).
fof(f7734,plain,
( spl0_621
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f324,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
fof(f7732,plain,
spl0_620,
inference(avatar_split_clause,[],[f322,f7730]) ).
fof(f7730,plain,
( spl0_620
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f322,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
fof(f7728,plain,
spl0_619,
inference(avatar_split_clause,[],[f320,f7726]) ).
fof(f7726,plain,
( spl0_619
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f320,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
fof(f7724,plain,
spl0_618,
inference(avatar_split_clause,[],[f310,f7722]) ).
fof(f7722,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(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f310,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(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
fof(f7720,plain,
spl0_617,
inference(avatar_split_clause,[],[f278,f7718]) ).
fof(f7718,plain,
( spl0_617
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f278,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f7701,plain,
spl0_616,
inference(avatar_split_clause,[],[f277,f7699]) ).
fof(f7699,plain,
( spl0_616
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f277,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f7697,plain,
spl0_615,
inference(avatar_split_clause,[],[f262,f7695]) ).
fof(f7695,plain,
( spl0_615
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f262,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
fof(f7693,plain,
spl0_614,
inference(avatar_split_clause,[],[f261,f7691]) ).
fof(f7691,plain,
( spl0_614
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f261,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
fof(f7689,plain,
spl0_613,
inference(avatar_split_clause,[],[f211,f7687]) ).
fof(f7687,plain,
( spl0_613
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f211,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
fof(f7685,plain,
spl0_612,
inference(avatar_split_clause,[],[f210,f7683]) ).
fof(f7683,plain,
( spl0_612
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f210,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
fof(f7681,plain,
spl0_611,
inference(avatar_split_clause,[],[f208,f7679]) ).
fof(f7679,plain,
( spl0_611
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f208,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
fof(f7677,plain,
spl0_610,
inference(avatar_split_clause,[],[f207,f7675]) ).
fof(f7675,plain,
( spl0_610
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f207,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
fof(f7673,plain,
spl0_609,
inference(avatar_split_clause,[],[f206,f7671]) ).
fof(f7671,plain,
( spl0_609
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f206,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
fof(f7669,plain,
spl0_608,
inference(avatar_split_clause,[],[f205,f7667]) ).
fof(f7667,plain,
( spl0_608
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f205,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
fof(f7665,plain,
spl0_607,
inference(avatar_split_clause,[],[f204,f7663]) ).
fof(f7663,plain,
( spl0_607
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f204,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
fof(f7656,plain,
spl0_606,
inference(avatar_split_clause,[],[f203,f7654]) ).
fof(f7654,plain,
( spl0_606
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f203,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
fof(f7652,plain,
spl0_605,
inference(avatar_split_clause,[],[f202,f7650]) ).
fof(f7650,plain,
( spl0_605
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f202,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
fof(f7648,plain,
spl0_604,
inference(avatar_split_clause,[],[f201,f7646]) ).
fof(f7646,plain,
( spl0_604
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f201,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
fof(f7644,plain,
spl0_603,
inference(avatar_split_clause,[],[f138,f7642]) ).
fof(f7642,plain,
( spl0_603
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X5,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f138,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oinverse__class_Odivide(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X5,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus1__divide_0) ).
fof(f7640,plain,
spl0_602,
inference(avatar_split_clause,[],[f133,f7638]) ).
fof(f7638,plain,
( spl0_602
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f133,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f7636,plain,
spl0_601,
inference(avatar_split_clause,[],[f131,f7634]) ).
fof(f7634,plain,
( spl0_601
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f131,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
fof(f7632,plain,
spl0_600,
inference(avatar_split_clause,[],[f80,f7630]) ).
fof(f7630,plain,
( spl0_600
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f80,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
fof(f7628,plain,
spl0_599,
inference(avatar_split_clause,[],[f79,f7626]) ).
fof(f7626,plain,
( spl0_599
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f79,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
fof(f7624,plain,
spl0_598,
inference(avatar_split_clause,[],[f73,f7622]) ).
fof(f7622,plain,
( spl0_598
<=> ! [X6,X0,X14,X5,X7] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X5,X7,X0) = X14
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) != c_HOL_Oplus__class_Oplus(X6,X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f73,axiom,
! [X0,X6,X7,X14,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X5,X7,X0) = X14
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) != c_HOL_Oplus__class_Oplus(X6,X14,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
fof(f7620,plain,
spl0_597,
inference(avatar_split_clause,[],[f71,f7618]) ).
fof(f7618,plain,
( spl0_597
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f71,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f7616,plain,
( ~ spl0_117
| ~ spl0_596
| ~ spl0_242
| ~ spl0_535 ),
inference(avatar_split_clause,[],[f7071,f6313,f2430,f7613,f1752]) ).
fof(f1752,plain,
( spl0_117
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f2430,plain,
( spl0_242
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f7071,plain,
( ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl0_242
| ~ spl0_535 ),
inference(resolution,[],[f6315,f2431]) ).
fof(f2431,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f2430]) ).
fof(f7611,plain,
spl0_595,
inference(avatar_split_clause,[],[f67,f7609]) ).
fof(f7609,plain,
( spl0_595
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f67,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f7607,plain,
spl0_594,
inference(avatar_split_clause,[],[f64,f7605]) ).
fof(f7605,plain,
( spl0_594
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f64,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
fof(f7603,plain,
spl0_593,
inference(avatar_split_clause,[],[f19,f7601]) ).
fof(f7601,plain,
( spl0_593
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f19,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f7599,plain,
spl0_592,
inference(avatar_split_clause,[],[f3,f7597]) ).
fof(f7597,plain,
( spl0_592
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f3,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f7182,plain,
spl0_591,
inference(avatar_split_clause,[],[f1151,f7179]) ).
fof(f7179,plain,
( spl0_591
<=> 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_591])]) ).
fof(f1151,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,[],[f870,f901]) ).
fof(f870,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/sandbox2/benchmark/theBenchmark.p',cls_cos__3over2__pi_0) ).
fof(f7176,plain,
spl0_590,
inference(avatar_split_clause,[],[f1069,f7173]) ).
fof(f7173,plain,
( spl0_590
<=> 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_590])]) ).
fof(f1069,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,[],[f550,f1066]) ).
fof(f550,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Otan(c_Transcendental_Opi),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tan__pi_0) ).
fof(f7171,plain,
spl0_589,
inference(avatar_split_clause,[],[f912,f7169]) ).
fof(f7169,plain,
( spl0_589
<=> ! [X5,X0,X6,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(X5,X6,X0),X7,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X7,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f912,axiom,
! [X0,X6,X7,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X7,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X7,X0),X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
fof(f7163,plain,
spl0_588,
inference(avatar_split_clause,[],[f797,f7160]) ).
fof(f7160,plain,
( spl0_588
<=> 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_588])]) ).
fof(f7158,plain,
spl0_587,
inference(avatar_split_clause,[],[f694,f7156]) ).
fof(f7156,plain,
( spl0_587
<=> ! [X6,X5,X7] :
( c_lessequals(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X7,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f694,axiom,
! [X6,X7,X5] :
( c_lessequals(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X7,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_0) ).
fof(f7154,plain,
spl0_586,
inference(avatar_split_clause,[],[f693,f7152]) ).
fof(f7152,plain,
( spl0_586
<=> ! [X6,X5,X7] :
( ~ c_lessequals(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X7,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f693,axiom,
! [X6,X7,X5] :
( ~ c_lessequals(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X7,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_1) ).
fof(f7150,plain,
spl0_585,
inference(avatar_split_clause,[],[f692,f7148]) ).
fof(f7148,plain,
( spl0_585
<=> ! [X6,X5,X7] :
( c_lessequals(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X7,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f692,axiom,
! [X6,X7,X5] :
( c_lessequals(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X7,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_0) ).
fof(f7146,plain,
spl0_584,
inference(avatar_split_clause,[],[f691,f7144]) ).
fof(f7144,plain,
( spl0_584
<=> ! [X6,X5,X7] :
( ~ c_lessequals(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X7,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f691,axiom,
! [X6,X7,X5] :
( ~ c_lessequals(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X7,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_1) ).
fof(f7142,plain,
spl0_583,
inference(avatar_split_clause,[],[f665,f7140]) ).
fof(f7140,plain,
( spl0_583
<=> ! [X0,X8] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X8),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X8,X0),X0),c_Int_Onumber__class_Onumber__of(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f665,axiom,
! [X0,X8] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit1(X8),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_Int_Onumber__class_Onumber__of(X8,X0),X0),c_Int_Onumber__class_Onumber__of(X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Bit1_0) ).
fof(f7138,plain,
spl0_582,
inference(avatar_split_clause,[],[f630,f7136]) ).
fof(f7136,plain,
( spl0_582
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Otimes__class_Otimes(X1,X1,X0) != c_HOL_Otimes__class_Otimes(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f630,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Otimes__class_Otimes(X1,X1,X0) != c_HOL_Otimes__class_Otimes(X2,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
fof(f7134,plain,
spl0_581,
inference(avatar_split_clause,[],[f612,f7132]) ).
fof(f7132,plain,
( spl0_581
<=> ! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_RealDef_Oreal)
| ~ c_lessequals(X5,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(X5),c_Transcendental_Ocos(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f612,axiom,
! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_RealDef_Oreal)
| ~ c_lessequals(X5,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(X5),c_Transcendental_Ocos(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__monotone__0__pi_H_0) ).
fof(f7130,plain,
spl0_580,
inference(avatar_split_clause,[],[f604,f7128]) ).
fof(f7128,plain,
( spl0_580
<=> ! [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_580])]) ).
fof(f604,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/sandbox2/benchmark/theBenchmark.p',cls_half_0) ).
fof(f7126,plain,
spl0_579,
inference(avatar_split_clause,[],[f569,f7124]) ).
fof(f7124,plain,
( spl0_579
<=> ! [X0,X8] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X8),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_Int_Onumber__class_Onumber__of(X8,X0),X0),c_Int_Onumber__class_Onumber__of(X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f569,axiom,
! [X0,X8] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X8),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_Int_Onumber__class_Onumber__of(X8,X0),X0),c_Int_Onumber__class_Onumber__of(X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_number__of__Bit0_0) ).
fof(f7122,plain,
( spl0_567
| ~ spl0_353
| ~ spl0_508 ),
inference(avatar_split_clause,[],[f6607,f5751,f3402,f6704]) ).
fof(f3402,plain,
( spl0_353
<=> ! [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_353])]) ).
fof(f6607,plain,
( c_lessequals(c_Transcendental_Opi,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_353
| ~ spl0_508 ),
inference(resolution,[],[f5753,f3403]) ).
fof(f3403,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_353 ),
inference(avatar_component_clause,[],[f3402]) ).
fof(f7121,plain,
spl0_578,
inference(avatar_split_clause,[],[f527,f7119]) ).
fof(f7119,plain,
( spl0_578
<=> ! [X6,X5,X7] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X7,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f527,axiom,
! [X6,X7,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X7,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__mono2_0) ).
fof(f7117,plain,
spl0_577,
inference(avatar_split_clause,[],[f526,f7115]) ).
fof(f7115,plain,
( spl0_577
<=> ! [X6,X5,X7] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X7,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f526,axiom,
! [X6,X7,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X7,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__iff1_1) ).
fof(f7113,plain,
spl0_576,
inference(avatar_split_clause,[],[f525,f7111]) ).
fof(f7111,plain,
( spl0_576
<=> ! [X6,X5,X7] :
( c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X7,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f525,axiom,
! [X6,X7,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X7,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X7,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__iff1_0) ).
fof(f7109,plain,
spl0_575,
inference(avatar_split_clause,[],[f409,f7107]) ).
fof(f7107,plain,
( spl0_575
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f409,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
fof(f7105,plain,
spl0_574,
inference(avatar_split_clause,[],[f391,f7103]) ).
fof(f7103,plain,
( spl0_574
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f391,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
fof(f7101,plain,
spl0_573,
inference(avatar_split_clause,[],[f343,f7099]) ).
fof(f7099,plain,
( spl0_573
<=> ! [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_573])]) ).
fof(f343,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
fof(f7097,plain,
spl0_572,
inference(avatar_split_clause,[],[f319,f7095]) ).
fof(f7095,plain,
( spl0_572
<=> ! [X6,X0,X5] :
( ~ 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(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f319,axiom,
! [X0,X6,X5] :
( ~ 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(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
fof(f7093,plain,
spl0_571,
inference(avatar_split_clause,[],[f318,f7091]) ).
fof(f7091,plain,
( spl0_571
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f318,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
fof(f7089,plain,
spl0_570,
inference(avatar_split_clause,[],[f220,f7087]) ).
fof(f7087,plain,
( spl0_570
<=> ! [X5,X24,X23,X0,X6] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_HOL_Oord__class_Oless(X23,X24,X0)
| c_HOL_Ominus__class_Ominus(X5,X6,X0) != c_HOL_Ominus__class_Ominus(X23,X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f220,axiom,
! [X0,X6,X24,X5,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_HOL_Oord__class_Oless(X23,X24,X0)
| c_HOL_Ominus__class_Ominus(X5,X6,X0) != c_HOL_Ominus__class_Ominus(X23,X24,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
fof(f7085,plain,
spl0_569,
inference(avatar_split_clause,[],[f218,f7083]) ).
fof(f7083,plain,
( spl0_569
<=> ! [X6,X23,X0,X5,X24] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X6,X5,X0)
| c_lessequals(X24,X23,X0)
| c_HOL_Ominus__class_Ominus(X5,X6,X0) != c_HOL_Ominus__class_Ominus(X23,X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f218,axiom,
! [X0,X6,X24,X5,X23] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X6,X5,X0)
| c_lessequals(X24,X23,X0)
| c_HOL_Ominus__class_Ominus(X5,X6,X0) != c_HOL_Ominus__class_Ominus(X23,X24,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
fof(f7067,plain,
spl0_568,
inference(avatar_split_clause,[],[f181,f7065]) ).
fof(f7065,plain,
( spl0_568
<=> ! [X6,X5] :
( ~ c_lessequals(X5,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X6,X5,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(X5),c_Transcendental_Ocos(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f181,axiom,
! [X6,X5] :
( ~ c_lessequals(X5,c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X6,X5,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(X5),c_Transcendental_Ocos(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__monotone__0__pi_0) ).
fof(f6707,plain,
( spl0_567
| ~ spl0_399
| spl0_450 ),
inference(avatar_split_clause,[],[f5241,f5157,f4025,f6704]) ).
fof(f4025,plain,
( spl0_399
<=> ! [X0] :
( c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),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_399])]) ).
fof(f5241,plain,
( c_lessequals(c_Transcendental_Opi,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_399
| spl0_450 ),
inference(resolution,[],[f5159,f4026]) ).
fof(f4026,plain,
( ! [X0] :
( c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),X0,tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_399 ),
inference(avatar_component_clause,[],[f4025]) ).
fof(f5159,plain,
( ~ c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| spl0_450 ),
inference(avatar_component_clause,[],[f5157]) ).
fof(f6636,plain,
spl0_566,
inference(avatar_split_clause,[],[f697,f6634]) ).
fof(f6634,plain,
( spl0_566
<=> ! [X32,X8,X33] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X32,X33,tc_RealDef_Oreal),X8,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X32,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X33,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f697,axiom,
! [X8,X32,X33] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X32,X33,tc_RealDef_Oreal),X8,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X32,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X33,X8,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__mult__distrib_0) ).
fof(f6632,plain,
spl0_565,
inference(avatar_split_clause,[],[f696,f6630]) ).
fof(f6630,plain,
( spl0_565
<=> ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X5
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,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_565])]) ).
fof(f696,axiom,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X5
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__square__gt__zero_0) ).
fof(f6628,plain,
spl0_564,
inference(avatar_split_clause,[],[f695,f6626]) ).
fof(f6626,plain,
( spl0_564
<=> ! [X6,X5] :
( 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(X5,X5,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_564])]) ).
fof(f695,axiom,
! [X6,X5] :
( 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(X5,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__square__gt__zero2_0) ).
fof(f6624,plain,
spl0_563,
inference(avatar_split_clause,[],[f659,f6622]) ).
fof(f6622,plain,
( spl0_563
<=> ! [X2,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),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f659,axiom,
! [X2,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),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).
fof(f6620,plain,
spl0_562,
inference(avatar_split_clause,[],[f658,f6618]) ).
fof(f6618,plain,
( spl0_562
<=> ! [X2,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),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f658,axiom,
! [X2,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),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
fof(f6606,plain,
spl0_561,
inference(avatar_split_clause,[],[f657,f6604]) ).
fof(f6604,plain,
( spl0_561
<=> ! [X2,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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f657,axiom,
! [X2,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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
fof(f6602,plain,
spl0_560,
inference(avatar_split_clause,[],[f656,f6600]) ).
fof(f6600,plain,
( spl0_560
<=> ! [X2,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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f656,axiom,
! [X2,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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).
fof(f6598,plain,
spl0_559,
inference(avatar_split_clause,[],[f650,f6596]) ).
fof(f6596,plain,
( spl0_559
<=> ! [X2,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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f650,axiom,
! [X2,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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
fof(f6594,plain,
spl0_558,
inference(avatar_split_clause,[],[f649,f6592]) ).
fof(f6592,plain,
( spl0_558
<=> ! [X2,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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f649,axiom,
! [X2,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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
fof(f6590,plain,
spl0_557,
inference(avatar_split_clause,[],[f647,f6588]) ).
fof(f6588,plain,
( spl0_557
<=> ! [X2,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),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f647,axiom,
! [X2,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),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
fof(f6586,plain,
spl0_556,
inference(avatar_split_clause,[],[f646,f6584]) ).
fof(f6584,plain,
( spl0_556
<=> ! [X2,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),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f646,axiom,
! [X2,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),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
fof(f6582,plain,
spl0_555,
inference(avatar_split_clause,[],[f562,f6580]) ).
fof(f6580,plain,
( spl0_555
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,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_555])]) ).
fof(f562,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,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/sandbox2/benchmark/theBenchmark.p',cls_real__less__half__sum_0) ).
fof(f6578,plain,
spl0_554,
inference(avatar_split_clause,[],[f561,f6576]) ).
fof(f6576,plain,
( spl0_554
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,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_554])]) ).
fof(f561,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,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/sandbox2/benchmark/theBenchmark.p',cls_real__gt__half__sum_0) ).
fof(f6574,plain,
spl0_553,
inference(avatar_split_clause,[],[f541,f6572]) ).
fof(f6572,plain,
( spl0_553
<=> ! [X6,X5] :
( ~ 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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f541,axiom,
! [X6,X5] :
( ~ 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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_5) ).
fof(f6570,plain,
spl0_552,
inference(avatar_split_clause,[],[f540,f6568]) ).
