TSTP Solution File: ALG386-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG386-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.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 : Mon May 20 18:37:32 EDT 2024
% Result : Unsatisfiable 1.88s 0.67s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1078
% Syntax : Number of formulae : 1740 ( 651 unt; 0 def)
% Number of atoms : 4003 ( 625 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 3876 (1613 ~;1704 |; 0 &)
% ( 559 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 621 ( 619 usr; 561 prp; 0-3 aty)
% Number of functors : 32 ( 32 usr; 5 con; 0-3 aty)
% Number of variables : 2224 (2224 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5514,plain,
$false,
inference(avatar_sat_refutation,[],[f600,f604,f609,f614,f619,f624,f629,f634,f639,f644,f649,f654,f659,f664,f669,f674,f679,f684,f689,f694,f699,f704,f709,f714,f719,f724,f729,f734,f739,f744,f749,f754,f759,f764,f769,f774,f779,f784,f789,f794,f799,f804,f809,f814,f819,f824,f829,f834,f839,f844,f849,f854,f859,f864,f869,f874,f879,f884,f889,f894,f899,f904,f909,f914,f919,f924,f929,f934,f939,f944,f949,f954,f959,f964,f969,f974,f979,f984,f989,f994,f999,f1004,f1009,f1014,f1019,f1024,f1029,f1034,f1039,f1044,f1049,f1054,f1059,f1064,f1069,f1074,f1079,f1084,f1089,f1094,f1099,f1104,f1109,f1114,f1119,f1124,f1129,f1134,f1139,f1144,f1149,f1154,f1159,f1164,f1169,f1174,f1179,f1184,f1189,f1194,f1199,f1204,f1209,f1214,f1219,f1224,f1228,f1233,f1237,f1241,f1245,f1249,f1253,f1257,f1261,f1265,f1269,f1273,f1277,f1281,f1285,f1289,f1293,f1297,f1301,f1305,f1309,f1313,f1317,f1321,f1325,f1329,f1333,f1337,f1341,f1345,f1349,f1353,f1357,f1361,f1365,f1369,f1373,f1377,f1381,f1385,f1389,f1393,f1397,f1401,f1405,f1409,f1413,f1417,f1421,f1426,f1430,f1434,f1438,f1443,f1447,f1454,f1458,f1462,f1466,f1470,f1474,f1478,f1482,f1486,f1490,f1494,f1498,f1502,f1506,f1510,f1514,f1518,f1522,f1526,f1530,f1534,f1538,f1542,f1547,f1551,f1575,f1606,f1612,f1616,f1620,f1624,f1628,f1632,f1636,f1640,f1644,f1648,f1652,f1656,f1660,f1664,f1668,f1672,f1676,f1680,f1684,f1688,f1711,f1730,f1734,f1738,f1742,f1746,f1750,f1754,f1758,f1762,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1806,f1810,f1815,f1819,f1823,f1852,f1874,f1913,f1917,f1921,f1925,f1929,f1933,f1937,f1941,f1945,f1949,f1953,f1957,f1961,f1965,f1969,f1973,f1977,f1985,f1989,f1993,f1997,f2005,f2044,f2112,f2116,f2120,f2124,f2128,f2132,f2144,f2148,f2152,f2156,f2160,f2164,f2168,f2172,f2176,f2180,f2184,f2188,f2192,f2196,f2200,f2204,f2208,f2212,f2216,f2220,f2224,f2234,f2238,f2242,f2246,f2250,f2269,f2369,f2450,f2454,f2458,f2462,f2467,f2471,f2475,f2479,f2483,f2487,f2491,f2495,f2499,f2503,f2507,f2516,f2520,f2524,f2528,f2532,f2536,f2540,f2544,f2548,f2552,f2561,f2565,f2569,f2605,f2823,f2827,f2831,f2835,f2839,f2843,f2847,f2851,f2855,f2859,f2863,f2888,f2892,f2896,f2900,f2904,f2908,f2912,f2916,f2920,f2924,f2928,f2932,f2936,f2940,f2944,f2948,f2952,f2956,f2960,f2964,f2968,f3014,f3117,f3121,f3125,f3129,f3133,f3137,f3141,f3145,f3149,f3153,f3157,f3173,f3177,f3181,f3185,f3189,f3193,f3197,f3215,f3299,f3333,f3337,f3341,f3345,f3349,f3353,f3372,f3376,f3380,f3384,f3388,f3392,f3396,f3400,f3404,f3408,f3427,f3431,f3435,f3439,f3443,f3447,f3451,f3455,f3459,f3463,f3467,f3471,f3475,f3507,f3617,f3621,f3625,f3629,f3633,f3637,f3641,f3677,f3770,f3774,f3778,f3782,f3786,f3790,f3807,f3811,f3815,f3819,f3823,f3827,f3831,f3839,f3889,f3893,f3897,f3901,f3905,f3909,f3913,f3917,f3921,f3925,f3930,f3934,f3938,f3942,f3946,f3950,f3954,f3958,f3962,f3966,f3970,f3989,f3993,f3997,f4001,f4005,f4009,f4013,f4017,f4021,f4025,f4029,f4033,f4037,f4041,f4045,f4049,f4053,f4057,f4061,f4065,f4069,f4073,f4077,f4081,f4085,f4089,f4093,f4116,f4569,f4573,f4577,f4581,f4585,f4589,f4593,f4597,f4601,f4684,f4688,f4692,f4696,f4700,f4704,f4708,f4713,f4717,f4721,f4725,f4729,f4733,f4737,f4741,f4745,f4846,f4871,f4875,f4879,f4883,f4887,f4891,f4895,f4927,f4931,f4966,f4970,f4976,f4980,f4984,f4988,f5001,f5007,f5011,f5015,f5019,f5023,f5027,f5096,f5100,f5104,f5108,f5246,f5302,f5306,f5320,f5324,f5342,f5346,f5350,f5354,f5358,f5362,f5494,f5508,f5509,f5510,f5511,f5512,f5513]) ).
fof(f5513,plain,
( ~ spl0_2
| ~ spl0_554 ),
inference(avatar_contradiction_clause,[],[f5495]) ).
fof(f5495,plain,
( $false
| ~ spl0_2
| ~ spl0_554 ),
inference(resolution,[],[f5345,f603]) ).
fof(f603,plain,
( ! [X18] : c_lessequals(X18,c_RealVector_Onorm__class_Onorm(v_x(X18),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f602,plain,
( spl0_2
<=> ! [X18] : c_lessequals(X18,c_RealVector_Onorm__class_Onorm(v_x(X18),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f5345,plain,
( ! [X0] : ~ c_lessequals(v_sko__CHAINED__1(v_c____,v_cs____),c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_554 ),
inference(avatar_component_clause,[],[f5344]) ).
fof(f5344,plain,
( spl0_554
<=> ! [X0] : ~ c_lessequals(v_sko__CHAINED__1(v_c____,v_cs____),c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f5512,plain,
( ~ spl0_375
| ~ spl0_554 ),
inference(avatar_contradiction_clause,[],[f5498]) ).
fof(f5498,plain,
( $false
| ~ spl0_375
| ~ spl0_554 ),
inference(resolution,[],[f5345,f3116]) ).
fof(f3116,plain,
( ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_375 ),
inference(avatar_component_clause,[],[f3115]) ).
fof(f3115,plain,
( spl0_375
<=> ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f5511,plain,
( ~ spl0_478
| ~ spl0_554 ),
inference(avatar_contradiction_clause,[],[f5499]) ).
fof(f5499,plain,
( $false
| ~ spl0_478
| ~ spl0_554 ),
inference(resolution,[],[f5345,f4028]) ).
fof(f4028,plain,
( ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex)),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_478 ),
inference(avatar_component_clause,[],[f4027]) ).
fof(f4027,plain,
( spl0_478
<=> ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex)),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f5510,plain,
( ~ spl0_537
| ~ spl0_554 ),
inference(avatar_contradiction_clause,[],[f5500]) ).
fof(f5500,plain,
( $false
| ~ spl0_537
| ~ spl0_554 ),
inference(resolution,[],[f5345,f5000]) ).
fof(f5000,plain,
( ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_537 ),
inference(avatar_component_clause,[],[f4999]) ).
fof(f4999,plain,
( spl0_537
<=> ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f5509,plain,
( ~ spl0_278
| ~ spl0_554 ),
inference(avatar_contradiction_clause,[],[f5501]) ).
fof(f5501,plain,
( $false
| ~ spl0_278
| ~ spl0_554 ),
inference(resolution,[],[f5345,f2043]) ).
fof(f2043,plain,
( ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f2042]) ).
fof(f2042,plain,
( spl0_278
<=> ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f5508,plain,
( ~ spl0_421
| ~ spl0_554 ),
inference(avatar_contradiction_clause,[],[f5503]) ).
fof(f5503,plain,
( $false
| ~ spl0_421
| ~ spl0_554 ),
inference(resolution,[],[f5345,f3466]) ).
fof(f3466,plain,
( ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_421 ),
inference(avatar_component_clause,[],[f3465]) ).
fof(f3465,plain,
( spl0_421
<=> ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f5494,plain,
spl0_559,
inference(avatar_split_clause,[],[f50,f5492]) ).
fof(f5492,plain,
( spl0_559
<=> ! [X5,X4,X7,X8,X9,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X4,X3),X7,X3),X9,X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X7,X3),X8,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X3),X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f50,axiom,
! [X3,X8,X9,X7,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X4,X3),X7,X3),X9,X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X7,X3),X8,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X3),X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
fof(f5362,plain,
spl0_558,
inference(avatar_split_clause,[],[f342,f5360]) ).
fof(f5360,plain,
( spl0_558
<=> ! [X4,X9,X8,X5,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X8,X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,X3),c_HOL_Otimes__class_Otimes(X5,X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f342,axiom,
! [X3,X8,X9,X4,X5] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X8,X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,X3),c_HOL_Otimes__class_Otimes(X5,X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
fof(f5358,plain,
spl0_557,
inference(avatar_split_clause,[],[f341,f5356]) ).
fof(f5356,plain,
( spl0_557
<=> ! [X4,X9,X8,X5,X3] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X8,X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,X3),c_HOL_Otimes__class_Otimes(X5,X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f341,axiom,
! [X3,X8,X9,X4,X5] :
( ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X8,X9,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,X3),c_HOL_Otimes__class_Otimes(X5,X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
fof(f5354,plain,
spl0_556,
inference(avatar_split_clause,[],[f177,f5352]) ).
fof(f5352,plain,
( spl0_556
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X5,c_HOL_Otimes__class_Otimes(X4,X8,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,X3),X5,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X8,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f177,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(X5,c_HOL_Otimes__class_Otimes(X4,X8,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,X3),X5,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X8,X3),X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).
fof(f5350,plain,
spl0_555,
inference(avatar_split_clause,[],[f176,f5348]) ).
fof(f5348,plain,
( spl0_555
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Otimes__class_Otimes(X4,X8,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,X3),X5,X3)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f176,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Otimes__class_Otimes(X4,X8,X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,X3),X5,X3)
| c_lessequals(X4,c_HOL_Oinverse__class_Odivide(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).
fof(f5346,plain,
( spl0_554
| ~ spl0_175
| ~ spl0_552 ),
inference(avatar_split_clause,[],[f5332,f5322,f1419,f5344]) ).
fof(f1419,plain,
( spl0_175
<=> ! [X18] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(X18),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f5322,plain,
( spl0_552
<=> ! [X14] :
( ~ c_lessequals(v_sko__CHAINED__1(v_c____,v_cs____),c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f5332,plain,
( ! [X0] : ~ c_lessequals(v_sko__CHAINED__1(v_c____,v_cs____),c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_175
| ~ spl0_552 ),
inference(resolution,[],[f5323,f1420]) ).
fof(f1420,plain,
( ! [X18] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(X18),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1419]) ).
fof(f5323,plain,
( ! [X14] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(v_sko__CHAINED__1(v_c____,v_cs____),c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_552 ),
inference(avatar_component_clause,[],[f5322]) ).
fof(f5342,plain,
spl0_553,
inference(avatar_split_clause,[],[f58,f5340]) ).
fof(f5340,plain,
( spl0_553
<=> ! [X5,X3,X4,X9,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Oplus__class_Oplus(X8,X9,X3),X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X8,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X9,X3),X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f58,axiom,
! [X3,X8,X9,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Oplus__class_Oplus(X8,X9,X3),X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X8,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X9,X3),X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__triangle__ineq_0) ).
fof(f5324,plain,
spl0_552,
inference(avatar_split_clause,[],[f421,f5322]) ).
fof(f421,axiom,
! [X14] :
( ~ c_lessequals(v_sko__CHAINED__1(v_c____,v_cs____),c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f5320,plain,
spl0_551,
inference(avatar_split_clause,[],[f14,f5318]) ).
fof(f5318,plain,
( spl0_551
<=> ! [X5,X3,X4,X7,X9,X8] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X4,X3),X7,X3),X9,X3) = X8
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X7,X3),X8,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X3),X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f14,axiom,
! [X3,X8,X9,X7,X4,X5] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X4,X3),X7,X3),X9,X3) = X8
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X7,X3),X8,X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X3),X9,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
fof(f5306,plain,
spl0_550,
inference(avatar_split_clause,[],[f317,f5304]) ).
fof(f5304,plain,
( spl0_550
<=> ! [X2,X14,X3,X15,X1] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X2
| c_HOL_Ozero__class_Ozero(X3) = X14
| c_HOL_Otimes__class_Otimes(X1,X14,X3) != c_HOL_Otimes__class_Otimes(X15,X2,X3)
| c_HOL_Oinverse__class_Odivide(X1,X2,X3) = c_HOL_Oinverse__class_Odivide(X15,X14,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f317,axiom,
! [X2,X3,X1,X14,X15] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X2
| c_HOL_Ozero__class_Ozero(X3) = X14
| c_HOL_Otimes__class_Otimes(X1,X14,X3) != c_HOL_Otimes__class_Otimes(X15,X2,X3)
| c_HOL_Oinverse__class_Odivide(X1,X2,X3) = c_HOL_Oinverse__class_Odivide(X15,X14,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
fof(f5302,plain,
spl0_549,
inference(avatar_split_clause,[],[f316,f5300]) ).
fof(f5300,plain,
( spl0_549
<=> ! [X2,X14,X3,X15,X1] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X2
| c_HOL_Ozero__class_Ozero(X3) = X14
| c_HOL_Oinverse__class_Odivide(X1,X2,X3) != c_HOL_Oinverse__class_Odivide(X15,X14,X3)
| c_HOL_Otimes__class_Otimes(X1,X14,X3) = c_HOL_Otimes__class_Otimes(X15,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f316,axiom,
! [X2,X3,X1,X14,X15] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X2
| c_HOL_Ozero__class_Ozero(X3) = X14
| c_HOL_Oinverse__class_Odivide(X1,X2,X3) != c_HOL_Oinverse__class_Odivide(X15,X14,X3)
| c_HOL_Otimes__class_Otimes(X1,X14,X3) = c_HOL_Otimes__class_Otimes(X15,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
fof(f5246,plain,
( spl0_548
| ~ spl0_374
| ~ spl0_393 ),
inference(avatar_split_clause,[],[f3410,f3213,f3012,f5244]) ).
fof(f5244,plain,
( spl0_548
<=> ! [X0,X1] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X1,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f3012,plain,
( spl0_374
<=> ! [X0,X1] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f3213,plain,
( spl0_393
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X1,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f3410,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X1,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_374
| ~ spl0_393 ),
inference(resolution,[],[f3214,f3013]) ).
fof(f3013,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) )
| ~ spl0_374 ),
inference(avatar_component_clause,[],[f3012]) ).
fof(f3214,plain,
( ! [X0,X1] :
( c_lessequals(X1,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) )
| ~ spl0_393 ),
inference(avatar_component_clause,[],[f3213]) ).
fof(f5108,plain,
spl0_547,
inference(avatar_split_clause,[],[f169,f5106]) ).
fof(f5106,plain,
( spl0_547
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f169,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_0) ).
fof(f5104,plain,
spl0_546,
inference(avatar_split_clause,[],[f168,f5102]) ).
fof(f5102,plain,
( spl0_546
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f168,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_1) ).
fof(f5100,plain,
spl0_545,
inference(avatar_split_clause,[],[f167,f5098]) ).
fof(f5098,plain,
( spl0_545
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f167,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_2) ).
fof(f5096,plain,
spl0_544,
inference(avatar_split_clause,[],[f166,f5094]) ).
fof(f5094,plain,
( spl0_544
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f166,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).
fof(f5027,plain,
spl0_543,
inference(avatar_split_clause,[],[f398,f5025]) ).
fof(f5025,plain,
( spl0_543
<=> ! [X4,X14,X9,X27] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X27
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(X4,X9,X27),c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X9,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(X4,X27,tc_Complex_Ocomplex),X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f398,axiom,
! [X9,X27,X4,X14] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X27
| ~ c_lessequals(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1(X4,X9,X27),c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X9,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(X4,X27,tc_Complex_Ocomplex),X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__infinity_0) ).
fof(f5023,plain,
spl0_542,
inference(avatar_split_clause,[],[f270,f5021]) ).
fof(f5021,plain,
( spl0_542
<=> ! [X14,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X2
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X14,X2,X3),X3),X2,X3) = c_HOL_Oplus__class_Oplus(X14,c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f270,axiom,
! [X2,X3,X1,X14] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X2
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X14,X2,X3),X3),X2,X3) = c_HOL_Oplus__class_Oplus(X14,c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
fof(f5019,plain,
spl0_541,
inference(avatar_split_clause,[],[f269,f5017]) ).
fof(f5017,plain,
( spl0_541
<=> ! [X14,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X14,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X14,X2,X3),X3),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f269,axiom,
! [X2,X3,X1,X14] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X14,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X14,X2,X3),X3),X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
fof(f5015,plain,
spl0_540,
inference(avatar_split_clause,[],[f235,f5013]) ).
fof(f5013,plain,
( spl0_540
<=> ! [X3,X8,X9,X28,X1] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| X8 = X9
| c_HOL_Ozero__class_Ozero(X3) = X28
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X28,X8,X3),X3) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X28,X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f235,axiom,
! [X3,X28,X1,X8,X9] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| X8 = X9
| c_HOL_Ozero__class_Ozero(X3) = X28
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X28,X8,X3),X3) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X28,X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(f5011,plain,
spl0_539,
inference(avatar_split_clause,[],[f88,f5009]) ).
fof(f5009,plain,
( spl0_539
<=> ! [X3,X4,X7,X5,X8] :
( ~ class_Ring__and__Field_Osemiring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X7,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X3),X8,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3),X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f88,axiom,
! [X3,X8,X7,X4,X5] :
( ~ class_Ring__and__Field_Osemiring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X7,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X3),X8,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X5,X3),X7,X3),X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
fof(f5007,plain,
spl0_538,
inference(avatar_split_clause,[],[f17,f5005]) ).
fof(f5005,plain,
( spl0_538
<=> ! [X5,X4,X7,X9,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X3),X9,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X7,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X4,X3),X7,X3),X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f17,axiom,
! [X3,X9,X7,X4,X5] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,X3),X9,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X7,X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X4,X3),X7,X3),X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
fof(f5001,plain,
( ~ spl0_43
| spl0_537
| ~ spl0_266
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f3166,f3115,f1951,f4999,f806]) ).
fof(f806,plain,
( spl0_43
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1951,plain,
( spl0_266
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f3166,plain,
( ! [X0] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) )
| ~ spl0_266
| ~ spl0_375 ),
inference(resolution,[],[f3116,f1952]) ).
fof(f1952,plain,
( ! [X3,X4,X5] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3)
| c_lessequals(X4,X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) )
| ~ spl0_266 ),
inference(avatar_component_clause,[],[f1951]) ).
fof(f4988,plain,
( spl0_536
| spl0_1 ),
inference(avatar_split_clause,[],[f406,f597,f4986]) ).
fof(f4986,plain,
( spl0_536
<=> ! [X28] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_sko__local__Xthat__1(v_c____,v_cs____,X28),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f597,plain,
( spl0_1
<=> v_thesis____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f406,axiom,
! [X28] :
( v_thesis____
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_sko__local__Xthat__1(v_c____,v_cs____,X28),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_1) ).
fof(f4984,plain,
spl0_535,
inference(avatar_split_clause,[],[f282,f4982]) ).
fof(f4982,plain,
( spl0_535
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X5,X3),c_HOL_Oinverse__class_Oinverse(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f282,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X5,X3),c_HOL_Oinverse__class_Oinverse(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
fof(f4980,plain,
spl0_534,
inference(avatar_split_clause,[],[f227,f4978]) ).
fof(f4978,plain,
( spl0_534
<=> ! [X15,X14,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Oinverse__class_Odivide(X14,X15,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X14,X3),c_HOL_Otimes__class_Otimes(X2,X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f227,axiom,
! [X2,X3,X1,X14,X15] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X3),c_HOL_Oinverse__class_Odivide(X14,X15,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X14,X3),c_HOL_Otimes__class_Otimes(X2,X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
fof(f4976,plain,
spl0_533,
inference(avatar_split_clause,[],[f106,f4974]) ).
fof(f4974,plain,
( spl0_533
<=> ! [X14,X3,X2,X1] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X14,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X14,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f106,axiom,
! [X2,X3,X1,X14] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X14,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X14,X3),c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
fof(f4970,plain,
spl0_532,
inference(avatar_split_clause,[],[f313,f4968]) ).
fof(f4968,plain,
( spl0_532
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X6,X3) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X4,X6,X3),c_Power_Opower__class_Opower(X5,X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f313,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X6,X3) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X4,X6,X3),c_Power_Opower__class_Opower(X5,X6,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
fof(f4966,plain,
( spl0_531
| ~ spl0_276
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f3159,f3115,f1995,f4964]) ).
fof(f4964,plain,
( spl0_531
<=> ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(X1),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f1995,plain,
( spl0_276
<=> ! [X34,X36,X35] :
( ~ c_lessequals(X34,X36,tc_RealDef_Oreal)
| ~ c_lessequals(X36,X35,tc_RealDef_Oreal)
| c_lessequals(X34,X35,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f3159,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(X1),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_276
| ~ spl0_375 ),
inference(resolution,[],[f3116,f1996]) ).
fof(f1996,plain,
( ! [X36,X34,X35] :
( ~ c_lessequals(X36,X35,tc_RealDef_Oreal)
| ~ c_lessequals(X34,X36,tc_RealDef_Oreal)
| c_lessequals(X34,X35,tc_RealDef_Oreal) )
| ~ spl0_276 ),
inference(avatar_component_clause,[],[f1995]) ).
fof(f4931,plain,
spl0_530,
inference(avatar_split_clause,[],[f372,f4929]) ).