fof(f6568,plain,
( spl0_552
<=> ! [X6,X5] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f540,axiom,
! [X6,X5] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_4) ).
fof(f6561,plain,
spl0_551,
inference(avatar_split_clause,[],[f539,f6559]) ).
fof(f6559,plain,
( spl0_551
<=> ! [X6,X5] :
( ~ c_lessequals(X5,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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f539,axiom,
! [X6,X5] :
( ~ c_lessequals(X5,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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_3) ).
fof(f6557,plain,
spl0_550,
inference(avatar_split_clause,[],[f538,f6555]) ).
fof(f6555,plain,
( spl0_550
<=> ! [X6,X5] :
( ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f538,axiom,
! [X6,X5] :
( ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_2) ).
fof(f6553,plain,
spl0_549,
inference(avatar_split_clause,[],[f537,f6551]) ).
fof(f6551,plain,
( spl0_549
<=> ! [X6,X5] :
( c_lessequals(X6,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f537,axiom,
! [X6,X5] :
( c_lessequals(X6,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_1) ).
fof(f6549,plain,
spl0_548,
inference(avatar_split_clause,[],[f536,f6547]) ).
fof(f6547,plain,
( spl0_548
<=> ! [X6,X5] :
( c_lessequals(X5,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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f536,axiom,
! [X6,X5] :
( c_lessequals(X5,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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_0) ).
fof(f6545,plain,
spl0_547,
inference(avatar_split_clause,[],[f528,f6543]) ).
fof(f6543,plain,
( spl0_547
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f528,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__order_0) ).
fof(f6541,plain,
spl0_546,
inference(avatar_split_clause,[],[f226,f6539]) ).
fof(f6539,plain,
( spl0_546
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(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(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f226,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(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(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f6537,plain,
spl0_545,
inference(avatar_split_clause,[],[f178,f6535]) ).
fof(f6535,plain,
( spl0_545
<=> ! [X0,X8] :
( ~ class_Int_Onumber__ring(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(X8,X0),X0) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X8),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f178,axiom,
! [X0,X8] :
( ~ class_Int_Onumber__ring(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(X8,X0),X0) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(X8),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__number__of__Bit0_0) ).
fof(f6533,plain,
spl0_544,
inference(avatar_split_clause,[],[f28,f6531]) ).
fof(f6531,plain,
( spl0_544
<=> ! [X0,X1,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X10,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X10,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f28,axiom,
! [X10,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X10,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X10,X0),X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(f6529,plain,
spl0_543,
inference(avatar_split_clause,[],[f27,f6527]) ).
fof(f27,axiom,
! [X10,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X10,c_HOL_Otimes__class_Otimes(X1,X10,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(f6344,plain,
spl0_542,
inference(avatar_split_clause,[],[f1149,f6342]) ).
fof(f6342,plain,
( spl0_542
<=> ! [X19] : 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(X19,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f1149,plain,
! [X19] : 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(X19,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(forward_demodulation,[],[f806,f901]) ).
fof(f806,axiom,
! [X19] : 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(X19,tc_nat),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__2npi_0) ).
fof(f6340,plain,
spl0_541,
inference(avatar_split_clause,[],[f1134,f6338]) ).
fof(f6338,plain,
( spl0_541
<=> ! [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_541])]) ).
fof(f1134,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,[],[f288]) ).
fof(f288,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f6336,plain,
spl0_540,
inference(avatar_split_clause,[],[f889,f6334]) ).
fof(f6334,plain,
( spl0_540
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f889,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
fof(f6332,plain,
spl0_539,
inference(avatar_split_clause,[],[f887,f6330]) ).
fof(f6330,plain,
( spl0_539
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f887,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
fof(f6328,plain,
spl0_538,
inference(avatar_split_clause,[],[f868,f6326]) ).
fof(f6326,plain,
( spl0_538
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f868,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f6324,plain,
spl0_537,
inference(avatar_split_clause,[],[f867,f6322]) ).
fof(f6322,plain,
( spl0_537
<=> ! [X37,X0,X36,X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X39,X0),X37,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X37,X0),X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f867,axiom,
! [X39,X0,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X39,X0),X37,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X37,X0),X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f6320,plain,
( spl0_535
| spl0_536
| ~ spl0_298
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f5382,f5157,f2843,f6317,f6313]) ).
fof(f5382,plain,
( c_Transcendental_Opi = c_Transcendental_Ocos(c_Transcendental_Opi)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ spl0_298
| ~ spl0_450 ),
inference(resolution,[],[f5158,f2844]) ).
fof(f6311,plain,
spl0_534,
inference(avatar_split_clause,[],[f864,f6309]) ).
fof(f6309,plain,
( spl0_534
<=> ! [X38,X0,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X36,c_HOL_Otimes__class_Otimes(X37,X38,X0),X0) = c_HOL_Otimes__class_Otimes(X37,c_HOL_Otimes__class_Otimes(X36,X38,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f864,axiom,
! [X38,X0,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X36,c_HOL_Otimes__class_Otimes(X37,X38,X0),X0) = c_HOL_Otimes__class_Otimes(X37,c_HOL_Otimes__class_Otimes(X36,X38,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f6307,plain,
spl0_533,
inference(avatar_split_clause,[],[f862,f6305]) ).
fof(f6305,plain,
( spl0_533
<=> ! [X5,X0,X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X6,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f862,axiom,
! [X0,X6,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X6,X0),X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
fof(f6303,plain,
spl0_532,
inference(avatar_split_clause,[],[f834,f6301]) ).
fof(f6301,plain,
( spl0_532
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X3,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f834,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X0),X3,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
fof(f6299,plain,
spl0_531,
inference(avatar_split_clause,[],[f728,f6297]) ).
fof(f6297,plain,
( spl0_531
<=> ! [X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(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_531])]) ).
fof(f728,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_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(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/sandbox2/benchmark/theBenchmark.p',cls_lemma__tan__total_1) ).
fof(f6295,plain,
spl0_530,
inference(avatar_split_clause,[],[f686,f6293]) ).
fof(f6293,plain,
( spl0_530
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f686,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
fof(f6291,plain,
spl0_529,
inference(avatar_split_clause,[],[f683,f6289]) ).
fof(f6289,plain,
( spl0_529
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f683,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
fof(f6287,plain,
spl0_528,
inference(avatar_split_clause,[],[f607,f6285]) ).
fof(f6285,plain,
( spl0_528
<=> ! [X14] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X14,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal),X14,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f607,axiom,
! [X14] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X14,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X14,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),tc_RealDef_Oreal),X14,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma__real__divide__sqrt__less_0) ).
fof(f6282,plain,
spl0_527,
inference(avatar_split_clause,[],[f534,f6279]) ).
fof(f6279,plain,
( spl0_527
<=> 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_527])]) ).
fof(f534,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/sandbox2/benchmark/theBenchmark.p',cls_real__two__squares__add__zero__iff_2) ).
fof(f6277,plain,
spl0_526,
inference(avatar_split_clause,[],[f530,f6275]) ).
fof(f6275,plain,
( spl0_526
<=> ! [X6,X5] :
( 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(X5,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f530,axiom,
! [X6,X5] :
( 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(X5,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel2_0) ).
fof(f6273,plain,
spl0_525,
inference(avatar_split_clause,[],[f529,f6271]) ).
fof(f6271,plain,
( spl0_525
<=> ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X5
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f529,axiom,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X5
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel_0) ).
fof(f6264,plain,
spl0_524,
inference(avatar_split_clause,[],[f301,f6262]) ).
fof(f6262,plain,
( spl0_524
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f301,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(f6260,plain,
spl0_523,
inference(avatar_split_clause,[],[f300,f6258]) ).
fof(f6258,plain,
( spl0_523
<=> ! [X4,X0,X3,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X1,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f300,axiom,
! [X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X1,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f6256,plain,
spl0_522,
inference(avatar_split_clause,[],[f299,f6254]) ).
fof(f6254,plain,
( spl0_522
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X3,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f299,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X3,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f6252,plain,
spl0_521,
inference(avatar_split_clause,[],[f297,f6250]) ).
fof(f6250,plain,
( spl0_521
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f297,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f6248,plain,
spl0_520,
inference(avatar_split_clause,[],[f296,f6246]) ).
fof(f6246,plain,
( spl0_520
<=> ! [X6,X0,X5,X7] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f296,axiom,
! [X0,X6,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f6244,plain,
spl0_519,
inference(avatar_split_clause,[],[f294,f6242]) ).
fof(f6242,plain,
( spl0_519
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f294,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f6240,plain,
spl0_518,
inference(avatar_split_clause,[],[f293,f6238]) ).
fof(f6238,plain,
( spl0_518
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f293,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f6231,plain,
( spl0_517
| ~ spl0_121
| ~ spl0_175
| ~ spl0_251
| ~ spl0_516 ),
inference(avatar_split_clause,[],[f6227,f6224,f2466,f2034,f1772,f6229]) ).
fof(f6229,plain,
( spl0_517
<=> ! [X5] :
( c_Transcendental_Ocos(c_Transcendental_Opi) = X5
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X5
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f6224,plain,
( spl0_516
<=> ! [X5] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X5
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X5
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f6227,plain,
( ! [X5] :
( c_Transcendental_Ocos(c_Transcendental_Opi) = X5
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X5
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal) )
| ~ spl0_121
| ~ spl0_175
| ~ spl0_251
| ~ spl0_516 ),
inference(forward_demodulation,[],[f6225,f2673]) ).
fof(f6225,plain,
( ! [X5] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X5
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X5
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal) )
| ~ spl0_516 ),
inference(avatar_component_clause,[],[f6224]) ).
fof(f6226,plain,
spl0_516,
inference(avatar_split_clause,[],[f232,f6224]) ).
fof(f232,axiom,
! [X5] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X5
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X5
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__is__one_0) ).
fof(f6218,plain,
spl0_515,
inference(avatar_split_clause,[],[f145,f6216]) ).
fof(f6216,plain,
( spl0_515
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f145,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
fof(f6214,plain,
spl0_514,
inference(avatar_split_clause,[],[f144,f6212]) ).
fof(f6212,plain,
( spl0_514
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f144,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).
fof(f6210,plain,
spl0_513,
inference(avatar_split_clause,[],[f118,f6208]) ).
fof(f6208,plain,
( spl0_513
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f118,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
fof(f6115,plain,
( spl0_508
| ~ spl0_356
| ~ spl0_481 ),
inference(avatar_split_clause,[],[f5700,f5290,f3450,f5751]) ).
fof(f3450,plain,
( spl0_356
<=> ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f5700,plain,
( c_lessequals(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_356
| ~ spl0_481 ),
inference(resolution,[],[f5292,f3451]) ).
fof(f3451,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_356 ),
inference(avatar_component_clause,[],[f3450]) ).
fof(f5771,plain,
spl0_512,
inference(avatar_split_clause,[],[f1072,f5768]) ).
fof(f5768,plain,
( spl0_512
<=> 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_512])]) ).
fof(f1072,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,[],[f857,f807]) ).
fof(f857,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__zero_0) ).
fof(f5766,plain,
spl0_511,
inference(avatar_split_clause,[],[f842,f5764]) ).
fof(f5764,plain,
( spl0_511
<=> ! [X2,X1,X3] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Otimes__class_Otimes(X3,X1,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X3,X2,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f842,axiom,
! [X2,X3,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Otimes__class_Otimes(X3,X1,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X3,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__left__cancel_0) ).
fof(f5762,plain,
spl0_510,
inference(avatar_split_clause,[],[f841,f5760]) ).
fof(f5760,plain,
( spl0_510
<=> ! [X2,X1,X3] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f841,axiom,
! [X2,X3,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__right__cancel_0) ).
fof(f5758,plain,
spl0_509,
inference(avatar_split_clause,[],[f667,f5756]) ).
fof(f5756,plain,
( spl0_509
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Oinverse__class_Odivide(X5,c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f667,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Oinverse__class_Odivide(X5,c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__minus1_0) ).
fof(f5754,plain,
( spl0_508
| ~ spl0_387
| spl0_450 ),
inference(avatar_split_clause,[],[f5242,f5157,f3667,f5751]) ).
fof(f3667,plain,
( spl0_387
<=> ! [X0] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f5242,plain,
( c_lessequals(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_387
| spl0_450 ),
inference(resolution,[],[f5159,f3668]) ).
fof(f3668,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_387 ),
inference(avatar_component_clause,[],[f3667]) ).
fof(f5749,plain,
spl0_507,
inference(avatar_split_clause,[],[f497,f5747]) ).
fof(f5747,plain,
( spl0_507
<=> ! [X6,X0,X5] :
( ~ 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(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f497,axiom,
! [X0,X6,X5] :
( ~ 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(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
fof(f5745,plain,
spl0_506,
inference(avatar_split_clause,[],[f492,f5743]) ).
fof(f5743,plain,
( spl0_506
<=> ! [X6,X0,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f492,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,X0),c_HOL_Otimes__class_Otimes(X6,X6,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
fof(f5741,plain,
spl0_505,
inference(avatar_split_clause,[],[f430,f5739]) ).
fof(f5739,plain,
( spl0_505
<=> ! [X6,X0,X5,X7] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X7,X0) = X5
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) != X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f430,axiom,
! [X0,X6,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X7,X0) = X5
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) != X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
fof(f5737,plain,
spl0_504,
inference(avatar_split_clause,[],[f400,f5735]) ).
fof(f5735,plain,
( spl0_504
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Odivide(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f400,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Odivide(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
fof(f5733,plain,
spl0_503,
inference(avatar_split_clause,[],[f246,f5731]) ).
fof(f5731,plain,
( spl0_503
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,X0),c_HOL_Oplus__class_Oplus(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f246,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,X0),c_HOL_Oplus__class_Oplus(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f5729,plain,
spl0_502,
inference(avatar_split_clause,[],[f245,f5727]) ).
fof(f5727,plain,
( spl0_502
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f245,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f5725,plain,
spl0_501,
inference(avatar_split_clause,[],[f244,f5723]) ).
fof(f5723,plain,
( spl0_501
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,X0),c_HOL_Oplus__class_Oplus(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f244,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,X0),c_HOL_Oplus__class_Oplus(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f5721,plain,
spl0_500,
inference(avatar_split_clause,[],[f243,f5719]) ).
fof(f5719,plain,
( spl0_500
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,X0),c_HOL_Oplus__class_Oplus(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f243,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X1,X0),c_HOL_Oplus__class_Oplus(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f5717,plain,
spl0_499,
inference(avatar_split_clause,[],[f242,f5715]) ).
fof(f5715,plain,
( spl0_499
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f242,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f5713,plain,
spl0_498,
inference(avatar_split_clause,[],[f241,f5711]) ).
fof(f5711,plain,
( spl0_498
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f241,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f5699,plain,
spl0_497,
inference(avatar_split_clause,[],[f238,f5697]) ).
fof(f5697,plain,
( spl0_497
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f238,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
fof(f5695,plain,
spl0_496,
inference(avatar_split_clause,[],[f237,f5693]) ).
fof(f5693,plain,
( spl0_496
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f237,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
fof(f5691,plain,
spl0_495,
inference(avatar_split_clause,[],[f124,f5689]) ).
fof(f5689,plain,
( spl0_495
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f124,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f5687,plain,
spl0_494,
inference(avatar_split_clause,[],[f123,f5685]) ).
fof(f5685,plain,
( spl0_494
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f123,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f5683,plain,
spl0_493,
inference(avatar_split_clause,[],[f122,f5681]) ).
fof(f5681,plain,
( spl0_493
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f122,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f5679,plain,
spl0_492,
inference(avatar_split_clause,[],[f121,f5677]) ).
fof(f5677,plain,
( spl0_492
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X0),c_HOL_Oplus__class_Oplus(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f121,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X0),c_HOL_Oplus__class_Oplus(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f5675,plain,
spl0_491,
inference(avatar_split_clause,[],[f120,f5673]) ).
fof(f5673,plain,
( spl0_491
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X0),c_HOL_Oplus__class_Oplus(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f120,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X0),c_HOL_Oplus__class_Oplus(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f5671,plain,
spl0_490,
inference(avatar_split_clause,[],[f119,f5669]) ).
fof(f5669,plain,
( spl0_490
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X0),c_HOL_Oplus__class_Oplus(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f119,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X0),c_HOL_Oplus__class_Oplus(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f5667,plain,
spl0_489,
inference(avatar_split_clause,[],[f84,f5665]) ).
fof(f5665,plain,
( spl0_489
<=> ! [X5,X0,X6,X7] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X6 = X7
| c_HOL_Oplus__class_Oplus(X5,X6,X0) != c_HOL_Oplus__class_Oplus(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f84,axiom,
! [X0,X6,X7,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X6 = X7
| c_HOL_Oplus__class_Oplus(X5,X6,X0) != c_HOL_Oplus__class_Oplus(X5,X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f5663,plain,
spl0_488,
inference(avatar_split_clause,[],[f43,f5661]) ).
fof(f5661,plain,
( spl0_488
<=> ! [X0,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X10,X10,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f43,axiom,
! [X10,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X10,X10,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(f5546,plain,
( spl0_487
| ~ spl0_332
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f5380,f5157,f3201,f5544]) ).
fof(f5314,plain,
spl0_486,
inference(avatar_split_clause,[],[f1148,f5312]) ).
fof(f5312,plain,
( spl0_486
<=> ! [X5] : c_Transcendental_Ocos(X5) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,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_486])]) ).
fof(f1148,plain,
! [X5] : c_Transcendental_Ocos(X5) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,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,[],[f794,f901]) ).
fof(f794,axiom,
! [X5] : c_Transcendental_Ocos(X5) = c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,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/sandbox2/benchmark/theBenchmark.p',cls_cos__periodic_0) ).
fof(f5310,plain,
spl0_485,
inference(avatar_split_clause,[],[f1070,f5307]) ).
fof(f5307,plain,
( spl0_485
<=> 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_485])]) ).
fof(f1070,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,[],[f903,f807]) ).
fof(f903,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_Transcendental_Opi),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__pi_0) ).
fof(f5305,plain,
spl0_484,
inference(avatar_split_clause,[],[f876,f5303]) ).
fof(f5303,plain,
( spl0_484
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X0),X3,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f876,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X0),X3,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
fof(f5301,plain,
spl0_483,
inference(avatar_split_clause,[],[f863,f5299]) ).
fof(f5299,plain,
( spl0_483
<=> ! [X32,X35,X33] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X32,X33,tc_RealDef_Oreal),X35,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X32,c_HOL_Otimes__class_Otimes(X33,X35,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f863,axiom,
! [X35,X32,X33] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X32,X33,tc_RealDef_Oreal),X35,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X32,c_HOL_Otimes__class_Otimes(X33,X35,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__assoc_0) ).