fof(f4929,plain,
( spl0_530
<=> ! [X2,X1,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X1
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f372,axiom,
! [X2,X3,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X1
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
fof(f4927,plain,
spl0_529,
inference(avatar_split_clause,[],[f371,f4925]) ).
fof(f4925,plain,
( spl0_529
<=> ! [X2,X1,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f371,axiom,
! [X2,X3,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X2,X3)
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
fof(f4895,plain,
spl0_528,
inference(avatar_split_clause,[],[f355,f4893]) ).
fof(f4893,plain,
( spl0_528
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X8,X3),c_HOL_Oinverse__class_Odivide(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f355,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X8,X3),c_HOL_Oinverse__class_Odivide(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).
fof(f4891,plain,
spl0_527,
inference(avatar_split_clause,[],[f354,f4889]) ).
fof(f4889,plain,
( spl0_527
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X8,X3),c_HOL_Oinverse__class_Odivide(X4,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f354,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X5,X8,X3),c_HOL_Oinverse__class_Odivide(X4,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).
fof(f4887,plain,
spl0_526,
inference(avatar_split_clause,[],[f271,f4885]) ).
fof(f4885,plain,
( spl0_526
<=> ! [X5,X3,X4,X9,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Oplus__class_Oplus(X8,X9,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X8,X3),c_HOL_Oplus__class_Oplus(X5,X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f271,axiom,
! [X3,X8,X9,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Oplus__class_Oplus(X8,X9,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X8,X3),c_HOL_Oplus__class_Oplus(X5,X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f4883,plain,
spl0_525,
inference(avatar_split_clause,[],[f111,f4881]) ).
fof(f4881,plain,
( spl0_525
<=> ! [X24,X23,X3,X25,X26] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X3),c_HOL_Otimes__class_Otimes(X25,X26,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X25,X3),c_HOL_Otimes__class_Otimes(X24,X26,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f111,axiom,
! [X3,X26,X24,X25,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X3),c_HOL_Otimes__class_Otimes(X25,X26,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X25,X3),c_HOL_Otimes__class_Otimes(X24,X26,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f4879,plain,
spl0_524,
inference(avatar_split_clause,[],[f79,f4877]) ).
fof(f4877,plain,
( spl0_524
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X8
| c_HOL_Oinverse__class_Odivide(X4,X5,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X8,X3),c_HOL_Otimes__class_Otimes(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f79,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X8
| c_HOL_Oinverse__class_Odivide(X4,X5,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X8,X3),c_HOL_Otimes__class_Otimes(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
fof(f4875,plain,
spl0_523,
inference(avatar_split_clause,[],[f78,f4873]) ).
fof(f4873,plain,
( spl0_523
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X8
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X4,X3),c_HOL_Otimes__class_Otimes(X8,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f78,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X8
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X8,X4,X3),c_HOL_Otimes__class_Otimes(X8,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
fof(f4871,plain,
spl0_522,
inference(avatar_split_clause,[],[f36,f4869]) ).
fof(f4869,plain,
( spl0_522
<=> ! [X5,X3,X4,X9,X8] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X8,X3),c_HOL_Oplus__class_Oplus(X5,X9,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,X5,X3),c_HOL_Ominus__class_Ominus(X8,X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f36,axiom,
! [X3,X8,X9,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X8,X3),c_HOL_Oplus__class_Oplus(X5,X9,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,X5,X3),c_HOL_Ominus__class_Ominus(X8,X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
fof(f4846,plain,
( spl0_521
| ~ spl0_295
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f3045,f3012,f2182,f4844]) ).
fof(f4844,plain,
( spl0_521
<=> ! [X0,X1] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),X1,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f2182,plain,
( spl0_295
<=> ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f3045,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),X1,tc_RealDef_Oreal) )
| ~ spl0_295
| ~ spl0_374 ),
inference(resolution,[],[f3013,f2183]) ).
fof(f2183,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) )
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f2182]) ).
fof(f4745,plain,
spl0_520,
inference(avatar_split_clause,[],[f401,f4743]) ).
fof(f4743,plain,
( spl0_520
<=> ! [X27,X28,X15] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X15,tc_Complex_Ocomplex),X28,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X27,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(X27,X28),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X27,X15,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f401,axiom,
! [X28,X27,X15] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X15,tc_Complex_Ocomplex),X28,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X27,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1(X27,X28),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X27,X15,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__minimum__modulus__disc_0) ).
fof(f4741,plain,
spl0_519,
inference(avatar_split_clause,[],[f381,f4739]) ).
fof(f4739,plain,
( spl0_519
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f381,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
fof(f4737,plain,
spl0_518,
inference(avatar_split_clause,[],[f380,f4735]) ).
fof(f4735,plain,
( spl0_518
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f380,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
fof(f4733,plain,
spl0_517,
inference(avatar_split_clause,[],[f379,f4731]) ).
fof(f4731,plain,
( spl0_517
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f379,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
fof(f4729,plain,
spl0_516,
inference(avatar_split_clause,[],[f378,f4727]) ).
fof(f4727,plain,
( spl0_516
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f378,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
fof(f4725,plain,
spl0_515,
inference(avatar_split_clause,[],[f374,f4723]) ).
fof(f4723,plain,
( spl0_515
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f374,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).
fof(f4721,plain,
spl0_514,
inference(avatar_split_clause,[],[f373,f4719]) ).
fof(f4719,plain,
( spl0_514
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f373,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).
fof(f4717,plain,
spl0_513,
inference(avatar_split_clause,[],[f225,f4715]) ).
fof(f4715,plain,
( spl0_513
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X6,X3) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X4,X6,X3),c_Power_Opower__class_Opower(X5,X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f225,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X6,X3) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X4,X6,X3),c_Power_Opower__class_Opower(X5,X6,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__divide_0) ).
fof(f4713,plain,
( ~ spl0_51
| spl0_512
| ~ spl0_229
| ~ spl0_289
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f2881,f2821,f2158,f1708,f4710,f846]) ).
fof(f846,plain,
( spl0_51
<=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f4710,plain,
( spl0_512
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f1708,plain,
( spl0_229
<=> 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_229])]) ).
fof(f2158,plain,
( spl0_289
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ozero__class_Ozero(X3) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f2821,plain,
( spl0_342
<=> ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f2881,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal)
| ~ spl0_229
| ~ spl0_289
| ~ spl0_342 ),
inference(forward_demodulation,[],[f2870,f1710]) ).
fof(f1710,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_229 ),
inference(avatar_component_clause,[],[f1708]) ).
fof(f2870,plain,
( ~ class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_289
| ~ spl0_342 ),
inference(resolution,[],[f2822,f2159]) ).
fof(f2159,plain,
( ! [X3,X4] :
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3) )
| ~ spl0_289 ),
inference(avatar_component_clause,[],[f2158]) ).
fof(f2822,plain,
( ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_342 ),
inference(avatar_component_clause,[],[f2821]) ).
fof(f4708,plain,
spl0_511,
inference(avatar_split_clause,[],[f210,f4706]) ).
fof(f4706,plain,
( spl0_511
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f210,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
fof(f4704,plain,
spl0_510,
inference(avatar_split_clause,[],[f209,f4702]) ).
fof(f4702,plain,
( spl0_510
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f209,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
fof(f4700,plain,
spl0_509,
inference(avatar_split_clause,[],[f208,f4698]) ).
fof(f4698,plain,
( spl0_509
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f208,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
fof(f4696,plain,
spl0_508,
inference(avatar_split_clause,[],[f207,f4694]) ).
fof(f4694,plain,
( spl0_508
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f207,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
fof(f4692,plain,
spl0_507,
inference(avatar_split_clause,[],[f205,f4690]) ).
fof(f4690,plain,
( spl0_507
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f205,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).
fof(f4688,plain,
spl0_506,
inference(avatar_split_clause,[],[f204,f4686]) ).
fof(f4686,plain,
( spl0_506
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f204,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).
fof(f4684,plain,
spl0_505,
inference(avatar_split_clause,[],[f118,f4682]) ).
fof(f4682,plain,
( spl0_505
<=> ! [X8,X3,X2,X1] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(X3) = X1
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,X3),c_HOL_Otimes__class_Otimes(X8,c_RealVector_Onorm__class_Onorm(X2,X3),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f118,axiom,
! [X2,X3,X1,X8] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(X3) = X1
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,X3),c_HOL_Otimes__class_Otimes(X8,c_RealVector_Onorm__class_Onorm(X2,X3),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ratiotest__lemma_0) ).
fof(f4601,plain,
spl0_504,
inference(avatar_split_clause,[],[f382,f4599]) ).
fof(f4599,plain,
( spl0_504
<=> ! [X5,X4,X6,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_Power_Opower__class_Opower(X4,X6,X3),c_Power_Opower__class_Opower(X5,X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f382,axiom,
! [X3,X6,X4,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_Power_Opower__class_Opower(X4,X6,X3),c_Power_Opower__class_Opower(X5,X6,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
fof(f4597,plain,
spl0_503,
inference(avatar_split_clause,[],[f360,f4595]) ).
fof(f4595,plain,
( spl0_503
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Omult__mono1(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X4,X3),c_HOL_Otimes__class_Otimes(X8,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f360,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Omult__mono1(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X4,X3),c_HOL_Otimes__class_Otimes(X8,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
fof(f4593,plain,
spl0_502,
inference(avatar_split_clause,[],[f359,f4591]) ).
fof(f4591,plain,
( spl0_502
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X4,X3),c_HOL_Otimes__class_Otimes(X8,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f359,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X4,X3),c_HOL_Otimes__class_Otimes(X8,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
fof(f4589,plain,
spl0_501,
inference(avatar_split_clause,[],[f358,f4587]) ).
fof(f4587,plain,
( spl0_501
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,X3),c_HOL_Otimes__class_Otimes(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f358,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Omult__mono(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,X3),c_HOL_Otimes__class_Otimes(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
fof(f4585,plain,
spl0_500,
inference(avatar_split_clause,[],[f357,f4583]) ).
fof(f4583,plain,
( spl0_500
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X5,X4,X3)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X4,X3),c_HOL_Otimes__class_Otimes(X8,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f357,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X5,X4,X3)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X4,X3),c_HOL_Otimes__class_Otimes(X8,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
fof(f4581,plain,
( ~ spl0_74
| spl0_499
| ~ spl0_265
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f2699,f2602,f1947,f4579,f961]) ).
fof(f961,plain,
( spl0_74
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f4579,plain,
( spl0_499
<=> ! [X0] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f1947,plain,
( spl0_265
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f2602,plain,
( spl0_341
<=> c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex) = c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f2699,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) )
| ~ spl0_265
| ~ spl0_341 ),
inference(superposition,[],[f1948,f2604]) ).
fof(f2604,plain,
( c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex) = c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_341 ),
inference(avatar_component_clause,[],[f2602]) ).
fof(f1948,plain,
( ! [X3,X6,X4] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3),X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) )
| ~ spl0_265 ),
inference(avatar_component_clause,[],[f1947]) ).
fof(f4577,plain,
spl0_498,
inference(avatar_split_clause,[],[f356,f4575]) ).
fof(f4575,plain,
( spl0_498
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X5,X4,X3)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,X3),c_HOL_Otimes__class_Otimes(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f356,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X5,X4,X3)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X8,X3),c_HOL_Otimes__class_Otimes(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
fof(f4573,plain,
spl0_497,
inference(avatar_split_clause,[],[f314,f4571]) ).
fof(f4571,plain,
( spl0_497
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f314,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
fof(f4569,plain,
spl0_496,
inference(avatar_split_clause,[],[f284,f4567]) ).
fof(f4567,plain,
( spl0_496
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f284,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__divide_0) ).
fof(f4116,plain,
( ~ spl0_43
| spl0_495
| ~ spl0_266
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f3362,f3297,f1951,f4114,f806]) ).
fof(f4114,plain,
( spl0_495
<=> ! [X0] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f3297,plain,
( spl0_394
<=> ! [X0] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f3362,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) )
| ~ spl0_266
| ~ spl0_394 ),
inference(resolution,[],[f3298,f1952]) ).
fof(f3298,plain,
( ! [X0] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_394 ),
inference(avatar_component_clause,[],[f3297]) ).
fof(f4093,plain,
spl0_494,
inference(avatar_split_clause,[],[f397,f4091]) ).
fof(f4091,plain,
( spl0_494
<=> ! [X4,X27,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X4,X27,X3),X8,X3) = c_Polynomial_OpCons(c_Polynomial_Opoly(X27,X8,X3),c_Polynomial_Osynthetic__div(X27,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f397,axiom,
! [X3,X8,X27,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X4,X27,X3),X8,X3) = c_Polynomial_OpCons(c_Polynomial_Opoly(X27,X8,X3),c_Polynomial_Osynthetic__div(X27,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthetic__div__pCons_0) ).
fof(f4089,plain,
spl0_493,
inference(avatar_split_clause,[],[f376,f4087]) ).
fof(f4087,plain,
( spl0_493
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ c_lessequals(X5,X8,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(X5,c_HOL_Oplus__class_Oplus(X4,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f376,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ c_lessequals(X5,X8,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(X5,c_HOL_Oplus__class_Oplus(X4,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f4085,plain,
spl0_492,
inference(avatar_split_clause,[],[f375,f4083]) ).
fof(f4083,plain,
( spl0_492
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ c_lessequals(X5,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| c_lessequals(X5,c_HOL_Oplus__class_Oplus(X4,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f375,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ c_lessequals(X5,X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X8,X3)
| c_lessequals(X5,c_HOL_Oplus__class_Oplus(X4,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f4081,plain,
spl0_491,
inference(avatar_split_clause,[],[f364,f4079]) ).
fof(f4079,plain,
( spl0_491
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f364,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
fof(f4077,plain,
spl0_490,
inference(avatar_split_clause,[],[f363,f4075]) ).
fof(f4075,plain,
( spl0_490
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f363,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
fof(f4073,plain,
( spl0_489
| ~ spl0_276
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f3355,f3297,f1995,f4071]) ).
fof(f4071,plain,
( spl0_489
<=> ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f3355,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_276
| ~ spl0_394 ),
inference(resolution,[],[f3298,f1996]) ).
fof(f4069,plain,
spl0_488,
inference(avatar_split_clause,[],[f362,f4067]) ).
fof(f4067,plain,
( spl0_488
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f362,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
fof(f4065,plain,
spl0_487,
inference(avatar_split_clause,[],[f361,f4063]) ).
fof(f4063,plain,
( spl0_487
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f361,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
fof(f4061,plain,
spl0_486,
inference(avatar_split_clause,[],[f353,f4059]) ).
fof(f4059,plain,
( spl0_486
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f353,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
fof(f4057,plain,
spl0_485,
inference(avatar_split_clause,[],[f351,f4055]) ).
fof(f4055,plain,
( spl0_485
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f351,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Opordered__ring(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
fof(f4053,plain,
spl0_484,
inference(avatar_split_clause,[],[f349,f4051]) ).
fof(f4051,plain,
( spl0_484
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f349,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
fof(f4049,plain,
spl0_483,
inference(avatar_split_clause,[],[f348,f4047]) ).
fof(f4047,plain,
( spl0_483
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f348,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
fof(f4045,plain,
spl0_482,
inference(avatar_split_clause,[],[f347,f4043]) ).
fof(f4043,plain,
( spl0_482
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f347,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
fof(f4041,plain,
spl0_481,
inference(avatar_split_clause,[],[f346,f4039]) ).
fof(f4039,plain,
( spl0_481
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f346,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
fof(f4037,plain,
spl0_480,
inference(avatar_split_clause,[],[f345,f4035]) ).
fof(f4035,plain,
( spl0_480
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f345,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
fof(f4033,plain,
spl0_479,
inference(avatar_split_clause,[],[f344,f4031]) ).
fof(f4031,plain,
( spl0_479
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f344,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
fof(f4029,plain,
( spl0_478
| ~ spl0_374
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f3158,f3115,f3012,f4027]) ).
fof(f3158,plain,
( ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex)),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_374
| ~ spl0_375 ),
inference(resolution,[],[f3116,f3013]) ).
fof(f4025,plain,
spl0_477,
inference(avatar_split_clause,[],[f343,f4023]) ).
fof(f4023,plain,
( spl0_477
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f343,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
fof(f4021,plain,
spl0_476,
inference(avatar_split_clause,[],[f339,f4019]) ).
fof(f4019,plain,
( spl0_476
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f339,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
fof(f4017,plain,
spl0_475,
inference(avatar_split_clause,[],[f338,f4015]) ).
fof(f4015,plain,
( spl0_475
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f338,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
fof(f4013,plain,
spl0_474,
inference(avatar_split_clause,[],[f337,f4011]) ).
fof(f4011,plain,
( spl0_474
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f337,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
fof(f4009,plain,
spl0_473,
inference(avatar_split_clause,[],[f336,f4007]) ).
fof(f4007,plain,
( spl0_473
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f336,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
fof(f4005,plain,
spl0_472,
inference(avatar_split_clause,[],[f327,f4003]) ).
fof(f4003,plain,
( spl0_472
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f327,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X5,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f4001,plain,
spl0_471,
inference(avatar_split_clause,[],[f285,f3999]) ).
fof(f3999,plain,
( spl0_471
<=> ! [X2,X0,X14,X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X1,X14,X3) = X0
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X14,X3),X3) != c_HOL_Oplus__class_Oplus(X2,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f285,axiom,
! [X2,X3,X0,X1,X14] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X1,X14,X3) = X0
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X14,X3),X3) != c_HOL_Oplus__class_Oplus(X2,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
fof(f3997,plain,
spl0_470,
inference(avatar_split_clause,[],[f256,f3995]) ).
fof(f3995,plain,
( spl0_470
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X5,X3),X8,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X8,X3),c_HOL_Otimes__class_Otimes(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f256,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X5,X3),X8,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X8,X3),c_HOL_Otimes__class_Otimes(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
fof(f3993,plain,
spl0_469,
inference(avatar_split_clause,[],[f255,f3991]) ).
fof(f3991,plain,
( spl0_469
<=> ! [X14,X3,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X14,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X14,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f255,axiom,
! [X2,X3,X1,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X3),c_HOL_Otimes__class_Otimes(X1,X14,X3),X3) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X14,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
fof(f3989,plain,
spl0_468,
inference(avatar_split_clause,[],[f254,f3987]) ).
fof(f3987,plain,
( spl0_468
<=> ! [X4,X20,X5,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X20,X3),X5,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Otimes__class_Otimes(X20,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f254,axiom,
! [X3,X4,X5,X20] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X20,X3),X5,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Otimes__class_Otimes(X20,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
fof(f3970,plain,
spl0_467,
inference(avatar_split_clause,[],[f252,f3968]) ).
fof(f3968,plain,
( spl0_467
<=> ! [X3,X4,X5,X19] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oplus__class_Oplus(X5,X19,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Otimes__class_Otimes(X4,X19,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f252,axiom,
! [X3,X19,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oplus__class_Oplus(X5,X19,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Otimes__class_Otimes(X4,X19,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
fof(f3966,plain,
spl0_466,
inference(avatar_split_clause,[],[f250,f3964]) ).
fof(f3964,plain,
( spl0_466
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X5,X3),X8,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X8,X3),c_HOL_Otimes__class_Otimes(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f250,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X4,X5,X3),X8,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X8,X3),c_HOL_Otimes__class_Otimes(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f3962,plain,
spl0_465,
inference(avatar_split_clause,[],[f241,f3960]) ).
fof(f3960,plain,
( spl0_465
<=> ! [X5,X4,X6,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X4,X5,X3),X6,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X4,X6,X3),c_Power_Opower__class_Opower(X5,X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f241,axiom,
! [X3,X6,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X3)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X4,X5,X3),X6,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X4,X6,X3),c_Power_Opower__class_Opower(X5,X6,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
fof(f3958,plain,
spl0_464,
inference(avatar_split_clause,[],[f240,f3956]) ).
fof(f3956,plain,
( spl0_464
<=> ! [X3,X29,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X29,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X29,X3),c_Power_Opower__class_Opower(X2,X29,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f240,axiom,
! [X2,X3,X29,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X3),X29,X3) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X29,X3),c_Power_Opower__class_Opower(X2,X29,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
fof(f3954,plain,
spl0_463,
inference(avatar_split_clause,[],[f199,f3952]) ).
fof(f3952,plain,
( spl0_463
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f199,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f3950,plain,
spl0_462,
inference(avatar_split_clause,[],[f196,f3948]) ).
fof(f3948,plain,
( spl0_462
<=> ! [X3,X4,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X4,X27,X3),X1,X3) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X27,X1,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f196,axiom,
! [X3,X1,X27,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X4,X27,X3),X1,X3) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X27,X1,X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
fof(f3946,plain,
spl0_461,
inference(avatar_split_clause,[],[f180,f3944]) ).
fof(f3944,plain,
( spl0_461
<=> ! [X4,X9,X8,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X8,X9,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X8,X3),c_HOL_Oplus__class_Oplus(X5,X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f180,axiom,
! [X3,X8,X9,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(X8,X9,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X8,X3),c_HOL_Oplus__class_Oplus(X5,X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f3942,plain,
spl0_460,
inference(avatar_split_clause,[],[f178,f3940]) ).
fof(f3940,plain,
( spl0_460
<=> ! [X5,X3,X4,X9,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X8,X9,X3)
| ~ c_lessequals(X4,c_HOL_Oplus__class_Oplus(X5,X8,X3),X3)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(X5,X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f178,axiom,
! [X3,X8,X9,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X8,X9,X3)
| ~ c_lessequals(X4,c_HOL_Oplus__class_Oplus(X5,X8,X3),X3)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(X5,X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
fof(f3938,plain,
spl0_459,
inference(avatar_split_clause,[],[f174,f3936]) ).
fof(f3936,plain,
( spl0_459
<=> ! [X2,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X1
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X3),c_HOL_Otimes__class_Otimes(X2,X2,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f174,axiom,
! [X2,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X1
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X3),c_HOL_Otimes__class_Otimes(X2,X2,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
fof(f3934,plain,
spl0_458,
inference(avatar_split_clause,[],[f173,f3932]) ).
fof(f3932,plain,
( spl0_458
<=> ! [X2,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X2
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X3),c_HOL_Otimes__class_Otimes(X2,X2,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f173,axiom,
! [X2,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X2
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X3),c_HOL_Otimes__class_Otimes(X2,X2,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
fof(f3930,plain,
( ~ spl0_43
| spl0_457
| ~ spl0_243
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f2697,f2602,f1780,f3927,f806]) ).
fof(f3927,plain,
( spl0_457
<=> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f1780,plain,
( spl0_243
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X4,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2697,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ spl0_243
| ~ spl0_341 ),
inference(superposition,[],[f1781,f2604]) ).
fof(f1781,plain,
( ! [X3,X4] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X4,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f1780]) ).
fof(f3925,plain,
spl0_456,
inference(avatar_split_clause,[],[f170,f3923]) ).