fof(f5297,plain,
spl0_482,
inference(avatar_split_clause,[],[f852,f5295]) ).
fof(f5295,plain,
( spl0_482
<=> ! [X5,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(X5,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f852,axiom,
! [X0,X5] :
( ~ 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(X5,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__Numeral0_0) ).
fof(f5293,plain,
( spl0_481
| ~ spl0_196
| spl0_450 ),
inference(avatar_split_clause,[],[f5243,f5157,f2135,f5290]) ).
fof(f5243,plain,
( c_lessequals(c_Transcendental_Opi,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_196
| spl0_450 ),
inference(resolution,[],[f5159,f2136]) ).
fof(f5288,plain,
spl0_480,
inference(avatar_split_clause,[],[f844,f5286]) ).
fof(f5286,plain,
( spl0_480
<=> ! [X17,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X17,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X17,X17,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X1,X17,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f844,axiom,
! [X1,X17] : c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X17,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X17,X17,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X1,X17,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__divide__square__eq_0) ).
fof(f5284,plain,
spl0_479,
inference(avatar_split_clause,[],[f814,f5282]) ).
fof(f5282,plain,
( spl0_479
<=> ! [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(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f814,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(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
fof(f5280,plain,
spl0_478,
inference(avatar_split_clause,[],[f791,f5277]) ).
fof(f5277,plain,
( spl0_478
<=> 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_478])]) ).
fof(f791,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/sandbox2/benchmark/theBenchmark.p',cls_pi__half__less__two_0) ).
fof(f5275,plain,
spl0_477,
inference(avatar_split_clause,[],[f790,f5272]) ).
fof(f5272,plain,
( spl0_477
<=> 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_477])]) ).
fof(f790,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/sandbox2/benchmark/theBenchmark.p',cls_pi__half__le__two_0) ).
fof(f5270,plain,
spl0_476,
inference(avatar_split_clause,[],[f776,f5268]) ).
fof(f5268,plain,
( spl0_476
<=> ! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X7,X7,X0) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f776,axiom,
! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X7,X7,X0) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__2_0) ).
fof(f5266,plain,
spl0_475,
inference(avatar_split_clause,[],[f775,f5264]) ).
fof(f775,axiom,
! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Otimes__class_Otimes(X7,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),X0),X0) = c_HOL_Oplus__class_Oplus(X7,X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__2__right_0) ).
fof(f5262,plain,
spl0_474,
inference(avatar_split_clause,[],[f687,f5260]) ).
fof(f5260,plain,
( spl0_474
<=> ! [X6,X0,X5] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f687,axiom,
! [X0,X6,X5] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
fof(f5258,plain,
spl0_473,
inference(avatar_split_clause,[],[f682,f5256]) ).
fof(f682,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
fof(f5254,plain,
spl0_472,
inference(avatar_split_clause,[],[f629,f5252]) ).
fof(f5252,plain,
( spl0_472
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f629,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
fof(f5250,plain,
spl0_471,
inference(avatar_split_clause,[],[f628,f5248]) ).
fof(f5248,plain,
( spl0_471
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f628,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
fof(f5240,plain,
spl0_470,
inference(avatar_split_clause,[],[f618,f5238]) ).
fof(f5238,plain,
( spl0_470
<=> ! [X6,X0,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f618,axiom,
! [X0,X6,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
fof(f5236,plain,
spl0_469,
inference(avatar_split_clause,[],[f616,f5234]) ).
fof(f5234,plain,
( spl0_469
<=> ! [X5,X25,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X25,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f616,axiom,
! [X0,X5,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X25,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X25,X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
fof(f5232,plain,
spl0_468,
inference(avatar_split_clause,[],[f615,f5230]) ).
fof(f5230,plain,
( spl0_468
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Otimes__class_Otimes(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f615,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Otimes__class_Otimes(X2,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
fof(f5228,plain,
spl0_467,
inference(avatar_split_clause,[],[f555,f5226]) ).
fof(f5226,plain,
( spl0_467
<=> ! [X19,X10] : c_RealDef_Oreal(c_HOL_Otimes__class_Otimes(X10,X19,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X10,tc_nat),c_RealDef_Oreal(X19,tc_nat),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f555,axiom,
! [X10,X19] : c_RealDef_Oreal(c_HOL_Otimes__class_Otimes(X10,X19,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(X10,tc_nat),c_RealDef_Oreal(X19,tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__of__nat__mult_0) ).
fof(f5224,plain,
spl0_466,
inference(avatar_split_clause,[],[f532,f5222]) ).
fof(f5222,plain,
( spl0_466
<=> ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Otimes__class_Otimes(X5,X5,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_466])]) ).
fof(f532,axiom,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_1) ).
fof(f5220,plain,
spl0_465,
inference(avatar_split_clause,[],[f531,f5218]) ).
fof(f5218,plain,
( spl0_465
<=> ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X5
| c_HOL_Otimes__class_Otimes(X5,X5,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_465])]) ).
fof(f531,axiom,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X5
| c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_0) ).
fof(f5216,plain,
spl0_464,
inference(avatar_split_clause,[],[f514,f5214]) ).
fof(f5214,plain,
( spl0_464
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f514,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
fof(f5212,plain,
spl0_463,
inference(avatar_split_clause,[],[f509,f5210]) ).
fof(f5210,plain,
( spl0_463
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f509,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
fof(f5208,plain,
spl0_462,
inference(avatar_split_clause,[],[f268,f5206]) ).
fof(f5206,plain,
( spl0_462
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f268,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
fof(f5204,plain,
spl0_461,
inference(avatar_split_clause,[],[f267,f5202]) ).
fof(f5202,plain,
( spl0_461
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f267,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
fof(f5200,plain,
spl0_460,
inference(avatar_split_clause,[],[f266,f5198]) ).
fof(f5198,plain,
( spl0_460
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f266,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(f5196,plain,
spl0_459,
inference(avatar_split_clause,[],[f265,f5194]) ).
fof(f5194,plain,
( spl0_459
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f265,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(f5192,plain,
spl0_458,
inference(avatar_split_clause,[],[f117,f5190]) ).
fof(f5190,plain,
( spl0_458
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f117,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f5188,plain,
spl0_457,
inference(avatar_split_clause,[],[f116,f5186]) ).
fof(f5186,plain,
( spl0_457
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f116,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f5184,plain,
spl0_456,
inference(avatar_split_clause,[],[f105,f5182]) ).
fof(f5182,plain,
( spl0_456
<=> ! [X20,X19,X10] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X19,tc_nat),X20,tc_nat) = c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X19,X20,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f105,axiom,
! [X10,X19,X20] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X19,tc_nat),X20,tc_nat) = c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X19,X20,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
fof(f5180,plain,
spl0_455,
inference(avatar_split_clause,[],[f103,f5178]) ).
fof(f5178,plain,
( spl0_455
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f103,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(f5176,plain,
spl0_454,
inference(avatar_split_clause,[],[f102,f5174]) ).
fof(f5174,plain,
( spl0_454
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f102,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(f5172,plain,
spl0_453,
inference(avatar_split_clause,[],[f99,f5170]) ).
fof(f5170,plain,
( spl0_453
<=> ! [X6,X5] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,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_453])]) ).
fof(f99,axiom,
! [X6,X5] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__mult__self__sum__ge__zero_0) ).
fof(f5168,plain,
spl0_452,
inference(avatar_split_clause,[],[f66,f5166]) ).
fof(f5166,plain,
( spl0_452
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f66,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f5164,plain,
spl0_451,
inference(avatar_split_clause,[],[f65,f5162]) ).
fof(f5162,plain,
( spl0_451
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f65,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f5160,plain,
( ~ spl0_449
| ~ spl0_450
| ~ spl0_431 ),
inference(avatar_split_clause,[],[f4237,f4176,f5157,f5153]) ).
fof(f5153,plain,
( spl0_449
<=> c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1(c_Transcendental_Opi),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f4176,plain,
( spl0_431
<=> ! [X5] :
( ~ c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),X5,tc_RealDef_Oreal)
| c_Transcendental_Ocos(X5) != c_Transcendental_Ocos(c_Transcendental_Opi)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1(X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f4237,plain,
( ~ c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Opi,tc_RealDef_Oreal)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1(c_Transcendental_Opi),tc_nat)
| ~ spl0_431 ),
inference(equality_resolution,[],[f4177]) ).
fof(f4177,plain,
( ! [X5] :
( c_Transcendental_Ocos(X5) != c_Transcendental_Ocos(c_Transcendental_Opi)
| ~ c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),X5,tc_RealDef_Oreal)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1(X5),tc_nat) )
| ~ spl0_431 ),
inference(avatar_component_clause,[],[f4176]) ).
fof(f4875,plain,
( ~ spl0_117
| ~ spl0_448
| ~ spl0_248
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f4350,f4128,f2454,f4872,f1752]) ).
fof(f2454,plain,
( spl0_248
<=> ! [X5,X0,X6] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f4128,plain,
( spl0_420
<=> c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f4350,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl0_248
| ~ spl0_420 ),
inference(resolution,[],[f4130,f2455]) ).
fof(f2455,plain,
( ! [X0,X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| ~ c_lessequals(X6,X5,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2454]) ).
fof(f4130,plain,
( c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_420 ),
inference(avatar_component_clause,[],[f4128]) ).
fof(f4483,plain,
( ~ spl0_117
| ~ spl0_447
| ~ spl0_242
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f4347,f4128,f2430,f4480,f1752]) ).
fof(f4480,plain,
( spl0_447
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f4347,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl0_242
| ~ spl0_420 ),
inference(resolution,[],[f4130,f2431]) ).
fof(f4308,plain,
spl0_446,
inference(avatar_split_clause,[],[f904,f4306]) ).
fof(f4306,plain,
( spl0_446
<=> ! [X6,X0,X5] :
( ~ class_Int_Oring__char__0(X0)
| ~ class_Int_Onumber__ring(X0)
| X5 = X6
| c_Int_Onumber__class_Onumber__of(X5,X0) != c_Int_Onumber__class_Onumber__of(X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f904,axiom,
! [X0,X6,X5] :
( ~ class_Int_Oring__char__0(X0)
| ~ class_Int_Onumber__ring(X0)
| X5 = X6
| c_Int_Onumber__class_Onumber__of(X5,X0) != c_Int_Onumber__class_Onumber__of(X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
fof(f4304,plain,
~ spl0_445,
inference(avatar_split_clause,[],[f854,f4301]) ).
fof(f4301,plain,
( spl0_445
<=> 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_445])]) ).
fof(f854,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/sandbox2/benchmark/theBenchmark.p',cls_pi__half__neq__two_0) ).
fof(f4299,plain,
spl0_444,
inference(avatar_split_clause,[],[f727,f4296]) ).
fof(f4296,plain,
( spl0_444
<=> 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_444])]) ).
fof(f727,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/sandbox2/benchmark/theBenchmark.p',cls_minus__pi__half__less__zero_0) ).
fof(f4294,plain,
spl0_443,
inference(avatar_split_clause,[],[f690,f4292]) ).
fof(f4292,plain,
( spl0_443
<=> ! [X6,X5] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,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_443])]) ).
fof(f690,axiom,
! [X6,X5] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__self__sum__ge__zero_0) ).
fof(f4290,plain,
spl0_442,
inference(avatar_split_clause,[],[f524,f4288]) ).
fof(f4288,plain,
( spl0_442
<=> ! [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_442])]) ).
fof(f524,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/sandbox2/benchmark/theBenchmark.p',cls_one__add__one__is__two_0) ).
fof(f4286,plain,
spl0_441,
inference(avatar_split_clause,[],[f476,f4284]) ).
fof(f4284,plain,
( spl0_441
<=> ! [X6,X0,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X5 = X6
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f476,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X5 = X6
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f4282,plain,
spl0_440,
inference(avatar_split_clause,[],[f471,f4280]) ).
fof(f4280,plain,
( spl0_440
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oplus__class_Oplus(X5,X1,X0) != X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f471,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oplus__class_Oplus(X5,X1,X0) != X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f4278,plain,
spl0_439,
inference(avatar_split_clause,[],[f457,f4276]) ).
fof(f4276,plain,
( spl0_439
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f457,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
fof(f4274,plain,
spl0_438,
inference(avatar_split_clause,[],[f455,f4272]) ).
fof(f4272,plain,
( spl0_438
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f455,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
fof(f4270,plain,
spl0_437,
inference(avatar_split_clause,[],[f452,f4268]) ).
fof(f4268,plain,
( spl0_437
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f452,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
fof(f4266,plain,
spl0_436,
inference(avatar_split_clause,[],[f451,f4264]) ).
fof(f4264,plain,
( spl0_436
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f451,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
fof(f4262,plain,
spl0_435,
inference(avatar_split_clause,[],[f438,f4260]) ).
fof(f4260,plain,
( spl0_435
<=> ! [X6,X5] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f438,axiom,
! [X6,X5] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__le__add__iff_1) ).
fof(f4256,plain,
( spl0_434
| ~ spl0_421
| ~ spl0_433 ),
inference(avatar_split_clause,[],[f4252,f4249,f4132,f4254]) ).
fof(f4254,plain,
( spl0_434
<=> ! [X6,X5] :
( ~ c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f4132,plain,
( spl0_421
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Transcendental_Opi) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f4249,plain,
( spl0_433
<=> ! [X6,X5] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f4252,plain,
( ! [X6,X5] :
( ~ c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),X6,tc_RealDef_Oreal) )
| ~ spl0_421
| ~ spl0_433 ),
inference(forward_demodulation,[],[f4250,f4134]) ).
fof(f4134,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Transcendental_Opi)
| ~ spl0_421 ),
inference(avatar_component_clause,[],[f4132]) ).
fof(f4250,plain,
( ! [X6,X5] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),X6,tc_RealDef_Oreal) )
| ~ spl0_433 ),
inference(avatar_component_clause,[],[f4249]) ).
fof(f4251,plain,
spl0_433,
inference(avatar_split_clause,[],[f437,f4249]) ).
fof(f437,axiom,
! [X6,X5] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__le__add__iff_0) ).
fof(f4247,plain,
spl0_432,
inference(avatar_split_clause,[],[f429,f4245]) ).
fof(f4245,plain,
( spl0_432
<=> ! [X6,X5] : c_lessequals(X5,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,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_432])]) ).
fof(f429,axiom,
! [X6,X5] : c_lessequals(X5,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X6,X6,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__real__sqrt__sumsq_0) ).
fof(f4178,plain,
( spl0_431
| ~ spl0_421
| ~ spl0_430 ),
inference(avatar_split_clause,[],[f4174,f4170,f4132,f4176]) ).
fof(f4170,plain,
( spl0_430
<=> ! [X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1(X5),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f4174,plain,
( ! [X5] :
( ~ c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),X5,tc_RealDef_Oreal)
| c_Transcendental_Ocos(X5) != c_Transcendental_Ocos(c_Transcendental_Opi)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1(X5),tc_nat) )
| ~ spl0_421
| ~ spl0_430 ),
inference(forward_demodulation,[],[f4173,f4134]) ).
fof(f4173,plain,
( ! [X5] :
( c_Transcendental_Ocos(X5) != c_Transcendental_Ocos(c_Transcendental_Opi)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1(X5),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) )
| ~ spl0_421
| ~ spl0_430 ),
inference(forward_demodulation,[],[f4171,f4134]) ).
fof(f4171,plain,
( ! [X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1(X5),tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) )
| ~ spl0_430 ),
inference(avatar_component_clause,[],[f4170]) ).
fof(f4172,plain,
spl0_430,
inference(avatar_split_clause,[],[f427,f4170]) ).
fof(f427,axiom,
! [X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1(X5),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__zero__lemma_0) ).
fof(f4168,plain,
spl0_429,
inference(avatar_split_clause,[],[f311,f4166]) ).
fof(f4166,plain,
( spl0_429
<=> ! [X24,X23,X0,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X23 = X24
| c_HOL_Ominus__class_Ominus(X23,X24,X0) != c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f311,axiom,
! [X0,X24,X5,X23] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X23 = X24
| c_HOL_Ominus__class_Ominus(X23,X24,X0) != c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
fof(f4164,plain,
spl0_428,
inference(avatar_split_clause,[],[f292,f4162]) ).
fof(f4162,plain,
( spl0_428
<=> ! [X5,X0,X6,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f292,axiom,
! [X0,X6,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f4160,plain,
spl0_427,
inference(avatar_split_clause,[],[f291,f4158]) ).
fof(f4158,plain,
( spl0_427
<=> ! [X6,X0,X5,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X6,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f291,axiom,
! [X0,X6,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X6,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f4156,plain,
spl0_426,
inference(avatar_split_clause,[],[f283,f4154]) ).
fof(f4154,plain,
( spl0_426
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f283,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
fof(f4152,plain,
spl0_425,
inference(avatar_split_clause,[],[f282,f4150]) ).
fof(f4150,plain,
( spl0_425
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f282,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
fof(f4148,plain,
spl0_424,
inference(avatar_split_clause,[],[f281,f4146]) ).
fof(f4146,plain,
( spl0_424
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f281,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
fof(f4144,plain,
spl0_423,
inference(avatar_split_clause,[],[f280,f4142]) ).
fof(f4142,plain,
( spl0_423
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f280,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
fof(f4140,plain,
spl0_422,
inference(avatar_split_clause,[],[f264,f4138]) ).
fof(f4138,plain,
( spl0_422
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f264,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
fof(f4135,plain,
( spl0_420
| spl0_421
| ~ spl0_189
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f3039,f2843,f2101,f4132,f4128]) ).
fof(f2101,plain,
( spl0_189
<=> c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f3039,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Transcendental_Opi)
| c_HOL_Oord__class_Oless(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_189
| ~ spl0_298 ),
inference(resolution,[],[f2844,f2103]) ).
fof(f2103,plain,
( c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f2101]) ).
fof(f4126,plain,
spl0_419,
inference(avatar_split_clause,[],[f263,f4124]) ).
fof(f4124,plain,
( spl0_419
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f263,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
fof(f4122,plain,
spl0_418,
inference(avatar_split_clause,[],[f247,f4120]) ).
fof(f4120,plain,
( spl0_418
<=> ! [X6,X5,X7] :
( ~ c_lessequals(X5,X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X7,X5,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X7,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f247,axiom,
! [X6,X7,X5] :
( ~ c_lessequals(X5,X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X7,X5,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X7,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__left__mono_0) ).
fof(f4118,plain,
spl0_417,
inference(avatar_split_clause,[],[f240,f4116]) ).
fof(f4116,plain,
( spl0_417
<=> ! [X6,X5] :
( ~ c_lessequals(X6,c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f240,axiom,
! [X6,X5] :
( ~ c_lessequals(X6,c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__le__0__iff_1) ).