fof(f3923,plain,
( spl0_456
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f170,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
fof(f3921,plain,
spl0_455,
inference(avatar_split_clause,[],[f162,f3919]) ).
fof(f3919,plain,
( spl0_455
<=> ! [X2,X1,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f162,axiom,
! [X2,X3,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X1,X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X3),X1,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X1,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).
fof(f3917,plain,
spl0_454,
inference(avatar_split_clause,[],[f136,f3915]) ).
fof(f3915,plain,
( spl0_454
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| X4 = X5
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Oinverse(X4,X3) != c_HOL_Oinverse__class_Oinverse(X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f136,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| X4 = X5
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Oinverse(X4,X3) != c_HOL_Oinverse__class_Oinverse(X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
fof(f3913,plain,
spl0_453,
inference(avatar_split_clause,[],[f76,f3911]) ).
fof(f3911,plain,
( spl0_453
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X5,X3),X8,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X8,X3),c_HOL_Oinverse__class_Odivide(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f76,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X4,X5,X3),X8,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X4,X8,X3),c_HOL_Oinverse__class_Odivide(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
fof(f3909,plain,
spl0_452,
inference(avatar_split_clause,[],[f75,f3907]) ).
fof(f3907,plain,
( spl0_452
<=> ! [X13,X3,X2,X1] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),X13,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X13,X3),c_HOL_Oinverse__class_Odivide(X2,X13,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f75,axiom,
! [X2,X3,X1,X13] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X3),X13,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X13,X3),c_HOL_Oinverse__class_Odivide(X2,X13,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
fof(f3905,plain,
spl0_451,
inference(avatar_split_clause,[],[f35,f3903]) ).
fof(f3903,plain,
( spl0_451
<=> ! [X13,X3,X2,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X13,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X13,X3),c_HOL_Otimes__class_Otimes(X2,X13,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f35,axiom,
! [X2,X3,X1,X13] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X3),X13,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X13,X3),c_HOL_Otimes__class_Otimes(X2,X13,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
fof(f3901,plain,
spl0_450,
inference(avatar_split_clause,[],[f33,f3899]) ).
fof(f3899,plain,
( spl0_450
<=> ! [X3,X4,X5,X19] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X5,X19,X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Otimes__class_Otimes(X4,X19,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f33,axiom,
! [X3,X19,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X5,X19,X3),X3) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X4,X5,X3),c_HOL_Otimes__class_Otimes(X4,X19,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
fof(f3897,plain,
spl0_449,
inference(avatar_split_clause,[],[f27,f3895]) ).
fof(f3895,plain,
( spl0_449
<=> ! [X13,X3,X2,X1] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X3),X13,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X13,X3),c_HOL_Oinverse__class_Odivide(X2,X13,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f27,axiom,
! [X2,X3,X1,X13] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X3),X13,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X13,X3),c_HOL_Oinverse__class_Odivide(X2,X13,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
fof(f3893,plain,
spl0_448,
inference(avatar_split_clause,[],[f26,f3891]) ).
fof(f3891,plain,
( spl0_448
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X4,X5,X3),X8,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X8,X3),c_HOL_Oinverse__class_Odivide(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f26,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X4,X5,X3),X8,X3) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X4,X8,X3),c_HOL_Oinverse__class_Odivide(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
fof(f3889,plain,
spl0_447,
inference(avatar_split_clause,[],[f6,f3887]) ).
fof(f3887,plain,
( spl0_447
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f6,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).
fof(f3839,plain,
( ~ spl0_50
| spl0_446
| ~ spl0_43
| ~ spl0_246
| ~ spl0_278
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f2651,f2489,f2042,f1792,f806,f3837,f841]) ).
fof(f841,plain,
( spl0_50
<=> class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f3837,plain,
( spl0_446
<=> ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f1792,plain,
( spl0_246
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f2489,plain,
( spl0_323
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f2651,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) )
| ~ spl0_43
| ~ spl0_246
| ~ spl0_278
| ~ spl0_323 ),
inference(forward_demodulation,[],[f2635,f1863]) ).
fof(f1863,plain,
( ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_43
| ~ spl0_246 ),
inference(resolution,[],[f1793,f808]) ).
fof(f808,plain,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f806]) ).
fof(f1793,plain,
( ! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) )
| ~ spl0_246 ),
inference(avatar_component_clause,[],[f1792]) ).
fof(f2635,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_278
| ~ spl0_323 ),
inference(resolution,[],[f2490,f2043]) ).
fof(f2490,plain,
( ! [X3,X4,X5] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X3),X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) )
| ~ spl0_323 ),
inference(avatar_component_clause,[],[f2489]) ).
fof(f3831,plain,
spl0_445,
inference(avatar_split_clause,[],[f383,f3829]) ).
fof(f3829,plain,
( spl0_445
<=> ! [X6,X1,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X1
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X6,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f383,axiom,
! [X3,X1,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X1
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,X6,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
fof(f3827,plain,
spl0_444,
inference(avatar_split_clause,[],[f315,f3825]) ).
fof(f3825,plain,
( spl0_444
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f315,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
fof(f3823,plain,
spl0_443,
inference(avatar_split_clause,[],[f301,f3821]) ).
fof(f3821,plain,
( spl0_443
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X4,X6,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X4,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f301,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X4,X6,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X4,X3),X6,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
fof(f3819,plain,
spl0_442,
inference(avatar_split_clause,[],[f281,f3817]) ).
fof(f3817,plain,
( spl0_442
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,X3),c_HOL_Oinverse__class_Oinverse(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f281,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,X3),c_HOL_Oinverse__class_Oinverse(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
fof(f3815,plain,
spl0_441,
inference(avatar_split_clause,[],[f272,f3813]) ).
fof(f3813,plain,
( spl0_441
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Odivide(X4,X5,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f272,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Oinverse__class_Odivide(X4,X5,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
fof(f3811,plain,
spl0_440,
inference(avatar_split_clause,[],[f237,f3809]) ).
fof(f3809,plain,
( spl0_440
<=> ! [X2,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X2
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X3),c_HOL_Otimes__class_Otimes(X2,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f237,axiom,
! [X2,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X2
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X3),c_HOL_Otimes__class_Otimes(X2,X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
fof(f3807,plain,
spl0_439,
inference(avatar_split_clause,[],[f236,f3805]) ).
fof(f3805,plain,
( spl0_439
<=> ! [X2,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X1
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X3),c_HOL_Otimes__class_Otimes(X2,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f236,axiom,
! [X2,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_HOL_Ozero__class_Ozero(X3) = X1
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X3),c_HOL_Otimes__class_Otimes(X2,X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
fof(f3790,plain,
spl0_438,
inference(avatar_split_clause,[],[f139,f3788]) ).
fof(f3788,plain,
( spl0_438
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Power_Opower(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_Power_Opower__class_Opower(X4,X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f139,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Ozero__neq__one(X3)
| ~ class_Power_Opower(X3)
| ~ class_Ring__and__Field_Omult__zero(X3)
| ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_Power_Opower__class_Opower(X4,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
fof(f3786,plain,
spl0_437,
inference(avatar_split_clause,[],[f110,f3784]) ).
fof(f3784,plain,
( spl0_437
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| X4 = X5
| c_HOL_Ouminus__class_Ouminus(X5,X3) = X4
| c_HOL_Otimes__class_Otimes(X4,X4,X3) != c_HOL_Otimes__class_Otimes(X5,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f110,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oidom(X3)
| X4 = X5
| c_HOL_Ouminus__class_Ouminus(X5,X3) = X4
| c_HOL_Otimes__class_Otimes(X4,X4,X3) != c_HOL_Otimes__class_Otimes(X5,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
fof(f3782,plain,
spl0_436,
inference(avatar_split_clause,[],[f107,f3780]) ).
fof(f3780,plain,
( spl0_436
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f107,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
fof(f3778,plain,
spl0_435,
inference(avatar_split_clause,[],[f81,f3776]) ).
fof(f3776,plain,
( spl0_435
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f81,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__divide_0) ).
fof(f3774,plain,
spl0_434,
inference(avatar_split_clause,[],[f77,f3772]) ).
fof(f3772,plain,
( spl0_434
<=> ! [X14,X3,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X14,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X14,X3),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f77,axiom,
! [X2,X3,X1,X14] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X14,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X14,X3),X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
fof(f3770,plain,
spl0_433,
inference(avatar_split_clause,[],[f47,f3768]) ).
fof(f3768,plain,
( spl0_433
<=> ! [X3,X17,X16,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X2,X1,X3)
| c_lessequals(X17,X16,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X16,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f47,axiom,
! [X2,X3,X1,X16,X17] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X2,X1,X3)
| c_lessequals(X17,X16,X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) != c_HOL_Ominus__class_Ominus(X16,X17,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
fof(f3677,plain,
( spl0_432
| ~ spl0_374
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f3354,f3297,f3012,f3675]) ).
fof(f3675,plain,
( spl0_432
<=> ! [X0] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f3354,plain,
( ! [X0] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_374
| ~ spl0_394 ),
inference(resolution,[],[f3298,f3013]) ).
fof(f3641,plain,
spl0_431,
inference(avatar_split_clause,[],[f274,f3639]) ).
fof(f3639,plain,
( spl0_431
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f274,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__leI_0) ).
fof(f3637,plain,
spl0_430,
inference(avatar_split_clause,[],[f116,f3635]) ).
fof(f3635,plain,
( spl0_430
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),X8,X3)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(X8,c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f116,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),X8,X3)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(X8,c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).
fof(f3633,plain,
spl0_429,
inference(avatar_split_clause,[],[f108,f3631]) ).
fof(f3631,plain,
( spl0_429
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Olordered__ring(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f108,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Olordered__ring(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).
fof(f3629,plain,
spl0_428,
inference(avatar_split_clause,[],[f91,f3627]) ).
fof(f3627,plain,
( spl0_428
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X4,X5,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f91,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X4,X5,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
fof(f3625,plain,
spl0_427,
inference(avatar_split_clause,[],[f60,f3623]) ).
fof(f3623,plain,
( spl0_427
<=> ! [X2,X1,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,X3),c_RealVector_Onorm__class_Onorm(X2,X3),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f60,axiom,
! [X2,X3,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,X3),c_RealVector_Onorm__class_Onorm(X2,X3),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult__ineq_0) ).
fof(f3621,plain,
spl0_426,
inference(avatar_split_clause,[],[f57,f3619]) ).
fof(f3619,plain,
( spl0_426
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f57,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq4_0) ).
fof(f3617,plain,
spl0_425,
inference(avatar_split_clause,[],[f5,f3615]) ).
fof(f3615,plain,
( spl0_425
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f5,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).
fof(f3507,plain,
( spl0_424
| ~ spl0_227
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f3046,f3012,f1682,f3505]) ).
fof(f3505,plain,
( spl0_424
<=> ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_sko__local__Xthat__1(v_c____,v_cs____,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f1682,plain,
( spl0_227
<=> ! [X28] : c_lessequals(X28,c_RealVector_Onorm__class_Onorm(v_sko__local__Xthat__1(v_c____,v_cs____,X28),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f3046,plain,
( ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_sko__local__Xthat__1(v_c____,v_cs____,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_227
| ~ spl0_374 ),
inference(resolution,[],[f3013,f1683]) ).
fof(f1683,plain,
( ! [X28] : c_lessequals(X28,c_RealVector_Onorm__class_Onorm(v_sko__local__Xthat__1(v_c____,v_cs____,X28),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_227 ),
inference(avatar_component_clause,[],[f1682]) ).
fof(f3475,plain,
spl0_423,
inference(avatar_split_clause,[],[f595,f3473]) ).
fof(f3473,plain,
( spl0_423
<=> ! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f595,plain,
! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
inference(duplicate_literal_removal,[],[f377]) ).
fof(f377,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f3471,plain,
spl0_422,
inference(avatar_split_clause,[],[f402,f3469]) ).
fof(f3469,plain,
( spl0_422
<=> ! [X27,X28,X14] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),X28,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X27,X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X27,X28),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f402,axiom,
! [X28,X14,X27] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X14,tc_Complex_Ocomplex),X28,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X27,X14,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X27,X28),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__bound__exists_1) ).
fof(f3467,plain,
( spl0_421
| ~ spl0_278
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f3043,f3012,f2042,f3465]) ).
fof(f3043,plain,
( ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_278
| ~ spl0_374 ),
inference(resolution,[],[f3013,f2043]) ).
fof(f3463,plain,
spl0_420,
inference(avatar_split_clause,[],[f320,f3461]) ).
fof(f3461,plain,
( spl0_420
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f320,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
fof(f3459,plain,
spl0_419,
inference(avatar_split_clause,[],[f319,f3457]) ).
fof(f3457,plain,
( spl0_419
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f319,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).
fof(f3455,plain,
spl0_418,
inference(avatar_split_clause,[],[f306,f3453]) ).
fof(f3453,plain,
( spl0_418
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X4,X6,X3),X3) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f306,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X4,X6,X3),X3) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X4,X3),X6,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).
fof(f3451,plain,
spl0_417,
inference(avatar_split_clause,[],[f304,f3449]) ).
fof(f3449,plain,
( spl0_417
<=> ! [X5,X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X8
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X5,X8,X3),X8,X3) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f304,axiom,
! [X3,X8,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X8
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X5,X8,X3),X8,X3) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
fof(f3447,plain,
spl0_416,
inference(avatar_split_clause,[],[f302,f3445]) ).
fof(f3445,plain,
( spl0_416
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f302,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
fof(f3443,plain,
spl0_415,
inference(avatar_split_clause,[],[f293,f3441]) ).
fof(f3441,plain,
( spl0_415
<=> ! [X6,X4,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X4,X6,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X4,c_Power_Opower__class_Opower(X4,X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f293,axiom,
! [X3,X6,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X4,X6,X3),X4,X3) = c_HOL_Otimes__class_Otimes(X4,c_Power_Opower__class_Opower(X4,X6,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).
fof(f3439,plain,
spl0_414,
inference(avatar_split_clause,[],[f283,f3437]) ).
fof(f3437,plain,
( spl0_414
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X4,X3),X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f283,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X4,X3),X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__inverse_0) ).
fof(f3435,plain,
spl0_413,
inference(avatar_split_clause,[],[f257,f3433]) ).
fof(f3433,plain,
( spl0_413
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f257,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
fof(f3431,plain,
spl0_412,
inference(avatar_split_clause,[],[f249,f3429]) ).
fof(f3429,plain,
( spl0_412
<=> ! [X14,X3,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X14,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X14,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f249,axiom,
! [X2,X3,X1,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X14,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X3),X14,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
fof(f3427,plain,
spl0_411,
inference(avatar_split_clause,[],[f248,f3425]) ).
fof(f3425,plain,
( spl0_411
<=> ! [X3,X23,X25,X26] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X25,X26,X3),X3) = c_HOL_Otimes__class_Otimes(X25,c_HOL_Otimes__class_Otimes(X23,X26,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f248,axiom,
! [X3,X26,X25,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X23,c_HOL_Otimes__class_Otimes(X25,X26,X3),X3) = c_HOL_Otimes__class_Otimes(X25,c_HOL_Otimes__class_Otimes(X23,X26,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f3408,plain,
spl0_410,
inference(avatar_split_clause,[],[f245,f3406]) ).
fof(f3406,plain,
( spl0_410
<=> ! [X24,X23,X3,X25] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X3),X25,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X25,X3),X24,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f245,axiom,
! [X3,X24,X25,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X24,X3),X25,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X23,X25,X3),X24,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f3404,plain,
spl0_409,
inference(avatar_split_clause,[],[f244,f3402]) ).
fof(f3402,plain,
( spl0_409
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X4,X5,X3),X8,X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f244,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X4,X5,X3),X8,X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f3400,plain,
spl0_408,
inference(avatar_split_clause,[],[f242,f3398]) ).
fof(f3398,plain,
( spl0_408
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X4,X6,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X4,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f242,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X4,X6,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X4,X3),X6,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inverse_0) ).
fof(f3396,plain,
spl0_407,
inference(avatar_split_clause,[],[f226,f3394]) ).
fof(f3394,plain,
( spl0_407
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f226,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult_0) ).
fof(f3392,plain,
spl0_406,
inference(avatar_split_clause,[],[f143,f3390]) ).
fof(f3390,plain,
( spl0_406
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Otimes__class_Otimes(X4,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f143,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Otimes__class_Otimes(X4,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
fof(f3388,plain,
spl0_405,
inference(avatar_split_clause,[],[f141,f3386]) ).
fof(f3386,plain,
( spl0_405
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Otimes__class_Otimes(X4,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f141,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) = X5
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Otimes__class_Otimes(X4,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
fof(f3384,plain,
spl0_404,
inference(avatar_split_clause,[],[f101,f3382]) ).
fof(f3382,plain,
( spl0_404
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X5,X8,X3),X3) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X4,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f101,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X5,X8,X3),X3) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X4,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f3380,plain,
spl0_403,
inference(avatar_split_clause,[],[f100,f3378]) ).
fof(f3378,plain,
( spl0_403
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X8,X3) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f100,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X8,X3) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f3376,plain,
spl0_402,
inference(avatar_split_clause,[],[f99,f3374]) ).
fof(f3374,plain,
( spl0_402
<=> ! [X14,X3,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X14,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X14,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f99,axiom,
! [X2,X3,X1,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X14,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X3),X14,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
fof(f3372,plain,
spl0_401,
inference(avatar_split_clause,[],[f98,f3370]) ).
fof(f3370,plain,
( spl0_401
<=> ! [X14,X3,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X14,X3),X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X14,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f98,axiom,
! [X2,X3,X1,X14] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X14,X3),X3) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X14,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f3353,plain,
spl0_400,
inference(avatar_split_clause,[],[f97,f3351]) ).
fof(f3351,plain,
( spl0_400
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X8,X3) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f97,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Oab__semigroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X8,X3) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f3349,plain,
spl0_399,
inference(avatar_split_clause,[],[f95,f3347]) ).
fof(f3347,plain,
( spl0_399
<=> ! [X3,X4,X5,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X8,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X8,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f95,axiom,
! [X3,X8,X4,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X8,X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X8,X3),X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f3345,plain,
spl0_398,
inference(avatar_split_clause,[],[f94,f3343]) ).
fof(f3343,plain,
( spl0_398
<=> ! [X3,X4,X9,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X8,X9,X3),X3) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X4,X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f94,axiom,
! [X3,X8,X9,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X8,X9,X3),X3) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X4,X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f3341,plain,
spl0_397,
inference(avatar_split_clause,[],[f90,f3339]) ).
fof(f3339,plain,
( spl0_397
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(X4,X5,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f90,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Odivide(X4,X5,X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
fof(f3337,plain,
spl0_396,
inference(avatar_split_clause,[],[f21,f3335]) ).
fof(f3335,plain,
( spl0_396
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f21,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
fof(f3333,plain,
spl0_395,
inference(avatar_split_clause,[],[f4,f3331]) ).
fof(f3331,plain,
( spl0_395
<=> ! [X2,X1,X3] :
( ~ class_RealVector_Oreal__normed__div__algebra(X3)
| c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,X3),c_RealVector_Onorm__class_Onorm(X2,X3),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f4,axiom,
! [X2,X3,X1] :
( ~ class_RealVector_Oreal__normed__div__algebra(X3)
| c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,X3),X3) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,X3),c_RealVector_Onorm__class_Onorm(X2,X3),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult_0) ).
fof(f3299,plain,
( ~ spl0_43
| spl0_394
| ~ spl0_180
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f3053,f3012,f1441,f3297,f806]) ).
fof(f1441,plain,
( spl0_180
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X4,c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f3053,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) )
| ~ spl0_180
| ~ spl0_374 ),
inference(resolution,[],[f3013,f1442]) ).
fof(f1442,plain,
( ! [X3,X4] :
( c_lessequals(X4,c_HOL_Oabs__class_Oabs(X4,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3) )
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f1441]) ).
fof(f3215,plain,
( spl0_393
| ~ spl0_181
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f3048,f3012,f1445,f3213]) ).
fof(f1445,plain,
( spl0_181
<=> ! [X14,X15] :
( c_lessequals(X14,X15,tc_RealDef_Oreal)
| c_lessequals(X15,X14,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f3048,plain,
( ! [X0,X1] :
( c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X1,c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_181
| ~ spl0_374 ),
inference(resolution,[],[f3013,f1446]) ).
fof(f1446,plain,
( ! [X14,X15] :
( c_lessequals(X14,X15,tc_RealDef_Oreal)
| c_lessequals(X15,X14,tc_RealDef_Oreal) )
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f1445]) ).
fof(f3197,plain,
spl0_392,
inference(avatar_split_clause,[],[f385,f3195]) ).
fof(f3195,plain,
( spl0_392
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f385,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).
fof(f3193,plain,
spl0_391,
inference(avatar_split_clause,[],[f384,f3191]) ).
fof(f3191,plain,
( spl0_391
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f384,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_1) ).
fof(f3189,plain,
spl0_390,
inference(avatar_split_clause,[],[f326,f3187]) ).
fof(f3187,plain,
( spl0_390
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f326,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).
fof(f3185,plain,
spl0_389,
inference(avatar_split_clause,[],[f325,f3183]) ).
fof(f3183,plain,
( spl0_389
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f325,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).
fof(f3181,plain,
spl0_388,
inference(avatar_split_clause,[],[f277,f3179]) ).
fof(f3179,plain,
( spl0_388
<=> ! [X14,X3,X2,X1] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| X2 = X14
| c_HOL_Oplus__class_Oplus(X1,X2,X3) != c_HOL_Oplus__class_Oplus(X1,X14,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f277,axiom,
! [X2,X3,X1,X14] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| X2 = X14
| c_HOL_Oplus__class_Oplus(X1,X2,X3) != c_HOL_Oplus__class_Oplus(X1,X14,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f3177,plain,
spl0_387,
inference(avatar_split_clause,[],[f186,f3175]) ).
fof(f3175,plain,
( spl0_387
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X4,X3),c_HOL_Oplus__class_Oplus(X8,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f186,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X4,X3),c_HOL_Oplus__class_Oplus(X8,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f3173,plain,
spl0_386,
inference(avatar_split_clause,[],[f185,f3171]) ).
fof(f3171,plain,
( spl0_386
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X8,X3),c_HOL_Oplus__class_Oplus(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f185,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X8,X3),c_HOL_Oplus__class_Oplus(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f3157,plain,
spl0_385,
inference(avatar_split_clause,[],[f184,f3155]) ).
fof(f3155,plain,
( spl0_385
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X4,X3),c_HOL_Oplus__class_Oplus(X8,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f184,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X4,X3),c_HOL_Oplus__class_Oplus(X8,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f3153,plain,
spl0_384,
inference(avatar_split_clause,[],[f183,f3151]) ).