fof(f4114,plain,
spl0_416,
inference(avatar_split_clause,[],[f239,f4112]) ).
fof(f4112,plain,
( spl0_416
<=> ! [X6,X5] :
( c_lessequals(X6,c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f239,axiom,
! [X6,X5] :
( c_lessequals(X6,c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__le__0__iff_0) ).
fof(f4110,plain,
spl0_415,
inference(avatar_split_clause,[],[f235,f4108]) ).
fof(f4108,plain,
( spl0_415
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f235,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
fof(f4106,plain,
spl0_414,
inference(avatar_split_clause,[],[f234,f4104]) ).
fof(f4104,plain,
( spl0_414
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f234,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
fof(f4102,plain,
spl0_413,
inference(avatar_split_clause,[],[f222,f4100]) ).
fof(f4100,plain,
( spl0_413
<=> ! [X20,X19,X10] :
( X10 = X19
| c_HOL_Otimes__class_Otimes(c_Suc(X20),X10,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X20),X19,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f222,axiom,
! [X10,X19,X20] :
( X10 = X19
| c_HOL_Otimes__class_Otimes(c_Suc(X20),X10,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X20),X19,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
fof(f4098,plain,
spl0_412,
inference(avatar_split_clause,[],[f141,f4096]) ).
fof(f4096,plain,
( spl0_412
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f141,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
fof(f4094,plain,
spl0_411,
inference(avatar_split_clause,[],[f140,f4092]) ).
fof(f4092,plain,
( spl0_411
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f140,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
fof(f4090,plain,
spl0_410,
inference(avatar_split_clause,[],[f136,f4088]) ).
fof(f136,axiom,
! [X0,X6,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X6,X5,X0)
| ~ c_lessequals(X7,X6,X0)
| c_lessequals(X7,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f4067,plain,
spl0_409,
inference(avatar_split_clause,[],[f135,f4065]) ).
fof(f4065,plain,
( spl0_409
<=> ! [X5,X0,X6,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X7,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f135,axiom,
! [X0,X6,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X7,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f4063,plain,
spl0_408,
inference(avatar_split_clause,[],[f134,f4061]) ).
fof(f4061,plain,
( spl0_408
<=> ! [X6,X0,X5,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X6,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f134,axiom,
! [X0,X6,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X6,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f4059,plain,
spl0_407,
inference(avatar_split_clause,[],[f132,f4057]) ).
fof(f4057,plain,
( spl0_407
<=> ! [X5,X0,X6,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X6,X0)
| ~ c_lessequals(X6,X7,X0)
| c_lessequals(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f132,axiom,
! [X0,X6,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X6,X0)
| ~ c_lessequals(X6,X7,X0)
| c_lessequals(X5,X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f4055,plain,
spl0_406,
inference(avatar_split_clause,[],[f130,f4053]) ).
fof(f4053,plain,
( spl0_406
<=> ! [X5,X0,X6,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X6,X7,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f130,axiom,
! [X0,X6,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X6,X7,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f4051,plain,
spl0_405,
inference(avatar_split_clause,[],[f129,f4049]) ).
fof(f4049,plain,
( spl0_405
<=> ! [X5,X0,X6,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f129,axiom,
! [X0,X6,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f4047,plain,
spl0_404,
inference(avatar_split_clause,[],[f108,f4045]) ).
fof(f4045,plain,
( spl0_404
<=> ! [X6,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f108,axiom,
! [X6,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__less__add__iff_0) ).
fof(f4043,plain,
spl0_403,
inference(avatar_split_clause,[],[f107,f4041]) ).
fof(f4041,plain,
( spl0_403
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f107,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X5,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(X5,X6,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__less__add__iff_1) ).
fof(f4039,plain,
spl0_402,
inference(avatar_split_clause,[],[f83,f4037]) ).
fof(f4037,plain,
( spl0_402
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X1,X3,X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f83,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X1,X3,X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f4035,plain,
spl0_401,
inference(avatar_split_clause,[],[f82,f4033]) ).
fof(f4033,plain,
( spl0_401
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X1,X3,X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f82,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X1,X3,X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f4031,plain,
spl0_400,
inference(avatar_split_clause,[],[f81,f4029]) ).
fof(f4029,plain,
( spl0_400
<=> ! [X0,X3,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X2,X1,X0) != c_HOL_Oplus__class_Oplus(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f81,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X3
| c_HOL_Oplus__class_Oplus(X2,X1,X0) != c_HOL_Oplus__class_Oplus(X3,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f4027,plain,
( spl0_399
| ~ spl0_353
| ~ spl0_387 ),
inference(avatar_split_clause,[],[f3961,f3667,f3402,f4025]) ).
fof(f3961,plain,
( ! [X0] :
( c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),X0,tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_353
| ~ spl0_387 ),
inference(resolution,[],[f3668,f3403]) ).
fof(f4023,plain,
spl0_398,
inference(avatar_split_clause,[],[f75,f4021]) ).
fof(f4021,plain,
( spl0_398
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f75,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
fof(f4019,plain,
spl0_397,
inference(avatar_split_clause,[],[f74,f4017]) ).
fof(f4017,plain,
( spl0_397
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f74,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
fof(f4015,plain,
spl0_396,
inference(avatar_split_clause,[],[f54,f4013]) ).
fof(f4013,plain,
( spl0_396
<=> ! [X6,X5] :
( c_HOL_Oord__class_Oless(X6,c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f54,axiom,
! [X6,X5] :
( c_HOL_Oord__class_Oless(X6,c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__less__0__iff_0) ).
fof(f4011,plain,
spl0_395,
inference(avatar_split_clause,[],[f53,f4009]) ).
fof(f4009,plain,
( spl0_395
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f53,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__less__0__iff_1) ).
fof(f4007,plain,
spl0_394,
inference(avatar_split_clause,[],[f35,f4005]) ).
fof(f4005,plain,
( spl0_394
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f35,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).
fof(f4003,plain,
spl0_393,
inference(avatar_split_clause,[],[f34,f4001]) ).
fof(f4001,plain,
( spl0_393
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f34,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
fof(f3999,plain,
spl0_392,
inference(avatar_split_clause,[],[f20,f3997]) ).
fof(f3997,plain,
( spl0_392
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X6,X0)
| c_lessequals(X6,X5,X0)
| c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f20,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X6,X0)
| c_lessequals(X6,X5,X0)
| c_HOL_Oord__class_Oless(X5,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f3995,plain,
spl0_391,
inference(avatar_split_clause,[],[f11,f3993]) ).
fof(f3993,plain,
( spl0_391
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
fof(f3991,plain,
spl0_390,
inference(avatar_split_clause,[],[f10,f3989]) ).
fof(f3989,plain,
( spl0_390
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
fof(f3987,plain,
spl0_389,
inference(avatar_split_clause,[],[f2,f3985]) ).
fof(f3985,plain,
( spl0_389
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
fof(f3960,plain,
spl0_388,
inference(avatar_split_clause,[],[f1,f3958]) ).
fof(f3958,plain,
( spl0_388
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
fof(f3669,plain,
( spl0_387
| ~ spl0_196
| ~ spl0_356 ),
inference(avatar_split_clause,[],[f3551,f3450,f2135,f3667]) ).
fof(f3551,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),X0,tc_RealDef_Oreal) )
| ~ spl0_196
| ~ spl0_356 ),
inference(resolution,[],[f3451,f2136]) ).
fof(f3603,plain,
( spl0_386
| ~ spl0_196
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f3494,f3402,f2135,f3601]) ).
fof(f3601,plain,
( spl0_386
<=> ! [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_386])]) ).
fof(f3494,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_196
| ~ spl0_353 ),
inference(resolution,[],[f3403,f2136]) ).
fof(f3599,plain,
spl0_385,
inference(avatar_split_clause,[],[f1145,f3596]) ).
fof(f3596,plain,
( spl0_385
<=> 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_385])]) ).
fof(f1145,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,[],[f609,f901]) ).
fof(f609,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/sandbox2/benchmark/theBenchmark.p',cls_m2pi__less__pi_0) ).
fof(f3594,plain,
spl0_384,
inference(avatar_split_clause,[],[f850,f3592]) ).
fof(f3592,plain,
( spl0_384
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f850,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oinverse__class_Odivide(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__numeral__1_0) ).
fof(f3590,plain,
spl0_383,
inference(avatar_split_clause,[],[f465,f3588]) ).
fof(f3588,plain,
( spl0_383
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f465,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
fof(f3586,plain,
spl0_382,
inference(avatar_split_clause,[],[f447,f3584]) ).
fof(f3584,plain,
( spl0_382
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X1,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f447,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X1,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
fof(f3582,plain,
spl0_381,
inference(avatar_split_clause,[],[f436,f3580]) ).
fof(f436,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
fof(f3578,plain,
spl0_380,
inference(avatar_split_clause,[],[f435,f3576]) ).
fof(f3576,plain,
( spl0_380
<=> ! [X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__1(X5),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__2(X5),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f435,axiom,
! [X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__1(X5),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Transcendental_Osko__Transcendental__Xcos__zero__iff__1__2(X5),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Ocos(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__zero__iff_0) ).
fof(f3574,plain,
spl0_379,
inference(avatar_split_clause,[],[f389,f3572]) ).
fof(f3572,plain,
( spl0_379
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f389,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self_0) ).
fof(f3570,plain,
spl0_378,
inference(avatar_split_clause,[],[f254,f3568]) ).
fof(f3568,plain,
( spl0_378
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X6
| c_HOL_Oord__class_Oless(X5,X6,X0)
| c_HOL_Oord__class_Oless(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f254,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X6
| c_HOL_Oord__class_Oless(X5,X6,X0)
| c_HOL_Oord__class_Oless(X6,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
fof(f3566,plain,
spl0_377,
inference(avatar_split_clause,[],[f252,f3564]) ).
fof(f3564,plain,
( spl0_377
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Oorder(X0)
| X5 = X6
| ~ c_lessequals(X6,X5,X0)
| ~ c_lessequals(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f252,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| X5 = X6
| ~ c_lessequals(X6,X5,X0)
| ~ c_lessequals(X5,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
fof(f3562,plain,
spl0_376,
inference(avatar_split_clause,[],[f248,f3560]) ).
fof(f3560,plain,
( spl0_376
<=> ! [X6,X0,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X5 = X6
| c_HOL_Oord__class_Oless(X5,X6,X0)
| c_HOL_Oord__class_Oless(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f248,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X5 = X6
| c_HOL_Oord__class_Oless(X5,X6,X0)
| c_HOL_Oord__class_Oless(X6,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f3549,plain,
spl0_375,
inference(avatar_split_clause,[],[f230,f3547]) ).
fof(f3547,plain,
( spl0_375
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f230,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
fof(f3545,plain,
spl0_374,
inference(avatar_split_clause,[],[f143,f3543]) ).
fof(f3543,plain,
( spl0_374
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f143,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
fof(f3541,plain,
spl0_373,
inference(avatar_split_clause,[],[f142,f3539]) ).
fof(f3539,plain,
( spl0_373
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f142,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
fof(f3531,plain,
( spl0_372
| ~ spl0_121
| ~ spl0_175
| ~ spl0_251
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f3526,f3522,f2466,f2034,f1772,f3528]) ).
fof(f3528,plain,
( spl0_372
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f3522,plain,
( spl0_371
<=> 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_371])]) ).
fof(f3526,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| ~ spl0_121
| ~ spl0_175
| ~ spl0_251
| ~ spl0_371 ),
inference(forward_demodulation,[],[f3524,f2673]) ).
fof(f3524,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_371 ),
inference(avatar_component_clause,[],[f3522]) ).
fof(f3525,plain,
spl0_371,
inference(avatar_split_clause,[],[f139,f3522]) ).
fof(f139,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__is__one_2) ).
fof(f3520,plain,
spl0_370,
inference(avatar_split_clause,[],[f111,f3518]) ).
fof(f3518,plain,
( spl0_370
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X6
| ~ c_lessequals(X5,X6,X0)
| c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f111,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X6
| ~ c_lessequals(X5,X6,X0)
| c_HOL_Oord__class_Oless(X5,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f3516,plain,
spl0_369,
inference(avatar_split_clause,[],[f110,f3514]) ).
fof(f3514,plain,
( spl0_369
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f110,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
fof(f3512,plain,
spl0_368,
inference(avatar_split_clause,[],[f106,f3510]) ).
fof(f3510,plain,
( spl0_368
<=> ! [X5,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f106,axiom,
! [X0,X5] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
fof(f3508,plain,
spl0_367,
inference(avatar_split_clause,[],[f90,f3506]) ).
fof(f3506,plain,
( spl0_367
<=> ! [X6,X0,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f90,axiom,
! [X0,X6,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__def_0) ).
fof(f3492,plain,
spl0_366,
inference(avatar_split_clause,[],[f89,f3490]) ).
fof(f3490,plain,
( spl0_366
<=> ! [X6,X0,X5] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f89,axiom,
! [X0,X6,X5] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
fof(f3488,plain,
spl0_365,
inference(avatar_split_clause,[],[f88,f3486]) ).
fof(f3486,plain,
( spl0_365
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f88,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus_0) ).
fof(f3484,plain,
spl0_364,
inference(avatar_split_clause,[],[f63,f3482]) ).
fof(f3482,plain,
( spl0_364
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f63,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
fof(f3480,plain,
spl0_363,
inference(avatar_split_clause,[],[f62,f3478]) ).
fof(f3478,plain,
( spl0_363
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f62,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
fof(f3476,plain,
spl0_362,
inference(avatar_split_clause,[],[f61,f3474]) ).
fof(f3474,plain,
( spl0_362
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f61,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
fof(f3472,plain,
spl0_361,
inference(avatar_split_clause,[],[f60,f3470]) ).
fof(f3470,plain,
( spl0_361
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f60,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
fof(f3468,plain,
spl0_360,
inference(avatar_split_clause,[],[f59,f3466]) ).
fof(f3466,plain,
( spl0_360
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f59,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
fof(f3464,plain,
spl0_359,
inference(avatar_split_clause,[],[f58,f3462]) ).
fof(f3462,plain,
( spl0_359
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f58,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
fof(f3460,plain,
spl0_358,
inference(avatar_split_clause,[],[f57,f3458]) ).
fof(f3458,plain,
( spl0_358
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f57,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
fof(f3456,plain,
spl0_357,
inference(avatar_split_clause,[],[f56,f3454]) ).
fof(f3454,plain,
( spl0_357
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f56,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
fof(f3452,plain,
( spl0_356
| ~ spl0_189
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f3329,f3201,f2101,f3450]) ).
fof(f3329,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_189
| ~ spl0_332 ),
inference(resolution,[],[f3202,f2103]) ).
fof(f3448,plain,
spl0_355,
inference(avatar_split_clause,[],[f8,f3446]) ).
fof(f3446,plain,
( spl0_355
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
fof(f3444,plain,
spl0_354,
inference(avatar_split_clause,[],[f7,f3442]) ).
fof(f3442,plain,
( spl0_354
<=> ! [X6,X0,X7] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f7,axiom,
! [X0,X6,X7] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
fof(f3404,plain,
( spl0_353
| ~ spl0_179
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f3318,f3201,f2058,f3402]) ).
fof(f2058,plain,
( spl0_179
<=> 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_179])]) ).
fof(f3318,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_179
| ~ spl0_332 ),
inference(resolution,[],[f3202,f2060]) ).
fof(f2060,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f2058]) ).
fof(f3289,plain,
spl0_352,
inference(avatar_split_clause,[],[f1163,f3287]) ).
fof(f3287,plain,
( spl0_352
<=> ! [X16,X15] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X16,X15,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X15,X16,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f1163,plain,
! [X16,X15] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X16,X15,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X15,X16,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f85,f91]) ).
fof(f91,axiom,
! [X18,X17] : c_HOL_Ominus__class_Ominus(X17,X18,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Ouminus__class_Ouminus(X18,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__diff__def_0) ).
fof(f85,axiom,
! [X16,X15] :
( c_HOL_Oord__class_Oless(X15,X16,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X16,c_HOL_Ouminus__class_Ouminus(X15,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__gt__zero__less_0) ).
fof(f3285,plain,
spl0_351,
inference(avatar_split_clause,[],[f1162,f3283]) ).
fof(f3283,plain,
( spl0_351
<=> ! [X16,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X16,X15,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X15,X16,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f1162,plain,
! [X16,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X16,X15,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X15,X16,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f86,f91]) ).
fof(f86,axiom,
! [X16,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X16,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X16,c_HOL_Ouminus__class_Ouminus(X15,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__sum__gt__zero_0) ).
fof(f3281,plain,
spl0_350,
inference(avatar_split_clause,[],[f1141,f3278]) ).
fof(f3278,plain,
( spl0_350
<=> 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_350])]) ).
fof(f1141,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,[],[f795,f901]) ).
fof(f795,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/sandbox2/benchmark/theBenchmark.p',cls_cos__two__pi_0) ).
fof(f3276,plain,
( ~ spl0_117
| ~ spl0_349
| ~ spl0_248
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f3148,f3086,f2454,f3273,f1752]) ).
fof(f3273,plain,
( spl0_349
<=> 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_349])]) ).
fof(f3086,plain,
( spl0_325
<=> 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_325])]) ).
fof(f3148,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_248
| ~ spl0_325 ),
inference(resolution,[],[f3088,f2455]) ).
fof(f3088,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_325 ),
inference(avatar_component_clause,[],[f3086]) ).
fof(f3271,plain,
spl0_348,
inference(avatar_split_clause,[],[f907,f3269]) ).
fof(f3269,plain,
( spl0_348
<=> ! [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(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f907,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(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).
fof(f3267,plain,
spl0_347,
inference(avatar_split_clause,[],[f885,f3264]) ).
fof(f3264,plain,
( spl0_347
<=> 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_347])]) ).
fof(f885,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/sandbox2/benchmark/theBenchmark.p',cls_cos__pi__half_0) ).
fof(f3262,plain,
spl0_346,
inference(avatar_split_clause,[],[f793,f3259]) ).
fof(f3259,plain,
( spl0_346
<=> 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_346])]) ).
fof(f793,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/sandbox2/benchmark/theBenchmark.p',cls_pi__half__gt__zero_0) ).
fof(f3257,plain,
spl0_345,
inference(avatar_split_clause,[],[f792,f3254]) ).
fof(f3254,plain,
( spl0_345
<=> 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_345])]) ).
fof(f792,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/sandbox2/benchmark/theBenchmark.p',cls_pi__half__ge__zero_0) ).
fof(f3252,plain,
spl0_344,
inference(avatar_split_clause,[],[f704,f3250]) ).
fof(f704,axiom,
! [X6,X5] : c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(X5,X6,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Odivide(c_NthRoot_Osqrt(X5),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__divide_0) ).
fof(f3248,plain,
spl0_343,
inference(avatar_split_clause,[],[f699,f3246]) ).
fof(f3246,plain,
( spl0_343
<=> ! [X6,X5] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X5,X6,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X5),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f699,axiom,
! [X6,X5] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X5,X6,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X5),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__mult_0) ).
fof(f3244,plain,
spl0_342,
inference(avatar_split_clause,[],[f645,f3242]) ).
fof(f3242,plain,
( spl0_342
<=> ! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X7,X0) = c_HOL_Otimes__class_Otimes(X7,c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f645,axiom,
! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X7,X0) = c_HOL_Otimes__class_Otimes(X7,c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__minus1__right_0) ).
fof(f3240,plain,
spl0_341,
inference(avatar_split_clause,[],[f644,f3238]) ).
fof(f3238,plain,
( spl0_341
<=> ! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X7,X0) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f644,axiom,
! [X0,X7] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X7,X0) = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0),X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__minus1_0) ).
fof(f3236,plain,
spl0_340,
inference(avatar_split_clause,[],[f535,f3234]) ).
fof(f3234,plain,
( spl0_340
<=> ! [X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X5
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f535,axiom,
! [X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X5
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_0) ).
fof(f3232,plain,
spl0_339,
inference(avatar_split_clause,[],[f475,f3230]) ).
fof(f3230,plain,
( spl0_339
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f475,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f3227,plain,
spl0_338,
inference(avatar_split_clause,[],[f474,f3225]) ).
fof(f3225,plain,
( spl0_338
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f474,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f3223,plain,
spl0_337,
inference(avatar_split_clause,[],[f473,f3221]) ).
fof(f3221,plain,
( spl0_337
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f473,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
fof(f3219,plain,
spl0_336,
inference(avatar_split_clause,[],[f428,f3217]) ).
fof(f3217,plain,
( spl0_336
<=> ! [X5,X14] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X14,X14,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f428,axiom,
! [X14,X5] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X14,X14,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X5,X5,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__minus__mult__self__le_0) ).
fof(f3215,plain,
spl0_335,
inference(avatar_split_clause,[],[f271,f3213]) ).
fof(f3213,plain,
( spl0_335
<=> ! [X5,X1] :
( X1 = X5
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f271,axiom,
! [X1,X5] :
( X1 = X5
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__minus__iff_0) ).
fof(f3211,plain,
spl0_334,
inference(avatar_split_clause,[],[f258,f3209]) ).
fof(f3209,plain,
( spl0_334
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f258,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f3207,plain,
spl0_333,
inference(avatar_split_clause,[],[f137,f3205]) ).
fof(f3205,plain,
( spl0_333
<=> ! [X6,X5] :
( c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f137,axiom,
! [X6,X5] :
( c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_0) ).
fof(f3203,plain,
spl0_332,
inference(avatar_split_clause,[],[f127,f3201]) ).
fof(f127,axiom,
! [X21,X22,X20] :
( ~ c_lessequals(X21,X22,tc_RealDef_Oreal)
| ~ c_lessequals(X22,X20,tc_RealDef_Oreal)
| c_lessequals(X21,X20,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f3199,plain,
spl0_331,
inference(avatar_split_clause,[],[f100,f3197]) ).
fof(f3197,plain,
( spl0_331
<=> ! [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_331])]) ).
fof(f100,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f3195,plain,
spl0_330,
inference(avatar_split_clause,[],[f98,f3193]) ).
fof(f3193,plain,
( spl0_330
<=> ! [X19] : c_RealDef_Oreal(c_Suc(X19),tc_nat) = c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X19,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f98,axiom,
! [X19] : c_RealDef_Oreal(c_Suc(X19),tc_nat) = c_HOL_Oplus__class_Oplus(c_RealDef_Oreal(X19,tc_nat),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__of__nat__Suc_0) ).
fof(f3191,plain,
spl0_329,
inference(avatar_split_clause,[],[f36,f3189]) ).
fof(f3189,plain,
( spl0_329
<=> ! [X6,X5] :
( c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal) = X6
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f36,axiom,
! [X6,X5] :
( c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal) = X6
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(X5,X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__eq__0__iff_0) ).
fof(f3187,plain,
( ~ spl0_117
| ~ spl0_328
| ~ spl0_242
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f3145,f3086,f2430,f3184,f1752]) ).
fof(f3184,plain,
( spl0_328
<=> 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_328])]) ).
fof(f3145,plain,
( ~ c_HOL_Oord__class_Oless(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_242
| ~ spl0_325 ),
inference(resolution,[],[f3088,f2431]) ).
fof(f3182,plain,
spl0_327,
inference(avatar_split_clause,[],[f16,f3180]) ).
fof(f3180,plain,
( spl0_327
<=> ! [X6,X5] :
( c_lessequals(X5,X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f16,axiom,
! [X6,X5] :
( c_lessequals(X5,X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__eq__diff_1) ).
fof(f3178,plain,
spl0_326,
inference(avatar_split_clause,[],[f15,f3176]) ).
fof(f3176,plain,
( spl0_326
<=> ! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ominus__class_Ominus(X5,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f15,axiom,
! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ominus__class_Ominus(X5,X6,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__eq__diff_0) ).
fof(f3089,plain,
( spl0_325
| spl0_164
| ~ spl0_179
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f3030,f2843,f2058,f1985,f3086]) ).
fof(f3030,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_179
| ~ spl0_298 ),
inference(resolution,[],[f2844,f2060]) ).
fof(f3002,plain,
( spl0_324
| ~ spl0_112
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2348,f2238,f1727,f3000]) ).
fof(f2238,plain,
( spl0_216
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f2348,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_112
| ~ spl0_216 ),
inference(resolution,[],[f2239,f1729]) ).
fof(f2239,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_216 ),
inference(avatar_component_clause,[],[f2238]) ).
fof(f2946,plain,
spl0_323,
inference(avatar_split_clause,[],[f902,f2944]) ).
fof(f2944,plain,
( spl0_323
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f902,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f2942,plain,
( spl0_322
| ~ spl0_65
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2347,f2238,f1492,f2940]) ).
fof(f2940,plain,
( spl0_322
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f1492,plain,
( spl0_65
<=> class_OrderedGroup_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f2347,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_65
| ~ spl0_216 ),
inference(resolution,[],[f2239,f1494]) ).
fof(f1494,plain,
( class_OrderedGroup_Ogroup__add(tc_Int_Oint)
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1492]) ).
fof(f2938,plain,
spl0_321,
inference(avatar_split_clause,[],[f896,f2936]) ).
fof(f2936,plain,
( spl0_321
<=> ! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f896,axiom,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__numeral__1__right_0) ).
fof(f2934,plain,
spl0_320,
inference(avatar_split_clause,[],[f895,f2932]) ).
fof(f2932,plain,
( spl0_320
<=> ! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f895,axiom,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__numeral__1_0) ).
fof(f2930,plain,
~ spl0_319,
inference(avatar_split_clause,[],[f845,f2927]) ).
fof(f2927,plain,
( spl0_319
<=> 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_319])]) ).
fof(f845,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/sandbox2/benchmark/theBenchmark.p',cls_pi__half__neq__zero_0) ).
fof(f2925,plain,
spl0_318,
inference(avatar_split_clause,[],[f480,f2923]) ).
fof(f2923,plain,
( spl0_318
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f480,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f2921,plain,
spl0_317,
inference(avatar_split_clause,[],[f472,f2919]) ).
fof(f2919,plain,
( spl0_317
<=> ! [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_317])]) ).
fof(f472,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f2917,plain,
spl0_316,
inference(avatar_split_clause,[],[f470,f2915]) ).
fof(f2915,plain,
( spl0_316
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f470,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f2913,plain,
spl0_315,
inference(avatar_split_clause,[],[f462,f2911]) ).
fof(f2911,plain,
( spl0_315
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f462,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f2909,plain,
spl0_314,
inference(avatar_split_clause,[],[f439,f2907]) ).
fof(f2907,plain,
( spl0_314
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f439,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f2905,plain,
spl0_313,
inference(avatar_split_clause,[],[f426,f2903]) ).
fof(f2903,plain,
( spl0_313
<=> ! [X5] :
( ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X5),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f426,axiom,
! [X5] :
( ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X5),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_1) ).
fof(f2901,plain,
spl0_312,
inference(avatar_split_clause,[],[f425,f2899]) ).
fof(f2899,plain,
( spl0_312
<=> ! [X5] :
( c_lessequals(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X5),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f425,axiom,
! [X5] :
( c_lessequals(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X5),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_0) ).
fof(f2897,plain,
( spl0_311
| ~ spl0_137
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2346,f2234,f1852,f2895]) ).
fof(f2895,plain,
( spl0_311
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f1852,plain,
( spl0_137
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f2234,plain,
( spl0_215
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f2346,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex)
| ~ spl0_137
| ~ spl0_215 ),
inference(resolution,[],[f2235,f1854]) ).
fof(f1854,plain,
( class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1852]) ).
fof(f2235,plain,
( ! [X0,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f2234]) ).
fof(f2893,plain,
spl0_310,
inference(avatar_split_clause,[],[f421,f2891]) ).
fof(f2891,plain,
( spl0_310
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f421,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).
fof(f2889,plain,
spl0_309,
inference(avatar_split_clause,[],[f420,f2887]) ).
fof(f2887,plain,
( spl0_309
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f420,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
fof(f2885,plain,
spl0_308,
inference(avatar_split_clause,[],[f419,f2883]) ).
fof(f2883,plain,
( spl0_308
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f419,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
fof(f2881,plain,
spl0_307,
inference(avatar_split_clause,[],[f416,f2879]) ).
fof(f2879,plain,
( spl0_307
<=> ! [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_307])]) ).
fof(f416,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/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__1__iff_1) ).
fof(f2877,plain,
spl0_306,
inference(avatar_split_clause,[],[f415,f2875]) ).
fof(f2875,plain,
( spl0_306
<=> ! [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_306])]) ).
fof(f415,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/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__1__iff_0) ).
fof(f2873,plain,
spl0_305,
inference(avatar_split_clause,[],[f287,f2871]) ).
fof(f2871,plain,
( spl0_305
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X5),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f287,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X5),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_1) ).
fof(f2869,plain,
spl0_304,
inference(avatar_split_clause,[],[f286,f2867]) ).
fof(f2867,plain,
( spl0_304
<=> ! [X5] :
( c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X5),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f286,axiom,
! [X5] :
( c_HOL_Oord__class_Oless(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X5),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_0) ).
fof(f2865,plain,
spl0_303,
inference(avatar_split_clause,[],[f284,f2863]) ).
fof(f2863,plain,
( spl0_303
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f284,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X2,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f2861,plain,
spl0_302,
inference(avatar_split_clause,[],[f256,f2859]) ).
fof(f256,axiom,
! [X8,X7] :
( X7 = X8
| ~ c_lessequals(X7,X8,tc_RealDef_Oreal)
| ~ c_lessequals(X8,X7,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f2857,plain,
spl0_301,
inference(avatar_split_clause,[],[f229,f2855]) ).
fof(f2855,plain,
( spl0_301
<=> ! [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_301])]) ).
fof(f229,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/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__0__iff_1) ).
fof(f2853,plain,
( spl0_300
| ~ spl0_106
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2345,f2234,f1697,f2851]) ).
fof(f2851,plain,
( spl0_300
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f1697,plain,
( spl0_106
<=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f2345,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,X0,tc_RealDef_Oreal)
| ~ spl0_106
| ~ spl0_215 ),
inference(resolution,[],[f2235,f1699]) ).
fof(f1699,plain,
( class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1697]) ).
fof(f2849,plain,
spl0_299,
inference(avatar_split_clause,[],[f228,f2847]) ).
fof(f2847,plain,
( spl0_299
<=> ! [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_299])]) ).
fof(f228,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/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__0__iff_0) ).
fof(f2845,plain,
spl0_298,
inference(avatar_split_clause,[],[f215,f2843]) ).
fof(f215,axiom,
! [X6,X5] :
( X5 = X6
| ~ c_lessequals(X5,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_2) ).
fof(f2841,plain,
spl0_297,
inference(avatar_split_clause,[],[f97,f2839]) ).
fof(f2839,plain,
( spl0_297
<=> ! [X5] :
( ~ c_lessequals(X5,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X5),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f97,axiom,
! [X5] :
( ~ c_lessequals(X5,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X5),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__1__iff_1) ).
fof(f2837,plain,
spl0_296,
inference(avatar_split_clause,[],[f96,f2835]) ).
fof(f2835,plain,
( spl0_296
<=> ! [X5] :
( c_lessequals(X5,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X5),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f96,axiom,
! [X5] :
( c_lessequals(X5,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X5),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__1__iff_0) ).
fof(f2833,plain,
spl0_295,
inference(avatar_split_clause,[],[f95,f2831]) ).
fof(f2831,plain,
( spl0_295
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f95,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
fof(f2829,plain,
spl0_294,
inference(avatar_split_clause,[],[f91,f2827]) ).
fof(f2827,plain,
( spl0_294
<=> ! [X18,X17] : c_HOL_Ominus__class_Ominus(X17,X18,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X17,c_HOL_Ouminus__class_Ouminus(X18,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f2825,plain,
spl0_293,
inference(avatar_split_clause,[],[f77,f2823]) ).
fof(f2823,plain,
( spl0_293
<=> ! [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_293])]) ).
fof(f77,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/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__0__iff_0) ).
fof(f2821,plain,
spl0_292,
inference(avatar_split_clause,[],[f76,f2819]) ).
fof(f2819,plain,
( spl0_292
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f76,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__zero_0) ).
fof(f2817,plain,
spl0_291,
inference(avatar_split_clause,[],[f68,f2815]) ).
fof(f2815,plain,
( spl0_291
<=> ! [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_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f68,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_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma__tan__total_0) ).
fof(f2813,plain,
spl0_290,
inference(avatar_split_clause,[],[f45,f2811]) ).
fof(f2811,plain,
( spl0_290
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f45,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X6,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
fof(f2809,plain,
( spl0_289
| ~ spl0_59
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2344,f2234,f1462,f2807]) ).
fof(f2807,plain,
( spl0_289
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f1462,plain,
( spl0_59
<=> class_OrderedGroup_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f2344,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint)
| ~ spl0_59
| ~ spl0_215 ),
inference(resolution,[],[f2235,f1464]) ).
fof(f1464,plain,
( class_OrderedGroup_Oab__group__add(tc_Int_Oint)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f1462]) ).
fof(f2805,plain,
spl0_288,
inference(avatar_split_clause,[],[f44,f2803]) ).
fof(f44,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f2801,plain,
spl0_287,
inference(avatar_split_clause,[],[f31,f2799]) ).
fof(f2799,plain,
( spl0_287
<=> ! [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_287])]) ).
fof(f31,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/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__1__iff_0) ).
fof(f2797,plain,
spl0_286,
inference(avatar_split_clause,[],[f30,f2795]) ).
fof(f2795,plain,
( spl0_286
<=> ! [X5] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f30,axiom,
! [X5] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__one_0) ).
fof(f2793,plain,
spl0_285,
inference(avatar_split_clause,[],[f26,f2791]) ).
fof(f2791,plain,
( spl0_285
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X5),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f26,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X5),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__1__iff_1) ).
fof(f2789,plain,
spl0_284,
inference(avatar_split_clause,[],[f25,f2787]) ).
fof(f2787,plain,
( spl0_284
<=> ! [X5] :
( c_HOL_Oord__class_Oless(X5,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X5),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f25,axiom,
! [X5] :
( c_HOL_Oord__class_Oless(X5,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X5),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__1__iff_0) ).
fof(f2785,plain,
spl0_283,
inference(avatar_split_clause,[],[f17,f2783]) ).
fof(f2783,plain,
( spl0_283
<=> ! [X5] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X5,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f17,axiom,
! [X5] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X5,tc_nat)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__Suc__mult__two__ex_1) ).
fof(f2772,plain,
( spl0_282
| ~ spl0_142
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2343,f2230,f1877,f2769]) ).
fof(f2769,plain,
( spl0_282
<=> 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_282])]) ).
fof(f1877,plain,
( spl0_142
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f2230,plain,
( spl0_214
<=> ! [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_214])]) ).
fof(f2343,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_214 ),
inference(resolution,[],[f2231,f1879]) ).
fof(f1879,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1877]) ).
fof(f2231,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_214 ),
inference(avatar_component_clause,[],[f2230]) ).
fof(f2678,plain,
( spl0_281
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2623,f2434,f2676]) ).
fof(f2676,plain,
( spl0_281
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f2434,plain,
( spl0_243
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X6,X0)
| c_lessequals(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2623,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_243 ),
inference(factoring,[],[f2435]) ).
fof(f2435,plain,
( ! [X0,X6,X5] :
( c_lessequals(X6,X5,X0)
| c_lessequals(X5,X6,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2434]) ).
fof(f2618,plain,
( spl0_280
| ~ spl0_86
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2340,f2226,f1597,f2615]) ).
fof(f2615,plain,
( spl0_280
<=> 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_280])]) ).
fof(f1597,plain,
( spl0_86
<=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f2226,plain,
( spl0_213
<=> ! [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_213])]) ).
fof(f2340,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_213 ),
inference(resolution,[],[f2227,f1599]) ).
fof(f1599,plain,
( class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal)
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f1597]) ).
fof(f2227,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_213 ),
inference(avatar_component_clause,[],[f2226]) ).
fof(f2587,plain,
spl0_279,
inference(avatar_split_clause,[],[f908,f2585]) ).
fof(f2585,plain,
( spl0_279
<=> ! [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_279])]) ).
fof(f908,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/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
fof(f2583,plain,
spl0_278,
inference(avatar_split_clause,[],[f905,f2581]) ).
fof(f905,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
fof(f2579,plain,
spl0_277,
inference(avatar_split_clause,[],[f890,f2577]) ).
fof(f2577,plain,
( spl0_277
<=> ! [X19,X10] :
( X10 = X19
| c_RealDef_Oreal(X19,tc_nat) != c_RealDef_Oreal(X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f890,axiom,
! [X10,X19] :
( X10 = X19
| c_RealDef_Oreal(X19,tc_nat) != c_RealDef_Oreal(X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__of__nat__inject_0) ).
fof(f2575,plain,
spl0_276,
inference(avatar_split_clause,[],[f832,f2573]) ).
fof(f2573,plain,
( spl0_276
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f832,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f2571,plain,
spl0_275,
inference(avatar_split_clause,[],[f830,f2569]) ).
fof(f2569,plain,
( spl0_275
<=> ! [X2,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f830,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
fof(f2567,plain,
( spl0_274
| ~ spl0_43
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2339,f2226,f1382,f2564]) ).