fof(f3151,plain,
( spl0_384
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X4,X3),c_HOL_Oplus__class_Oplus(X8,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f183,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X4,X3),c_HOL_Oplus__class_Oplus(X8,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f3149,plain,
spl0_383,
inference(avatar_split_clause,[],[f182,f3147]) ).
fof(f3147,plain,
( spl0_383
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X8,X3),c_HOL_Oplus__class_Oplus(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f182,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X8,X3),c_HOL_Oplus__class_Oplus(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f3145,plain,
spl0_382,
inference(avatar_split_clause,[],[f181,f3143]) ).
fof(f3143,plain,
( spl0_382
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X8,X3),c_HOL_Oplus__class_Oplus(X5,X8,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f181,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X8,X3),c_HOL_Oplus__class_Oplus(X5,X8,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f3141,plain,
spl0_381,
inference(avatar_split_clause,[],[f171,f3139]) ).
fof(f3139,plain,
( spl0_381
<=> ! [X2,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X3),c_HOL_Otimes__class_Otimes(X2,X2,X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f171,axiom,
! [X2,X3,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X3),c_HOL_Otimes__class_Otimes(X2,X2,X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
fof(f3137,plain,
spl0_380,
inference(avatar_split_clause,[],[f165,f3135]) ).
fof(f3135,plain,
( spl0_380
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f165,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
fof(f3133,plain,
spl0_379,
inference(avatar_split_clause,[],[f164,f3131]) ).
fof(f3131,plain,
( spl0_379
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f164,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
fof(f3129,plain,
spl0_378,
inference(avatar_split_clause,[],[f80,f3127]) ).
fof(f3127,plain,
( spl0_378
<=> ! [X14,X3,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(X14,X3) = X1
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X14,X3),X3) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f80,axiom,
! [X2,X3,X1,X14] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ouminus__class_Ouminus(X14,X3) = X1
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X14,X3),X3) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
fof(f3125,plain,
spl0_377,
inference(avatar_split_clause,[],[f23,f3123]) ).
fof(f3123,plain,
( spl0_377
<=> ! [X4,X5,X8] :
( X4 = X5
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X8
| c_HOL_Otimes__class_Otimes(X8,X4,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X8,X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f23,axiom,
! [X8,X4,X5] :
( X4 = X5
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X8
| c_HOL_Otimes__class_Otimes(X8,X4,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X8,X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__left__cancel_0) ).
fof(f3121,plain,
spl0_376,
inference(avatar_split_clause,[],[f22,f3119]) ).
fof(f3119,plain,
( spl0_376
<=> ! [X4,X5,X8] :
( X4 = X5
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X8
| c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X5,X8,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f22,axiom,
! [X8,X4,X5] :
( X4 = X5
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X8
| c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X5,X8,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__right__cancel_0) ).
fof(f3117,plain,
( spl0_375
| ~ spl0_2
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f3042,f3012,f602,f3115]) ).
fof(f3042,plain,
( ! [X0] : c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_2
| ~ spl0_374 ),
inference(resolution,[],[f3013,f603]) ).
fof(f3014,plain,
( ~ spl0_90
| spl0_374
| ~ spl0_2
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f2740,f2550,f602,f3012,f1041]) ).
fof(f1041,plain,
( spl0_90
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f2550,plain,
( spl0_337
<=> ! [X14,X3,X2,X1] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X14,X2,X3)
| c_lessequals(X14,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f2740,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),X1,tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) )
| ~ spl0_2
| ~ spl0_337 ),
inference(resolution,[],[f2551,f603]) ).
fof(f2551,plain,
( ! [X2,X3,X1,X14] :
( ~ c_lessequals(X14,X2,X3)
| ~ c_lessequals(X2,X1,X3)
| ~ class_Orderings_Oorder(X3)
| c_lessequals(X14,X1,X3) )
| ~ spl0_337 ),
inference(avatar_component_clause,[],[f2550]) ).
fof(f2968,plain,
spl0_373,
inference(avatar_split_clause,[],[f404,f2966]) ).
fof(f2966,plain,
( spl0_373
<=> ! [X15] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,v_sko__local__XpCons__Xhyps__1(v_cs____),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,X15,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f404,axiom,
! [X15] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,v_sko__local__XpCons__Xhyps__1(v_cs____),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,X15,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons_Ohyps_0) ).
fof(f2964,plain,
spl0_372,
inference(avatar_split_clause,[],[f403,f2962]) ).
fof(f2962,plain,
( spl0_372
<=> ! [X15] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,v_sko__local__XpCons__1(v_cs____),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,X15,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f403,axiom,
! [X15] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,v_sko__local__XpCons__1(v_cs____),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,X15,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons_0) ).
fof(f2960,plain,
spl0_371,
inference(avatar_split_clause,[],[f324,f2958]) ).
fof(f2958,plain,
( spl0_371
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f324,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f2956,plain,
spl0_370,
inference(avatar_split_clause,[],[f323,f2954]) ).
fof(f2954,plain,
( spl0_370
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f323,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oplus__class_Oplus(X4,X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f2952,plain,
spl0_369,
inference(avatar_split_clause,[],[f322,f2950]) ).
fof(f2950,plain,
( spl0_369
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X4,X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f322,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X4,X6,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
fof(f2948,plain,
spl0_368,
inference(avatar_split_clause,[],[f321,f2946]) ).
fof(f2946,plain,
( spl0_368
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X4,X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f321,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X4,X6,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
fof(f2944,plain,
spl0_367,
inference(avatar_split_clause,[],[f318,f2942]) ).
fof(f2942,plain,
( spl0_367
<=> ! [X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X8,X3),X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f318,axiom,
! [X3,X8] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X8,X3),X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
fof(f2940,plain,
spl0_366,
inference(avatar_split_clause,[],[f310,f2938]) ).
fof(f2938,plain,
( spl0_366
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f310,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
fof(f2936,plain,
spl0_365,
inference(avatar_split_clause,[],[f300,f2934]) ).
fof(f2934,plain,
( spl0_365
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Otimes__class_Otimes(X4,X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f300,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Otimes__class_Otimes(X4,X4,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
fof(f2932,plain,
spl0_364,
inference(avatar_split_clause,[],[f265,f2930]) ).
fof(f2930,plain,
( spl0_364
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Otimes__class_Otimes(X4,X5,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f265,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Otimes__class_Otimes(X4,X5,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
fof(f2928,plain,
( spl0_363
| ~ spl0_43
| ~ spl0_2
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f2669,f2497,f602,f806,f2926]) ).
fof(f2926,plain,
( spl0_363
<=> ! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f2497,plain,
( spl0_325
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f2669,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_2
| ~ spl0_325 ),
inference(resolution,[],[f2498,f603]) ).
fof(f2498,plain,
( ! [X3,X4,X5] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) )
| ~ spl0_325 ),
inference(avatar_component_clause,[],[f2497]) ).
fof(f2924,plain,
spl0_362,
inference(avatar_split_clause,[],[f264,f2922]) ).
fof(f2922,plain,
( spl0_362
<=> ! [X5,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Otimes__class_Otimes(X5,X5,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f264,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Otimes__class_Otimes(X5,X5,X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
fof(f2920,plain,
spl0_361,
inference(avatar_split_clause,[],[f262,f2918]) ).
fof(f2918,plain,
( spl0_361
<=> ! [X4,X5,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f262,axiom,
! [X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
fof(f2916,plain,
spl0_360,
inference(avatar_split_clause,[],[f260,f2914]) ).
fof(f2914,plain,
( spl0_360
<=> ! [X4,X5,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f260,axiom,
! [X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
fof(f2912,plain,
spl0_359,
inference(avatar_split_clause,[],[f258,f2910]) ).
fof(f2910,plain,
( spl0_359
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f258,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
fof(f2908,plain,
spl0_358,
inference(avatar_split_clause,[],[f243,f2906]) ).
fof(f2906,plain,
( spl0_358
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f243,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
fof(f2904,plain,
spl0_357,
inference(avatar_split_clause,[],[f233,f2902]) ).
fof(f2902,plain,
( spl0_357
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(X5,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f233,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X4,X5,X3),X3) = c_HOL_Oinverse__class_Odivide(X5,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
fof(f2900,plain,
spl0_356,
inference(avatar_split_clause,[],[f229,f2898]) ).
fof(f2898,plain,
( spl0_356
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f229,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
fof(f2896,plain,
spl0_355,
inference(avatar_split_clause,[],[f228,f2894]) ).
fof(f2894,plain,
( spl0_355
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f228,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Oring(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X5,X3),X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
fof(f2892,plain,
spl0_354,
inference(avatar_split_clause,[],[f222,f2890]) ).
fof(f2890,plain,
( spl0_354
<=> ! [X4,X8,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X8
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X8,X3),X8,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f222,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = X8
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X8,X3),X8,X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
fof(f2888,plain,
spl0_353,
inference(avatar_split_clause,[],[f201,f2886]) ).
fof(f2886,plain,
( spl0_353
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f201,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f2863,plain,
spl0_352,
inference(avatar_split_clause,[],[f200,f2861]) ).
fof(f2861,plain,
( spl0_352
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f200,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f2859,plain,
spl0_351,
inference(avatar_split_clause,[],[f195,f2857]) ).
fof(f2857,plain,
( spl0_351
<=> ! [X4,X27,X3] :
( ~ class_HOL_Ozero(X3)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X27
| c_Polynomial_OpCons(X4,X27,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f195,axiom,
! [X3,X27,X4] :
( ~ class_HOL_Ozero(X3)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X27
| c_Polynomial_OpCons(X4,X27,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).
fof(f2855,plain,
spl0_350,
inference(avatar_split_clause,[],[f89,f2853]) ).
fof(f2853,plain,
( spl0_350
<=> ! [X2,X1,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f89,axiom,
! [X2,X3,X1] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X3),X2,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
fof(f2851,plain,
spl0_349,
inference(avatar_split_clause,[],[f83,f2849]) ).
fof(f2849,plain,
( spl0_349
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X4,X6,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f83,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X4,X6,X3),X3) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__abs_0) ).
fof(f2847,plain,
spl0_348,
inference(avatar_split_clause,[],[f82,f2845]) ).
fof(f2845,plain,
( spl0_348
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X4,X3),X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f82,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X4,X3),X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__inverse_0) ).
fof(f2843,plain,
spl0_347,
inference(avatar_split_clause,[],[f49,f2841]) ).
fof(f2841,plain,
( spl0_347
<=> ! [X4,X5,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X5,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f49,axiom,
! [X3,X4,X5] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X5,X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__commute_0) ).
fof(f2839,plain,
spl0_346,
inference(avatar_split_clause,[],[f25,f2837]) ).
fof(f2837,plain,
( spl0_346
<=> ! [X11,X12,X10] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X11,tc_RealDef_Oreal),X12,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X11,X12,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f25,axiom,
! [X10,X11,X12] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X10,X11,tc_RealDef_Oreal),X12,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X10,c_HOL_Otimes__class_Otimes(X11,X12,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__assoc_0) ).
fof(f2835,plain,
spl0_345,
inference(avatar_split_clause,[],[f24,f2833]) ).
fof(f2833,plain,
( spl0_345
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f24,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
fof(f2831,plain,
spl0_344,
inference(avatar_split_clause,[],[f3,f2829]) ).
fof(f2829,plain,
( spl0_344
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f3,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_0) ).
fof(f2827,plain,
spl0_343,
inference(avatar_split_clause,[],[f2,f2825]) ).
fof(f2825,plain,
( spl0_343
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X2
| c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f2,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X2
| c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_1) ).
fof(f2823,plain,
( spl0_342
| ~ spl0_50
| ~ spl0_2
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f2634,f2489,f602,f841,f2821]) ).