fof(f2564,plain,
( spl0_274
<=> 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_274])]) ).
fof(f1382,plain,
( spl0_43
<=> class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f2339,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_213 ),
inference(resolution,[],[f2227,f1384]) ).
fof(f1384,plain,
( class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f1382]) ).
fof(f2562,plain,
spl0_273,
inference(avatar_split_clause,[],[f828,f2560]) ).
fof(f2560,plain,
( spl0_273
<=> ! [X5,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f828,axiom,
! [X0,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
fof(f2558,plain,
spl0_272,
inference(avatar_split_clause,[],[f827,f2556]) ).
fof(f2556,plain,
( spl0_272
<=> ! [X5,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),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f827,axiom,
! [X0,X5] :
( ~ 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),X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
fof(f2554,plain,
spl0_271,
inference(avatar_split_clause,[],[f826,f2552]) ).
fof(f2552,plain,
( spl0_271
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f826,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f2550,plain,
spl0_270,
inference(avatar_split_clause,[],[f825,f2548]) ).
fof(f2548,plain,
( spl0_270
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f825,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f2546,plain,
spl0_269,
inference(avatar_split_clause,[],[f824,f2544]) ).
fof(f824,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f2542,plain,
spl0_268,
inference(avatar_split_clause,[],[f823,f2540]) ).
fof(f2540,plain,
( spl0_268
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f823,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f2538,plain,
spl0_267,
inference(avatar_split_clause,[],[f788,f2535]) ).
fof(f2535,plain,
( spl0_267
<=> 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_267])]) ).
fof(f788,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/sandbox2/benchmark/theBenchmark.p',cls_cos__two__le__zero_0) ).
fof(f2533,plain,
spl0_266,
inference(avatar_split_clause,[],[f787,f2530]) ).
fof(f2530,plain,
( spl0_266
<=> 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_266])]) ).
fof(f787,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/sandbox2/benchmark/theBenchmark.p',cls_cos__two__less__zero_0) ).
fof(f2528,plain,
spl0_265,
inference(avatar_split_clause,[],[f714,f2525]) ).
fof(f2525,plain,
( spl0_265
<=> 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_265])]) ).
fof(f714,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/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__two__gt__one_0) ).
fof(f2523,plain,
spl0_264,
inference(avatar_split_clause,[],[f708,f2521]) ).
fof(f708,axiom,
! [X5] : c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(X5,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(X5),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__periodic__pi_0) ).
fof(f2519,plain,
( spl0_263
| ~ spl0_142
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2338,f2222,f1877,f2517]) ).
fof(f2517,plain,
( spl0_263
<=> ! [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_263])]) ).
fof(f2222,plain,
( spl0_212
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f2338,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_142
| ~ spl0_212 ),
inference(resolution,[],[f2223,f1879]) ).
fof(f2223,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2222]) ).
fof(f2515,plain,
spl0_262,
inference(avatar_split_clause,[],[f674,f2513]) ).
fof(f2513,plain,
( spl0_262
<=> ! [X5] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X5,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f674,axiom,
! [X5] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X5,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__mult__two__ex_1) ).
fof(f2511,plain,
spl0_261,
inference(avatar_split_clause,[],[f558,f2508]) ).
fof(f2508,plain,
( spl0_261
<=> 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_261])]) ).
fof(f558,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/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__two__ge__zero_0) ).
fof(f2506,plain,
spl0_260,
inference(avatar_split_clause,[],[f557,f2503]) ).
fof(f2503,plain,
( spl0_260
<=> 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_260])]) ).
fof(f557,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/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__two__gt__zero_0) ).
fof(f2501,plain,
~ spl0_259,
inference(avatar_split_clause,[],[f533,f2498]) ).
fof(f2498,plain,
( spl0_259
<=> 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_259])]) ).
fof(f533,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_1) ).
fof(f2496,plain,
spl0_258,
inference(avatar_split_clause,[],[f523,f2494]) ).
fof(f2494,plain,
( spl0_258
<=> ! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f523,axiom,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__numeral__0_0) ).
fof(f2492,plain,
spl0_257,
inference(avatar_split_clause,[],[f522,f2490]) ).
fof(f2490,plain,
( spl0_257
<=> ! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f522,axiom,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__numeral__0__right_0) ).
fof(f2488,plain,
spl0_256,
inference(avatar_split_clause,[],[f434,f2486]) ).
fof(f2486,plain,
( spl0_256
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X5),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f434,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X5),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_1) ).
fof(f2484,plain,
spl0_255,
inference(avatar_split_clause,[],[f433,f2482]) ).
fof(f2482,plain,
( spl0_255
<=> ! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X5),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f433,axiom,
! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X5),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_0) ).
fof(f2480,plain,
spl0_254,
inference(avatar_split_clause,[],[f335,f2478]) ).
fof(f2478,plain,
( spl0_254
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f335,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f2476,plain,
spl0_253,
inference(avatar_split_clause,[],[f323,f2474]) ).
fof(f2474,plain,
( spl0_253
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f323,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
fof(f2472,plain,
( spl0_252
| ~ spl0_112
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2337,f2222,f1727,f2470]) ).
fof(f2470,plain,
( spl0_252
<=> ! [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_252])]) ).
fof(f2337,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_112
| ~ spl0_212 ),
inference(resolution,[],[f2223,f1729]) ).
fof(f2468,plain,
spl0_251,
inference(avatar_split_clause,[],[f314,f2466]) ).
fof(f314,axiom,
! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Int_Onumber__class_Onumber__of(c_Int_OMin,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_arith__simps_I31_J_0) ).
fof(f2464,plain,
spl0_250,
inference(avatar_split_clause,[],[f306,f2462]) ).
fof(f2462,plain,
( spl0_250
<=> ! [X5,X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f306,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
fof(f2460,plain,
spl0_249,
inference(avatar_split_clause,[],[f303,f2458]) ).
fof(f303,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X6,X5,X0)
| c_HOL_Oord__class_Oless(X5,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f2456,plain,
spl0_248,
inference(avatar_split_clause,[],[f302,f2454]) ).
fof(f302,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f2452,plain,
spl0_247,
inference(avatar_split_clause,[],[f259,f2450]) ).
fof(f2450,plain,
( spl0_247
<=> ! [X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f259,axiom,
! [X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X5)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__not__eq__zero_0) ).
fof(f2448,plain,
spl0_246,
inference(avatar_split_clause,[],[f236,f2446]) ).
fof(f2446,plain,
( spl0_246
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f236,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f2444,plain,
spl0_245,
inference(avatar_split_clause,[],[f151,f2442]) ).
fof(f2442,plain,
( spl0_245
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f151,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f2440,plain,
spl0_244,
inference(avatar_split_clause,[],[f150,f2438]) ).
fof(f2438,plain,
( spl0_244
<=> ! [X5,X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f150,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f2436,plain,
spl0_243,
inference(avatar_split_clause,[],[f148,f2434]) ).
fof(f148,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X6,X0)
| c_lessequals(X6,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f2432,plain,
spl0_242,
inference(avatar_split_clause,[],[f146,f2430]) ).
fof(f146,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f2428,plain,
( spl0_241
| ~ spl0_65
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2336,f2222,f1492,f2426]) ).
fof(f2426,plain,
( spl0_241
<=> ! [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_241])]) ).
fof(f2336,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_65
| ~ spl0_212 ),
inference(resolution,[],[f2223,f1494]) ).
fof(f2424,plain,
spl0_240,
inference(avatar_split_clause,[],[f70,f2422]) ).
fof(f2422,plain,
( spl0_240
<=> ! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X5),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f70,axiom,
! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X5),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_1) ).
fof(f2420,plain,
spl0_239,
inference(avatar_split_clause,[],[f69,f2418]) ).
fof(f2418,plain,
( spl0_239
<=> ! [X6,X5] :
( c_lessequals(X5,X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X5),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f69,axiom,
! [X6,X5] :
( c_lessequals(X5,X6,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X5),c_NthRoot_Osqrt(X6),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_0) ).
fof(f2416,plain,
spl0_238,
inference(avatar_split_clause,[],[f6,f2414]) ).
fof(f2414,plain,
( spl0_238
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_lessequals(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f6,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_lessequals(X5,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f2412,plain,
spl0_237,
inference(avatar_split_clause,[],[f4,f2410]) ).
fof(f2410,plain,
( spl0_237
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_lessequals(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f4,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_lessequals(X5,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f2324,plain,
spl0_236,
inference(avatar_split_clause,[],[f901,f2322]) ).
fof(f2322,plain,
( spl0_236
<=> ! [X7,X8] : c_HOL_Otimes__class_Otimes(X7,X8,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X8,X7,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f2320,plain,
~ spl0_235,
inference(avatar_split_clause,[],[f898,f2317]) ).
fof(f2317,plain,
( spl0_235
<=> 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_235])]) ).
fof(f898,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/sandbox2/benchmark/theBenchmark.p',cls_cos__two__neq__zero_0) ).
fof(f2315,plain,
spl0_234,
inference(avatar_split_clause,[],[f780,f2312]) ).
fof(f2312,plain,
( spl0_234
<=> 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_234])]) ).
fof(f780,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/sandbox2/benchmark/theBenchmark.p',cls_pi__less__4_0) ).
fof(f2310,plain,
spl0_233,
inference(avatar_split_clause,[],[f681,f2308]) ).
fof(f2308,plain,
( spl0_233
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f681,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).
fof(f2306,plain,
spl0_232,
inference(avatar_split_clause,[],[f678,f2304]) ).
fof(f2304,plain,
( spl0_232
<=> ! [X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X5
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f678,axiom,
! [X5] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X5
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__0__iff_0) ).
fof(f2302,plain,
( spl0_231
| ~ spl0_148
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2177,f2152,f1907,f2299]) ).
fof(f2299,plain,
( spl0_231
<=> 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_231])]) ).
fof(f1907,plain,
( spl0_148
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f2152,plain,
( spl0_200
<=> ! [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_200])]) ).
fof(f2177,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Complex_Ocomplex)
| ~ spl0_148
| ~ spl0_200 ),
inference(resolution,[],[f2153,f1909]) ).
fof(f1909,plain,
( class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1907]) ).
fof(f2153,plain,
( ! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X0) )
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f2152]) ).
fof(f2297,plain,
spl0_230,
inference(avatar_split_clause,[],[f635,f2295]) ).
fof(f2295,plain,
( spl0_230
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f635,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(f2293,plain,
spl0_229,
inference(avatar_split_clause,[],[f634,f2291]) ).
fof(f2291,plain,
( spl0_229
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f634,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
fof(f2289,plain,
spl0_228,
inference(avatar_split_clause,[],[f633,f2287]) ).
fof(f2287,plain,
( spl0_228
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f633,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
fof(f2285,plain,
spl0_227,
inference(avatar_split_clause,[],[f632,f2283]) ).
fof(f2283,plain,
( spl0_227
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f632,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
fof(f2281,plain,
spl0_226,
inference(avatar_split_clause,[],[f631,f2279]) ).
fof(f2279,plain,
( spl0_226
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f631,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
fof(f2277,plain,
spl0_225,
inference(avatar_split_clause,[],[f605,f2275]) ).
fof(f2275,plain,
( spl0_225
<=> ! [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_225])]) ).
fof(f605,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/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I110_J_0) ).
fof(f2273,plain,
spl0_224,
inference(avatar_split_clause,[],[f484,f2271]) ).
fof(f2271,plain,
( spl0_224
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f484,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f2269,plain,
spl0_223,
inference(avatar_split_clause,[],[f483,f2267]) ).
fof(f2267,plain,
( spl0_223
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f483,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f2265,plain,
spl0_222,
inference(avatar_split_clause,[],[f482,f2263]) ).
fof(f2263,plain,
( spl0_222
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f482,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f2261,plain,
spl0_221,
inference(avatar_split_clause,[],[f479,f2259]) ).
fof(f2259,plain,
( spl0_221
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f479,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f2257,plain,
( spl0_220
| ~ spl0_121
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2176,f2152,f1772,f2254]) ).
fof(f2254,plain,
( spl0_220
<=> 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_220])]) ).
fof(f2176,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_RealDef_Oreal)
| ~ spl0_121
| ~ spl0_200 ),
inference(resolution,[],[f2153,f1774]) ).
fof(f2252,plain,
spl0_219,
inference(avatar_split_clause,[],[f478,f2250]) ).
fof(f2250,plain,
( spl0_219
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f478,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f2248,plain,
spl0_218,
inference(avatar_split_clause,[],[f477,f2246]) ).
fof(f2246,plain,
( spl0_218
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f477,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f2244,plain,
spl0_217,
inference(avatar_split_clause,[],[f469,f2242]) ).
fof(f2242,plain,
( spl0_217
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f469,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
fof(f2240,plain,
spl0_216,
inference(avatar_split_clause,[],[f468,f2238]) ).
fof(f468,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f2236,plain,
spl0_215,
inference(avatar_split_clause,[],[f466,f2234]) ).
fof(f466,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f2232,plain,
spl0_214,
inference(avatar_split_clause,[],[f459,f2230]) ).
fof(f459,axiom,
! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
fof(f2228,plain,
spl0_213,
inference(avatar_split_clause,[],[f458,f2226]) ).
fof(f458,axiom,
! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
fof(f2224,plain,
spl0_212,
inference(avatar_split_clause,[],[f446,f2222]) ).
fof(f446,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
fof(f2220,plain,
spl0_211,
inference(avatar_split_clause,[],[f440,f2218]) ).
fof(f440,axiom,
! [X7,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X7,tc_RealDef_Oreal),X7,tc_RealDef_Oreal) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__eq_H_1) ).
fof(f2216,plain,
spl0_210,
inference(avatar_split_clause,[],[f422,f2214]) ).
fof(f2214,plain,
( spl0_210
<=> ! [X5] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f422,axiom,
! [X5] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__eq__0__iff_1) ).
fof(f2212,plain,
( spl0_209
| ~ spl0_72
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2175,f2152,f1527,f2209]) ).
fof(f2209,plain,
( spl0_209
<=> 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_209])]) ).
fof(f1527,plain,
( spl0_72
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f2175,plain,
( c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint)
| ~ spl0_72
| ~ spl0_200 ),
inference(resolution,[],[f2153,f1529]) ).
fof(f1529,plain,
( class_Int_Onumber__ring(tc_Int_Oint)
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f1527]) ).
fof(f2207,plain,
spl0_208,
inference(avatar_split_clause,[],[f289,f2205]) ).
fof(f2205,plain,
( spl0_208
<=> ! [X19,X10] : c_HOL_Otimes__class_Otimes(X10,X19,tc_nat) = c_HOL_Otimes__class_Otimes(X19,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f289,axiom,
! [X10,X19] : c_HOL_Otimes__class_Otimes(X10,X19,tc_nat) = c_HOL_Otimes__class_Otimes(X19,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f2203,plain,
spl0_207,
inference(avatar_split_clause,[],[f285,f2201]) ).
fof(f2201,plain,
( spl0_207
<=> ! [X6,X7] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X6,X7,tc_RealDef_Oreal),X7,tc_RealDef_Oreal) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f285,axiom,
! [X6,X7] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X6,X7,tc_RealDef_Oreal),X7,tc_RealDef_Oreal) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__eq_H_0) ).
fof(f2199,plain,
spl0_206,
inference(avatar_split_clause,[],[f272,f2197]) ).
fof(f2197,plain,
( spl0_206
<=> ! [X5] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X5
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f272,axiom,
! [X5] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X5
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__1__iff_0) ).
fof(f2195,plain,
spl0_205,
inference(avatar_split_clause,[],[f49,f2193]) ).
fof(f2193,plain,
( spl0_205
<=> ! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f49,axiom,
! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_2) ).
fof(f2191,plain,
spl0_204,
inference(avatar_split_clause,[],[f48,f2189]) ).
fof(f2189,plain,
( spl0_204
<=> ! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f48,axiom,
! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_1) ).
fof(f2187,plain,
spl0_203,
inference(avatar_split_clause,[],[f47,f2185]) ).
fof(f2185,plain,
( spl0_203
<=> ! [X5] : c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f47,axiom,
! [X5] : c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(X5),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__minus_0) ).
fof(f2162,plain,
spl0_202,
inference(avatar_split_clause,[],[f899,f2160]) ).
fof(f2160,plain,
( spl0_202
<=> ! [X20,X31] :
( X20 = X31
| c_Int_OBit1(X20) != c_Int_OBit1(X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f899,axiom,
! [X31,X20] :
( X20 = X31
| c_Int_OBit1(X20) != c_Int_OBit1(X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I51_J_0) ).
fof(f2158,plain,
spl0_201,
inference(avatar_split_clause,[],[f848,f2156]) ).
fof(f2156,plain,
( spl0_201
<=> ! [X20,X31] :
( X20 = X31
| c_Int_OBit0(X31) != c_Int_OBit0(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f848,axiom,
! [X31,X20] :
( X20 = X31
| c_Int_OBit0(X31) != c_Int_OBit0(X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I48_J_0) ).
fof(f2154,plain,
spl0_200,
inference(avatar_split_clause,[],[f815,f2152]) ).
fof(f815,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/sandbox2/benchmark/theBenchmark.p',cls_comp__arith_I112_J_0) ).
fof(f2150,plain,
spl0_199,
inference(avatar_split_clause,[],[f779,f2147]) ).
fof(f2147,plain,
( spl0_199
<=> 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_199])]) ).
fof(f779,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/sandbox2/benchmark/theBenchmark.p',cls_pi__ge__two_0) ).
fof(f2145,plain,
spl0_198,
inference(avatar_split_clause,[],[f701,f2143]) ).
fof(f2143,plain,
( spl0_198
<=> ! [X19] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(X19),tc_nat),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f701,axiom,
! [X19] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(X19),tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__of__nat__Suc__gt__zero_0) ).
fof(f2141,plain,
spl0_197,
inference(avatar_split_clause,[],[f225,f2139]) ).
fof(f2139,plain,
( spl0_197
<=> ! [X6,X5] :
( X5 = X6
| c_NthRoot_Osqrt(X5) != c_NthRoot_Osqrt(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f225,axiom,
! [X6,X5] :
( X5 = X6
| c_NthRoot_Osqrt(X5) != c_NthRoot_Osqrt(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__iff_0) ).
fof(f2137,plain,
spl0_196,
inference(avatar_split_clause,[],[f149,f2135]) ).
fof(f149,axiom,
! [X8,X7] :
( c_lessequals(X7,X8,tc_RealDef_Oreal)
| c_lessequals(X8,X7,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
fof(f2133,plain,
spl0_195,
inference(avatar_split_clause,[],[f42,f2131]) ).
fof(f2131,plain,
( spl0_195
<=> ! [X13,X12] :
( X12 = X13
| c_Suc(X12) != c_Suc(X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f42,axiom,
! [X12,X13] :
( X12 = X13
| c_Suc(X12) != c_Suc(X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
fof(f2129,plain,
spl0_194,
inference(avatar_split_clause,[],[f33,f2127]) ).
fof(f2127,plain,
( spl0_194
<=> ! [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_194])]) ).
fof(f33,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f2125,plain,
spl0_193,
inference(avatar_split_clause,[],[f29,f2123]) ).
fof(f2123,plain,
( spl0_193
<=> ! [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_193])]) ).
fof(f29,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f2121,plain,
spl0_192,
inference(avatar_split_clause,[],[f18,f2119]) ).
fof(f2119,plain,
( spl0_192
<=> ! [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_192])]) ).
fof(f18,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f2117,plain,
spl0_191,
inference(avatar_split_clause,[],[f12,f2115]) ).
fof(f2115,plain,
( spl0_191
<=> ! [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_191])]) ).
fof(f12,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f2113,plain,
spl0_190,
inference(avatar_split_clause,[],[f5,f2111]) ).
fof(f5,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_RealDef_Oreal)
| c_lessequals(X5,X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_0) ).
fof(f2104,plain,
( spl0_189
| ~ spl0_160
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f2044,f2039,f1965,f2101]) ).
fof(f2039,plain,
( spl0_176
<=> ! [X5] : c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Ocos(X5),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f2044,plain,
( c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_160
| ~ spl0_176 ),
inference(superposition,[],[f2040,f1967]) ).
fof(f2040,plain,
( ! [X5] : c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Ocos(X5),tc_RealDef_Oreal)
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f2039]) ).
fof(f2099,plain,
spl0_188,
inference(avatar_split_clause,[],[f897,f2097]) ).
fof(f2097,plain,
( spl0_188
<=> ! [X31] :
( c_Int_OPls = X31
| c_Int_OPls != c_Int_OBit0(X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f897,axiom,
! [X31] :
( c_Int_OPls = X31
| c_Int_OPls != c_Int_OBit0(X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I38_J_0) ).
fof(f2095,plain,
spl0_187,
inference(avatar_split_clause,[],[f709,f2093]) ).
fof(f2093,plain,
( spl0_187
<=> ! [X5] : c_Transcendental_Ocos(X5) = c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(X5,tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f2091,plain,
spl0_186,
inference(avatar_split_clause,[],[f698,f2089]) ).
fof(f2089,plain,
( spl0_186
<=> ! [X7] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X7,tc_RealDef_Oreal) = X7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f698,axiom,
! [X7] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X7,tc_RealDef_Oreal) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__1_0) ).
fof(f2087,plain,
spl0_185,
inference(avatar_split_clause,[],[f669,f2085]) ).
fof(f2085,plain,
( spl0_185
<=> ! [X20] :
( c_Int_OMin = X20
| c_Int_OMin != c_Int_OBit1(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f669,axiom,
! [X20] :
( c_Int_OMin = X20
| c_Int_OMin != c_Int_OBit1(X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I47_J_0) ).
fof(f2083,plain,
spl0_184,
inference(avatar_split_clause,[],[f548,f2081]) ).
fof(f2081,plain,
( spl0_184
<=> ! [X19] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X19,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f548,axiom,
! [X19] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X19,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__of__nat__less__zero_0) ).
fof(f2079,plain,
spl0_183,
inference(avatar_split_clause,[],[f547,f2077]) ).
fof(f2077,plain,
( spl0_183
<=> ! [X19] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X19,tc_nat),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f547,axiom,
! [X19] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X19,tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__of__nat__ge__zero_0) ).
fof(f2075,plain,
spl0_182,
inference(avatar_split_clause,[],[f464,f2073]) ).
fof(f2073,plain,
( spl0_182
<=> ! [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_182])]) ).
fof(f464,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f2071,plain,
spl0_181,
inference(avatar_split_clause,[],[f432,f2069]) ).
fof(f2069,plain,
( spl0_181
<=> ! [X5] :
( c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f432,axiom,
! [X5] :
( c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__Suc_1) ).
fof(f2067,plain,
spl0_180,
inference(avatar_split_clause,[],[f431,f2065]) ).
fof(f2065,plain,
( spl0_180
<=> ! [X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f431,axiom,
! [X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__Suc_0) ).
fof(f2061,plain,
( spl0_179
| ~ spl0_160
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f2042,f2020,f1965,f2058]) ).
fof(f2020,plain,
( spl0_172
<=> ! [X5] : c_lessequals(c_Transcendental_Ocos(X5),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f2042,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_160
| ~ spl0_172 ),
inference(superposition,[],[f2021,f1967]) ).
fof(f2021,plain,
( ! [X5] : c_lessequals(c_Transcendental_Ocos(X5),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f2020]) ).
fof(f2056,plain,
( spl0_178
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f2051,f2047,f2053]) ).
fof(f2047,plain,
( spl0_177
<=> 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_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_177])]) ).
fof(f2051,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_177 ),
inference(forward_demodulation,[],[f2049,f901]) ).
fof(f2049,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_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_177 ),
inference(avatar_component_clause,[],[f2047]) ).
fof(f2050,plain,
spl0_177,
inference(avatar_split_clause,[],[f1068,f2047]) ).
fof(f1068,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_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,[],[f916,f807]) ).
fof(f916,axiom,
c_HOL_Ozero__class_Ozero(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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f2041,plain,
spl0_176,
inference(avatar_split_clause,[],[f1137,f2039]) ).
fof(f1137,plain,
! [X5] : c_lessequals(c_Transcendental_Ocos(c_Transcendental_Opi),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f706,f716]) ).
fof(f716,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_RealDef_Oreal) = c_Transcendental_Ocos(c_Transcendental_Opi),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__pi_0) ).
fof(f706,axiom,
! [X5] : c_lessequals(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_RealDef_Oreal),c_Transcendental_Ocos(X5),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__ge__minus__one_0) ).
fof(f2037,plain,
spl0_175,
inference(avatar_split_clause,[],[f716,f2034]) ).
fof(f2032,plain,
spl0_174,
inference(avatar_split_clause,[],[f680,f2029]) ).
fof(f2029,plain,
( spl0_174
<=> 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_174])]) ).
fof(f680,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__zero_0) ).
fof(f2027,plain,
spl0_173,
inference(avatar_split_clause,[],[f553,f2024]) ).
fof(f2024,plain,
( spl0_173
<=> 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_173])]) ).
fof(f2022,plain,
spl0_172,
inference(avatar_split_clause,[],[f231,f2020]) ).
fof(f231,axiom,
! [X5] : c_lessequals(c_Transcendental_Ocos(X5),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__le__one_0) ).
fof(f2018,plain,
spl0_171,
inference(avatar_split_clause,[],[f126,f2016]) ).
fof(f2016,plain,
( spl0_171
<=> ! [X5,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f126,axiom,
! [X0,X5] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X5,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f2014,plain,
spl0_170,
inference(avatar_split_clause,[],[f125,f2012]) ).
fof(f2012,plain,
( spl0_170
<=> ! [X5,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f125,axiom,
! [X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X5,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f2010,plain,
spl0_169,
inference(avatar_split_clause,[],[f115,f2007]) ).
fof(f115,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__one_0) ).
fof(f2005,plain,
spl0_168,
inference(avatar_split_clause,[],[f24,f2003]) ).
fof(f2003,plain,
( spl0_168
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f24,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f2001,plain,
spl0_167,
inference(avatar_split_clause,[],[f23,f1999]) ).
fof(f1999,plain,
( spl0_167
<=> ! [X5,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f23,axiom,
! [X0,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1997,plain,
spl0_166,
inference(avatar_split_clause,[],[f21,f1995]) ).
fof(f1995,plain,
( spl0_166
<=> ! [X5,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f21,axiom,
! [X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1992,plain,
spl0_165,
inference(avatar_split_clause,[],[f858,f1990]) ).
fof(f1990,plain,
( spl0_165
<=> ! [X20,X31] : c_Int_OBit1(X20) != c_Int_OBit0(X31) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f858,axiom,
! [X31,X20] : c_Int_OBit1(X20) != c_Int_OBit0(X31),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I50_J_0) ).
fof(f1988,plain,
~ spl0_164,
inference(avatar_split_clause,[],[f679,f1985]) ).
fof(f679,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
fof(f1983,plain,
spl0_163,
inference(avatar_split_clause,[],[f552,f1980]) ).
fof(f1980,plain,
( spl0_163
<=> 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_163])]) ).
fof(f552,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__gt__zero_0) ).
fof(f1978,plain,
spl0_162,
inference(avatar_split_clause,[],[f551,f1975]) ).
fof(f551,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__ge__zero_0) ).
fof(f1973,plain,
~ spl0_161,
inference(avatar_split_clause,[],[f549,f1970]) ).
fof(f1970,plain,
( spl0_161
<=> 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_161])]) ).
fof(f549,axiom,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__not__less__zero_0) ).
fof(f1968,plain,
( spl0_160
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1963,f1959,f1965]) ).
fof(f1959,plain,
( spl0_159
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = 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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1963,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_159 ),
inference(forward_demodulation,[],[f1961,f901]) ).
fof(f1961,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = 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))
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1959]) ).
fof(f1962,plain,
spl0_159,
inference(avatar_split_clause,[],[f915,f1959]) ).
fof(f915,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = 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)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1955,plain,
~ spl0_158,
inference(avatar_split_clause,[],[f851,f1952]) ).
fof(f851,axiom,
c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__neq__zero_0) ).
fof(f1950,plain,
spl0_157,
inference(avatar_split_clause,[],[f843,f1948]) ).
fof(f1948,plain,
( spl0_157
<=> ! [X31] : c_Int_OPls != c_Int_OBit1(X31) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f843,axiom,
! [X31] : c_Int_OPls != c_Int_OBit1(X31),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I39_J_0) ).
fof(f1946,plain,
spl0_156,
inference(avatar_split_clause,[],[f819,f1943]) ).
fof(f1943,plain,
( spl0_156
<=> c_Int_OPls = c_Int_OBit0(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f819,axiom,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Bit0__Pls_0) ).
fof(f1941,plain,
spl0_155,
inference(avatar_split_clause,[],[f676,f1939]) ).
fof(f1939,plain,
( spl0_155
<=> ! [X20] : c_Int_OMin != c_Int_OBit0(X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f676,axiom,
! [X20] : c_Int_OMin != c_Int_OBit0(X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I45_J_0) ).
fof(f1937,plain,
spl0_154,
inference(avatar_split_clause,[],[f671,f1934]) ).
fof(f1934,plain,
( spl0_154
<=> c_Int_OMin = c_Int_OBit1(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f671,axiom,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I43_J_1) ).
fof(f1932,plain,
spl0_153,
inference(avatar_split_clause,[],[f224,f1930]) ).
fof(f1930,plain,
( spl0_153
<=> ! [X19] : c_Suc(X19) != X19 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f224,axiom,
! [X19] : c_Suc(X19) != X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
fof(f1928,plain,
spl0_152,
inference(avatar_split_clause,[],[f128,f1926]) ).
fof(f128,axiom,
! [X8] : c_lessequals(X8,X8,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
fof(f1924,plain,
spl0_151,
inference(avatar_split_clause,[],[f22,f1922]) ).
fof(f1922,plain,
( spl0_151
<=> ! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f22,axiom,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_1) ).
fof(f1920,plain,
~ spl0_150,
inference(avatar_split_clause,[],[f673,f1917]) ).
fof(f1917,plain,
( spl0_150
<=> c_Int_OPls = c_Int_OMin ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f673,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__simps_I40_J_0) ).
fof(f1915,plain,
spl0_149,
inference(avatar_split_clause,[],[f1065,f1912]) ).
fof(f1912,plain,
( spl0_149
<=> class_Int_Onumber(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1065,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).
fof(f1910,plain,
spl0_148,
inference(avatar_split_clause,[],[f1064,f1907]) ).
fof(f1064,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f1905,plain,
spl0_147,
inference(avatar_split_clause,[],[f1063,f1902]) ).
fof(f1902,plain,
( spl0_147
<=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1063,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(f1900,plain,
spl0_146,
inference(avatar_split_clause,[],[f1062,f1897]) ).
fof(f1897,plain,
( spl0_146
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1062,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f1895,plain,
spl0_145,
inference(avatar_split_clause,[],[f1061,f1892]) ).
fof(f1892,plain,
( spl0_145
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1061,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(f1890,plain,
spl0_144,
inference(avatar_split_clause,[],[f1060,f1887]) ).
fof(f1887,plain,
( spl0_144
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1060,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f1885,plain,
spl0_143,
inference(avatar_split_clause,[],[f1059,f1882]) ).
fof(f1882,plain,
( spl0_143
<=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1059,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(f1880,plain,
spl0_142,
inference(avatar_split_clause,[],[f1058,f1877]) ).
fof(f1058,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(f1875,plain,
spl0_141,
inference(avatar_split_clause,[],[f1057,f1872]) ).
fof(f1872,plain,
( spl0_141
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1057,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(f1870,plain,
spl0_140,
inference(avatar_split_clause,[],[f1056,f1867]) ).
fof(f1867,plain,
( spl0_140
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1056,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(f1865,plain,
spl0_139,
inference(avatar_split_clause,[],[f1055,f1862]) ).
fof(f1862,plain,
( spl0_139
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1055,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f1860,plain,
spl0_138,
inference(avatar_split_clause,[],[f1054,f1857]) ).
fof(f1857,plain,
( spl0_138
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1054,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
fof(f1855,plain,
spl0_137,
inference(avatar_split_clause,[],[f1053,f1852]) ).
fof(f1053,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f1850,plain,
spl0_136,
inference(avatar_split_clause,[],[f1052,f1847]) ).
fof(f1847,plain,
( spl0_136
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1052,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
fof(f1845,plain,
spl0_135,
inference(avatar_split_clause,[],[f1051,f1842]) ).
fof(f1842,plain,
( spl0_135
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1051,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f1840,plain,
spl0_134,
inference(avatar_split_clause,[],[f1050,f1837]) ).
fof(f1837,plain,
( spl0_134
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1050,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f1835,plain,
spl0_133,
inference(avatar_split_clause,[],[f1049,f1832]) ).
fof(f1832,plain,
( spl0_133
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1049,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
fof(f1830,plain,
spl0_132,
inference(avatar_split_clause,[],[f1048,f1827]) ).
fof(f1827,plain,
( spl0_132
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1048,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(f1825,plain,
spl0_131,
inference(avatar_split_clause,[],[f1047,f1822]) ).
fof(f1822,plain,
( spl0_131
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1047,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1820,plain,
spl0_130,
inference(avatar_split_clause,[],[f1046,f1817]) ).
fof(f1817,plain,
( spl0_130
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1046,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f1815,plain,
spl0_129,
inference(avatar_split_clause,[],[f1045,f1812]) ).
fof(f1812,plain,
( spl0_129
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1045,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1810,plain,
spl0_128,
inference(avatar_split_clause,[],[f1044,f1807]) ).
fof(f1807,plain,
( spl0_128
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1044,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1805,plain,
spl0_127,
inference(avatar_split_clause,[],[f1043,f1802]) ).
fof(f1802,plain,
( spl0_127
<=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1043,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
fof(f1800,plain,
spl0_126,
inference(avatar_split_clause,[],[f1042,f1797]) ).
fof(f1797,plain,
( spl0_126
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1042,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
fof(f1795,plain,
spl0_125,
inference(avatar_split_clause,[],[f1041,f1792]) ).
fof(f1792,plain,
( spl0_125
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1041,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1790,plain,
spl0_124,
inference(avatar_split_clause,[],[f1040,f1787]) ).
fof(f1787,plain,
( spl0_124
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1040,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1785,plain,
spl0_123,
inference(avatar_split_clause,[],[f1039,f1782]) ).
fof(f1782,plain,
( spl0_123
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1039,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1780,plain,
spl0_122,
inference(avatar_split_clause,[],[f1038,f1777]) ).
fof(f1777,plain,
( spl0_122
<=> class_Int_Onumber(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1038,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber) ).
fof(f1775,plain,
spl0_121,
inference(avatar_split_clause,[],[f1037,f1772]) ).
fof(f1037,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f1770,plain,
spl0_120,
inference(avatar_split_clause,[],[f1036,f1767]) ).
fof(f1767,plain,
( spl0_120
<=> class_Int_Oring__char__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1036,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Oring__char__0) ).
fof(f1765,plain,
spl0_119,
inference(avatar_split_clause,[],[f1035,f1762]) ).
fof(f1035,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
fof(f1760,plain,
spl0_118,
inference(avatar_split_clause,[],[f1034,f1757]) ).
fof(f1034,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f1755,plain,
spl0_117,
inference(avatar_split_clause,[],[f1033,f1752]) ).
fof(f1033,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f1750,plain,
spl0_116,
inference(avatar_split_clause,[],[f1032,f1747]) ).
fof(f1747,plain,
( spl0_116
<=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1032,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
fof(f1745,plain,
spl0_115,
inference(avatar_split_clause,[],[f1031,f1742]) ).
fof(f1742,plain,
( spl0_115
<=> class_Ring__and__Field_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1031,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
fof(f1740,plain,
spl0_114,
inference(avatar_split_clause,[],[f1030,f1737]) ).
fof(f1030,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
fof(f1735,plain,
spl0_113,
inference(avatar_split_clause,[],[f1029,f1732]) ).
fof(f1732,plain,
( spl0_113
<=> class_RealVector_Oreal__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1029,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__field) ).
fof(f1730,plain,
spl0_112,
inference(avatar_split_clause,[],[f1028,f1727]) ).
fof(f1028,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f1725,plain,
spl0_111,
inference(avatar_split_clause,[],[f1027,f1722]) ).
fof(f1722,plain,
( spl0_111
<=> class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1027,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
fof(f1720,plain,
spl0_110,
inference(avatar_split_clause,[],[f1026,f1717]) ).
fof(f1717,plain,
( spl0_110
<=> class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1026,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
fof(f1715,plain,
spl0_109,
inference(avatar_split_clause,[],[f1025,f1712]) ).
fof(f1712,plain,
( spl0_109
<=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1025,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
fof(f1710,plain,
spl0_108,
inference(avatar_split_clause,[],[f1024,f1707]) ).
fof(f1707,plain,
( spl0_108
<=> class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1024,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) ).
fof(f1705,plain,
spl0_107,
inference(avatar_split_clause,[],[f1023,f1702]) ).
fof(f1702,plain,
( spl0_107
<=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1023,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
fof(f1700,plain,
spl0_106,
inference(avatar_split_clause,[],[f1022,f1697]) ).
fof(f1022,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
fof(f1695,plain,
spl0_105,
inference(avatar_split_clause,[],[f1021,f1692]) ).
fof(f1692,plain,
( spl0_105
<=> class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1021,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).
fof(f1690,plain,
spl0_104,
inference(avatar_split_clause,[],[f1020,f1687]) ).
fof(f1687,plain,
( spl0_104
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1020,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
fof(f1685,plain,
spl0_103,
inference(avatar_split_clause,[],[f1019,f1682]) ).
fof(f1682,plain,
( spl0_103
<=> class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1019,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).
fof(f1680,plain,
spl0_102,
inference(avatar_split_clause,[],[f1018,f1677]) ).
fof(f1018,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
fof(f1675,plain,
spl0_101,
inference(avatar_split_clause,[],[f1017,f1672]) ).
fof(f1672,plain,
( spl0_101
<=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1017,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(f1670,plain,
spl0_100,
inference(avatar_split_clause,[],[f1016,f1667]) ).
fof(f1667,plain,
( spl0_100
<=> class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1016,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
fof(f1665,plain,
spl0_99,
inference(avatar_split_clause,[],[f1015,f1662]) ).
fof(f1662,plain,
( spl0_99
<=> class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1015,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
fof(f1660,plain,
spl0_98,
inference(avatar_split_clause,[],[f1014,f1657]) ).
fof(f1657,plain,
( spl0_98
<=> class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1014,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) ).
fof(f1655,plain,
spl0_97,
inference(avatar_split_clause,[],[f1013,f1652]) ).
fof(f1652,plain,
( spl0_97
<=> class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1013,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
fof(f1650,plain,
spl0_96,
inference(avatar_split_clause,[],[f1012,f1647]) ).
fof(f1647,plain,
( spl0_96
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1012,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1645,plain,
spl0_95,
inference(avatar_split_clause,[],[f1011,f1642]) ).
fof(f1642,plain,
( spl0_95
<=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1011,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
fof(f1640,plain,
spl0_94,
inference(avatar_split_clause,[],[f1010,f1637]) ).
fof(f1637,plain,
( spl0_94
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1010,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f1635,plain,
spl0_93,
inference(avatar_split_clause,[],[f1009,f1632]) ).
fof(f1009,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1630,plain,
spl0_92,
inference(avatar_split_clause,[],[f1008,f1627]) ).
fof(f1627,plain,
( spl0_92
<=> class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1008,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
fof(f1625,plain,
spl0_91,
inference(avatar_split_clause,[],[f1007,f1622]) ).
fof(f1622,plain,
( spl0_91
<=> class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1007,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
fof(f1620,plain,
spl0_90,
inference(avatar_split_clause,[],[f1006,f1617]) ).
fof(f1617,plain,
( spl0_90
<=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1006,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).
fof(f1615,plain,
spl0_89,
inference(avatar_split_clause,[],[f1005,f1612]) ).
fof(f1612,plain,
( spl0_89
<=> class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1005,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).
fof(f1610,plain,
spl0_88,
inference(avatar_split_clause,[],[f1004,f1607]) ).
fof(f1607,plain,
( spl0_88
<=> class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1004,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) ).
fof(f1605,plain,
spl0_87,
inference(avatar_split_clause,[],[f1003,f1602]) ).
fof(f1602,plain,
( spl0_87
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1003,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1600,plain,
spl0_86,
inference(avatar_split_clause,[],[f1002,f1597]) ).
fof(f1002,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
fof(f1595,plain,
spl0_85,
inference(avatar_split_clause,[],[f1001,f1592]) ).
fof(f1592,plain,
( spl0_85
<=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1001,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
fof(f1590,plain,
spl0_84,
inference(avatar_split_clause,[],[f1000,f1587]) ).
fof(f1587,plain,
( spl0_84
<=> class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1000,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
fof(f1585,plain,
spl0_83,
inference(avatar_split_clause,[],[f999,f1582]) ).
fof(f1582,plain,
( spl0_83
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f999,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
fof(f1580,plain,
spl0_82,
inference(avatar_split_clause,[],[f998,f1577]) ).
fof(f1577,plain,
( spl0_82
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f998,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1575,plain,
spl0_81,
inference(avatar_split_clause,[],[f997,f1572]) ).
fof(f997,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1570,plain,
spl0_80,
inference(avatar_split_clause,[],[f996,f1567]) ).
fof(f1567,plain,
( spl0_80
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f996,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1565,plain,
spl0_79,
inference(avatar_split_clause,[],[f995,f1562]) ).
fof(f1562,plain,
( spl0_79
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f995,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1560,plain,
spl0_78,
inference(avatar_split_clause,[],[f994,f1557]) ).
fof(f1557,plain,
( spl0_78
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f994,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1555,plain,
spl0_77,
inference(avatar_split_clause,[],[f993,f1552]) ).
fof(f1552,plain,
( spl0_77
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f993,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1550,plain,
spl0_76,
inference(avatar_split_clause,[],[f992,f1547]) ).
fof(f1547,plain,
( spl0_76
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f992,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1545,plain,
spl0_75,
inference(avatar_split_clause,[],[f991,f1542]) ).
fof(f1542,plain,
( spl0_75
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f991,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1540,plain,
spl0_74,
inference(avatar_split_clause,[],[f990,f1537]) ).
fof(f1537,plain,
( spl0_74
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f990,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1535,plain,
spl0_73,
inference(avatar_split_clause,[],[f989,f1532]) ).
fof(f1532,plain,
( spl0_73
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f989,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
fof(f1530,plain,
spl0_72,
inference(avatar_split_clause,[],[f988,f1527]) ).
fof(f988,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
fof(f1525,plain,
spl0_71,
inference(avatar_split_clause,[],[f987,f1522]) ).
fof(f1522,plain,
( spl0_71
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f987,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
fof(f1520,plain,
spl0_70,
inference(avatar_split_clause,[],[f986,f1517]) ).
fof(f1517,plain,
( spl0_70
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f986,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
fof(f1515,plain,
spl0_69,
inference(avatar_split_clause,[],[f985,f1512]) ).
fof(f1512,plain,
( spl0_69
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f985,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
fof(f1510,plain,
spl0_68,
inference(avatar_split_clause,[],[f984,f1507]) ).
fof(f1507,plain,
( spl0_68
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f984,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
fof(f1505,plain,
spl0_67,
inference(avatar_split_clause,[],[f983,f1502]) ).
fof(f1502,plain,
( spl0_67
<=> class_Ring__and__Field_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f983,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
fof(f1500,plain,
spl0_66,
inference(avatar_split_clause,[],[f982,f1497]) ).
fof(f1497,plain,
( spl0_66
<=> class_Ring__and__Field_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f982,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).
fof(f1495,plain,
spl0_65,
inference(avatar_split_clause,[],[f981,f1492]) ).
fof(f981,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
fof(f1490,plain,
spl0_64,
inference(avatar_split_clause,[],[f980,f1487]) ).
fof(f1487,plain,
( spl0_64
<=> class_OrderedGroup_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f980,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
fof(f1485,plain,
spl0_63,
inference(avatar_split_clause,[],[f979,f1482]) ).
fof(f1482,plain,
( spl0_63
<=> class_Ring__and__Field_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f979,axiom,
class_Ring__and__Field_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).
fof(f1480,plain,
spl0_62,
inference(avatar_split_clause,[],[f978,f1477]) ).
fof(f1477,plain,
( spl0_62
<=> class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f978,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
fof(f1475,plain,
spl0_61,
inference(avatar_split_clause,[],[f977,f1472]) ).
fof(f1472,plain,
( spl0_61
<=> class_Ring__and__Field_Omult__mono(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f977,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).
fof(f1470,plain,
spl0_60,
inference(avatar_split_clause,[],[f976,f1467]) ).
fof(f1467,plain,
( spl0_60
<=> class_Ring__and__Field_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f976,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
fof(f1465,plain,
spl0_59,
inference(avatar_split_clause,[],[f975,f1462]) ).
fof(f975,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
fof(f1460,plain,
spl0_58,
inference(avatar_split_clause,[],[f974,f1457]) ).
fof(f1457,plain,
( spl0_58
<=> class_Ring__and__Field_Omult__mono1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f974,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).
fof(f1455,plain,
spl0_57,
inference(avatar_split_clause,[],[f973,f1452]) ).
fof(f1452,plain,
( spl0_57
<=> class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f973,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
fof(f1450,plain,
spl0_56,
inference(avatar_split_clause,[],[f972,f1447]) ).
fof(f1447,plain,
( spl0_56
<=> class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f972,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
fof(f1445,plain,
spl0_55,
inference(avatar_split_clause,[],[f971,f1442]) ).
fof(f1442,plain,
( spl0_55
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f971,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
fof(f1440,plain,
spl0_54,
inference(avatar_split_clause,[],[f970,f1437]) ).
fof(f1437,plain,
( spl0_54
<=> class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f970,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) ).
fof(f1435,plain,
spl0_53,
inference(avatar_split_clause,[],[f969,f1432]) ).
fof(f1432,plain,
( spl0_53
<=> class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f969,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).
fof(f1430,plain,
spl0_52,
inference(avatar_split_clause,[],[f968,f1427]) ).
fof(f1427,plain,
( spl0_52
<=> class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f968,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
fof(f1425,plain,
spl0_51,
inference(avatar_split_clause,[],[f967,f1422]) ).
fof(f1422,plain,
( spl0_51
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f967,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1420,plain,
spl0_50,
inference(avatar_split_clause,[],[f966,f1417]) ).
fof(f1417,plain,
( spl0_50
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f966,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).
fof(f1415,plain,
spl0_49,
inference(avatar_split_clause,[],[f965,f1412]) ).
fof(f1412,plain,
( spl0_49
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f965,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1410,plain,
spl0_48,
inference(avatar_split_clause,[],[f964,f1407]) ).
fof(f1407,plain,
( spl0_48
<=> class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f964,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
fof(f1405,plain,
spl0_47,
inference(avatar_split_clause,[],[f963,f1402]) ).
fof(f1402,plain,
( spl0_47
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f963,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
fof(f1400,plain,
spl0_46,
inference(avatar_split_clause,[],[f962,f1397]) ).
fof(f1397,plain,
( spl0_46
<=> class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f962,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).
fof(f1395,plain,
spl0_45,
inference(avatar_split_clause,[],[f961,f1392]) ).
fof(f1392,plain,
( spl0_45
<=> class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f961,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).
fof(f1390,plain,
spl0_44,
inference(avatar_split_clause,[],[f960,f1387]) ).
fof(f1387,plain,
( spl0_44
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f960,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1385,plain,
spl0_43,
inference(avatar_split_clause,[],[f959,f1382]) ).
fof(f959,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) ).
fof(f1380,plain,
spl0_42,
inference(avatar_split_clause,[],[f958,f1377]) ).
fof(f1377,plain,
( spl0_42
<=> class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f958,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
fof(f1375,plain,
spl0_41,
inference(avatar_split_clause,[],[f957,f1372]) ).
fof(f1372,plain,
( spl0_41
<=> class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f957,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
fof(f1370,plain,
spl0_40,
inference(avatar_split_clause,[],[f956,f1367]) ).
fof(f1367,plain,
( spl0_40
<=> class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f956,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).
fof(f1365,plain,
spl0_39,
inference(avatar_split_clause,[],[f955,f1362]) ).
fof(f1362,plain,
( spl0_39
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f955,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1360,plain,
spl0_38,
inference(avatar_split_clause,[],[f954,f1357]) ).
fof(f1357,plain,
( spl0_38
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f954,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1355,plain,
spl0_37,
inference(avatar_split_clause,[],[f953,f1352]) ).
fof(f1352,plain,
( spl0_37
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f953,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1350,plain,
spl0_36,
inference(avatar_split_clause,[],[f952,f1347]) ).
fof(f1347,plain,
( spl0_36
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f952,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1345,plain,
spl0_35,
inference(avatar_split_clause,[],[f951,f1342]) ).
fof(f1342,plain,
( spl0_35
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f951,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1340,plain,
spl0_34,
inference(avatar_split_clause,[],[f950,f1337]) ).
fof(f1337,plain,
( spl0_34
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f950,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1335,plain,
spl0_33,
inference(avatar_split_clause,[],[f949,f1332]) ).
fof(f1332,plain,
( spl0_33
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f949,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1330,plain,
spl0_32,
inference(avatar_split_clause,[],[f948,f1327]) ).
fof(f1327,plain,
( spl0_32
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f948,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1325,plain,
spl0_31,
inference(avatar_split_clause,[],[f947,f1322]) ).
fof(f1322,plain,
( spl0_31
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f947,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1320,plain,
spl0_30,
inference(avatar_split_clause,[],[f946,f1317]) ).
fof(f1317,plain,
( spl0_30
<=> class_Int_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f946,axiom,
class_Int_Onumber(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
fof(f1315,plain,
spl0_29,
inference(avatar_split_clause,[],[f945,f1312]) ).
fof(f1312,plain,
( spl0_29
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f945,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1310,plain,
spl0_28,
inference(avatar_split_clause,[],[f944,f1307]) ).
fof(f1307,plain,
( spl0_28
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f944,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1305,plain,
spl0_27,
inference(avatar_split_clause,[],[f943,f1302]) ).
fof(f1302,plain,
( spl0_27
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f943,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1300,plain,
spl0_26,
inference(avatar_split_clause,[],[f942,f1297]) ).
fof(f1297,plain,
( spl0_26
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f942,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f1295,plain,
spl0_25,
inference(avatar_split_clause,[],[f941,f1292]) ).
fof(f1292,plain,
( spl0_25
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f941,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f1290,plain,
spl0_24,
inference(avatar_split_clause,[],[f940,f1287]) ).
fof(f1287,plain,
( spl0_24
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f940,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f1285,plain,
spl0_23,
inference(avatar_split_clause,[],[f939,f1282]) ).
fof(f1282,plain,
( spl0_23
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f939,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f1280,plain,
spl0_22,
inference(avatar_split_clause,[],[f938,f1277]) ).
fof(f1277,plain,
( spl0_22
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f938,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f1275,plain,
spl0_21,
inference(avatar_split_clause,[],[f937,f1272]) ).
fof(f1272,plain,
( spl0_21
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f937,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f1270,plain,
spl0_20,
inference(avatar_split_clause,[],[f936,f1267]) ).
fof(f1267,plain,
( spl0_20
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f936,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f1265,plain,
spl0_19,
inference(avatar_split_clause,[],[f935,f1262]) ).
fof(f1262,plain,
( spl0_19
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f935,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1260,plain,
spl0_18,
inference(avatar_split_clause,[],[f934,f1257]) ).
fof(f1257,plain,
( spl0_18
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f934,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f1255,plain,
spl0_17,
inference(avatar_split_clause,[],[f933,f1252]) ).
fof(f1252,plain,
( spl0_17
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f933,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1250,plain,
spl0_16,
inference(avatar_split_clause,[],[f932,f1247]) ).
fof(f1247,plain,
( spl0_16
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f932,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1245,plain,
spl0_15,
inference(avatar_split_clause,[],[f931,f1242]) ).
fof(f1242,plain,
( spl0_15
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f931,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f1240,plain,
spl0_14,
inference(avatar_split_clause,[],[f930,f1237]) ).
fof(f1237,plain,
( spl0_14
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f930,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1235,plain,
spl0_13,
inference(avatar_split_clause,[],[f929,f1232]) ).
fof(f1232,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f929,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f1230,plain,
spl0_12,
inference(avatar_split_clause,[],[f928,f1227]) ).
fof(f1227,plain,
( spl0_12
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f928,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f1225,plain,
spl0_11,
inference(avatar_split_clause,[],[f927,f1222]) ).
fof(f1222,plain,
( spl0_11
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f927,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f1220,plain,
spl0_10,
inference(avatar_split_clause,[],[f926,f1217]) ).
fof(f1217,plain,
( spl0_10
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f926,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f1215,plain,
spl0_9,
inference(avatar_split_clause,[],[f925,f1212]) ).
fof(f1212,plain,
( spl0_9
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f925,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1210,plain,
spl0_8,
inference(avatar_split_clause,[],[f924,f1207]) ).
fof(f1207,plain,
( spl0_8
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f924,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1205,plain,
spl0_7,
inference(avatar_split_clause,[],[f923,f1202]) ).
fof(f1202,plain,
( spl0_7
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f923,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1200,plain,
spl0_6,
inference(avatar_split_clause,[],[f922,f1197]) ).
fof(f1197,plain,
( spl0_6
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f922,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1195,plain,
spl0_5,
inference(avatar_split_clause,[],[f921,f1192]) ).
fof(f1192,plain,
( spl0_5
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f921,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1190,plain,
spl0_4,
inference(avatar_split_clause,[],[f920,f1187]) ).
fof(f1187,plain,
( spl0_4
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f920,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1185,plain,
spl0_3,
inference(avatar_split_clause,[],[f919,f1182]) ).
fof(f1182,plain,
( spl0_3
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f919,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1180,plain,
spl0_2,
inference(avatar_split_clause,[],[f918,f1177]) ).
fof(f1177,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f918,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1175,plain,
spl0_1,
inference(avatar_split_clause,[],[f917,f1172]) ).
fof(f1172,plain,
( spl0_1
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f917,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : SWV602-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.38 % Computer : n021.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Tue Apr 30 05:02:40 EDT 2024
% 0.14/0.38 % CPUTime :
% 0.14/0.39 % (32020)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.46 % (32023)WARNING: value z3 for option sas not known
% 0.22/0.46 % (32025)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.46 % (32022)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.46 % (32027)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.46 % (32023)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.46 % (32024)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.46 % (32026)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.46 % (32021)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 1.50/0.66 TRYING [1]
% 1.50/0.69 TRYING [2]
% 3.12/0.89 TRYING [1]
% 3.12/0.90 TRYING [2]
% 3.81/0.98 TRYING [3]
% 4.30/1.06 TRYING [3]
% 4.30/1.07 TRYING [1]
% 5.01/1.18 TRYING [2]
% 13.28/2.32 % (32025)First to succeed.
% 13.28/2.37 % (32025)Refutation found. Thanks to Tanya!
% 13.28/2.37 % SZS status Unsatisfiable for theBenchmark
% 13.28/2.37 % SZS output start Proof for theBenchmark
% See solution above
% 13.28/2.39 % (32025)------------------------------
% 13.28/2.39 % (32025)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 13.28/2.39 % (32025)Termination reason: Refutation
% 13.28/2.39
% 13.28/2.39 % (32025)Memory used [KB]: 15598
% 13.28/2.39 % (32025)Time elapsed: 1.909 s
% 13.28/2.39 % (32025)Instructions burned: 3974 (million)
% 13.28/2.39 % (32025)------------------------------
% 13.28/2.39 % (32025)------------------------------
% 13.28/2.39 % (32020)Success in time 1.992 s
%------------------------------------------------------------------------------