fof(f2634,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_2
| ~ spl0_323 ),
inference(resolution,[],[f2490,f603]) ).
fof(f2605,plain,
( spl0_341
| ~ spl0_43
| ~ spl0_2
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2069,f1987,f602,f806,f2602]) ).
fof(f1987,plain,
( spl0_274
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2069,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex) = c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_2
| ~ spl0_274 ),
inference(resolution,[],[f1988,f603]) ).
fof(f1988,plain,
( ! [X3,X4] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4 )
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f1987]) ).
fof(f2569,plain,
spl0_340,
inference(avatar_split_clause,[],[f416,f2567]) ).
fof(f2567,plain,
( spl0_340
<=> ! [X5,X4,X29,X27,X3] :
( ~ class_HOL_Ozero(X3)
| X27 = X29
| c_Polynomial_OpCons(X4,X27,X3) != c_Polynomial_OpCons(X5,X29,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f416,axiom,
! [X3,X29,X27,X4,X5] :
( ~ class_HOL_Ozero(X3)
| X27 = X29
| c_Polynomial_OpCons(X4,X27,X3) != c_Polynomial_OpCons(X5,X29,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).
fof(f2565,plain,
spl0_339,
inference(avatar_split_clause,[],[f415,f2563]) ).
fof(f2563,plain,
( spl0_339
<=> ! [X5,X4,X29,X27,X3] :
( ~ class_HOL_Ozero(X3)
| X4 = X5
| c_Polynomial_OpCons(X4,X27,X3) != c_Polynomial_OpCons(X5,X29,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f415,axiom,
! [X3,X29,X27,X4,X5] :
( ~ class_HOL_Ozero(X3)
| X4 = X5
| c_Polynomial_OpCons(X4,X27,X3) != c_Polynomial_OpCons(X5,X29,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).
fof(f2561,plain,
spl0_338,
inference(avatar_split_clause,[],[f410,f2559]) ).
fof(f2559,plain,
( spl0_338
<=> ! [X14,X3,X2,X1] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X14,X3)
| c_lessequals(X1,X14,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f410,axiom,
! [X2,X3,X1,X14] :
( ~ class_Orderings_Opreorder(X3)
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X14,X3)
| c_lessequals(X1,X14,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f2552,plain,
spl0_337,
inference(avatar_split_clause,[],[f409,f2550]) ).
fof(f409,axiom,
! [X2,X3,X1,X14] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X2,X1,X3)
| ~ c_lessequals(X14,X2,X3)
| c_lessequals(X14,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f2548,plain,
spl0_336,
inference(avatar_split_clause,[],[f390,f2546]) ).
fof(f2546,plain,
( spl0_336
<=> ! [X4,X27,X3] :
( ~ class_HOL_Ozero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_Polynomial_OpCons(X4,X27,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f390,axiom,
! [X3,X27,X4] :
( ~ class_HOL_Ozero(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_Polynomial_OpCons(X4,X27,X3) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).
fof(f2544,plain,
spl0_335,
inference(avatar_split_clause,[],[f366,f2542]) ).
fof(f2542,plain,
( spl0_335
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f366,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
fof(f2540,plain,
spl0_334,
inference(avatar_split_clause,[],[f365,f2538]) ).
fof(f2538,plain,
( spl0_334
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f365,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
fof(f2536,plain,
spl0_333,
inference(avatar_split_clause,[],[f331,f2534]) ).
fof(f2534,plain,
( spl0_333
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f331,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
fof(f2532,plain,
spl0_332,
inference(avatar_split_clause,[],[f330,f2530]) ).
fof(f2530,plain,
( spl0_332
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f330,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
fof(f2528,plain,
spl0_331,
inference(avatar_split_clause,[],[f297,f2526]) ).
fof(f2526,plain,
( spl0_331
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X5,X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X4,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f297,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X5,X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X4,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
fof(f2524,plain,
spl0_330,
inference(avatar_split_clause,[],[f296,f2522]) ).
fof(f2522,plain,
( spl0_330
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = X5
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X4,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f296,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(X4,X3) = X5
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X4,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).
fof(f2520,plain,
spl0_329,
inference(avatar_split_clause,[],[f280,f2518]) ).
fof(f2518,plain,
( spl0_329
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X5 = X8
| c_HOL_Oplus__class_Oplus(X8,X4,X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f280,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X5 = X8
| c_HOL_Oplus__class_Oplus(X8,X4,X3) != c_HOL_Oplus__class_Oplus(X5,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f2516,plain,
spl0_328,
inference(avatar_split_clause,[],[f279,f2514]) ).
fof(f2514,plain,
( spl0_328
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X5 = X8
| c_HOL_Oplus__class_Oplus(X4,X5,X3) != c_HOL_Oplus__class_Oplus(X4,X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f279,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X3)
| X5 = X8
| c_HOL_Oplus__class_Oplus(X4,X5,X3) != c_HOL_Oplus__class_Oplus(X4,X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f2507,plain,
spl0_327,
inference(avatar_split_clause,[],[f278,f2505]) ).
fof(f2505,plain,
( spl0_327
<=> ! [X3,X4,X5,X8] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| X5 = X8
| c_HOL_Oplus__class_Oplus(X4,X5,X3) != c_HOL_Oplus__class_Oplus(X4,X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f278,axiom,
! [X3,X8,X4,X5] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X3)
| X5 = X8
| c_HOL_Oplus__class_Oplus(X4,X5,X3) != c_HOL_Oplus__class_Oplus(X4,X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f2503,plain,
spl0_326,
inference(avatar_split_clause,[],[f239,f2501]) ).
fof(f2501,plain,
( spl0_326
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| X4 = X5
| c_HOL_Oinverse__class_Oinverse(X4,X3) != c_HOL_Oinverse__class_Oinverse(X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f239,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| X4 = X5
| c_HOL_Oinverse__class_Oinverse(X4,X3) != c_HOL_Oinverse__class_Oinverse(X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
fof(f2499,plain,
spl0_325,
inference(avatar_split_clause,[],[f231,f2497]) ).
fof(f231,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
fof(f2495,plain,
spl0_324,
inference(avatar_split_clause,[],[f192,f2493]) ).
fof(f2493,plain,
( spl0_324
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X5,c_HOL_Ouminus__class_Ouminus(X4,X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f192,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X5,c_HOL_Ouminus__class_Ouminus(X4,X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
fof(f2491,plain,
spl0_323,
inference(avatar_split_clause,[],[f190,f2489]) ).
fof(f190,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
fof(f2487,plain,
spl0_322,
inference(avatar_split_clause,[],[f188,f2485]) ).
fof(f2485,plain,
( spl0_322
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f188,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
fof(f2483,plain,
spl0_321,
inference(avatar_split_clause,[],[f187,f2481]) ).
fof(f2481,plain,
( spl0_321
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f187,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X5,X3),c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
fof(f2479,plain,
spl0_320,
inference(avatar_split_clause,[],[f175,f2477]) ).
fof(f2477,plain,
( spl0_320
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Ouminus__class_Ouminus(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f175,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Ouminus__class_Ouminus(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).
fof(f2475,plain,
spl0_319,
inference(avatar_split_clause,[],[f145,f2473]) ).
fof(f2473,plain,
( spl0_319
<=> ! [X4,X1,X3] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oplus__class_Oplus(X1,X4,X3) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f145,axiom,
! [X3,X1,X4] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oplus__class_Oplus(X1,X4,X3) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f2471,plain,
spl0_318,
inference(avatar_split_clause,[],[f61,f2469]) ).
fof(f2469,plain,
( spl0_318
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Ominus__class_Ominus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f61,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Ominus__class_Ominus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__prts_0) ).
fof(f2467,plain,
( spl0_317
| ~ spl0_51
| ~ spl0_2
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f2383,f2236,f602,f846,f2464]) ).
fof(f2464,plain,
( spl0_317
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f2236,plain,
( spl0_307
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Ozero__class_Ozero(X3) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f2383,plain,
( ~ class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_2
| ~ spl0_307 ),
inference(resolution,[],[f2237,f603]) ).
fof(f2237,plain,
( ! [X3,X4] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3) )
| ~ spl0_307 ),
inference(avatar_component_clause,[],[f2236]) ).
fof(f2462,plain,
spl0_316,
inference(avatar_split_clause,[],[f46,f2460]) ).
fof(f2460,plain,
( spl0_316
<=> ! [X2,X1,X3] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f46,axiom,
! [X2,X3,X1] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ominus__class_Ominus(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f2458,plain,
spl0_315,
inference(avatar_split_clause,[],[f30,f2456]) ).
fof(f2456,plain,
( spl0_315
<=> ! [X17,X3,X16,X1] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X16 = X17
| c_HOL_Ominus__class_Ominus(X1,X1,X3) != c_HOL_Ominus__class_Ominus(X16,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f30,axiom,
! [X3,X1,X16,X17] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X16 = X17
| c_HOL_Ominus__class_Ominus(X1,X1,X3) != c_HOL_Ominus__class_Ominus(X16,X17,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
fof(f2454,plain,
spl0_314,
inference(avatar_split_clause,[],[f20,f2452]) ).
fof(f2452,plain,
( spl0_314
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f20,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X4,X5,X3)
| c_lessequals(c_HOL_Ominus__class_Ominus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
fof(f2450,plain,
spl0_313,
inference(avatar_split_clause,[],[f19,f2448]) ).
fof(f2448,plain,
( spl0_313
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f19,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X4,X5,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
fof(f2369,plain,
( spl0_312
| ~ spl0_51
| ~ spl0_2
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2051,f1983,f602,f846,f2366]) ).
fof(f2366,plain,
( spl0_312
<=> c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f1983,plain,
( spl0_273
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2051,plain,
( ~ class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_2
| ~ spl0_273 ),
inference(resolution,[],[f1984,f603]) ).
fof(f1984,plain,
( ! [X3,X4] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3) = X4 )
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f1983]) ).
fof(f2269,plain,
( spl0_311
| ~ spl0_276
| ~ spl0_278 ),
inference(avatar_split_clause,[],[f2133,f2042,f1995,f2267]) ).
fof(f2267,plain,
( spl0_311
<=> ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f2133,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_276
| ~ spl0_278 ),
inference(resolution,[],[f2043,f1996]) ).
fof(f2250,plain,
spl0_310,
inference(avatar_split_clause,[],[f419,f2248]) ).
fof(f2248,plain,
( spl0_310
<=> ! [X2,X1,X3] :
( ~ class_Orderings_Oorder(X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f419,axiom,
! [X2,X3,X1] :
( ~ class_Orderings_Oorder(X3)
| X1 = X2
| ~ c_lessequals(X1,X2,X3)
| ~ c_lessequals(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
fof(f2246,plain,
spl0_309,
inference(avatar_split_clause,[],[f400,f2244]) ).
fof(f2244,plain,
( spl0_309
<=> ! [X1,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(X3) = X1
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f400,axiom,
! [X3,X1] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(X3) = X1
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_0) ).
fof(f2242,plain,
spl0_308,
inference(avatar_split_clause,[],[f391,f2240]) ).
fof(f2240,plain,
( spl0_308
<=> ! [X3] :
( ~ class_HOL_Ozero(X3)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f391,axiom,
! [X3] :
( ~ class_HOL_Ozero(X3)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).
fof(f2238,plain,
spl0_307,
inference(avatar_split_clause,[],[f370,f2236]) ).
fof(f370,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Ozero__class_Ozero(X3) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__iff__zero__nprt_0) ).
fof(f2234,plain,
spl0_306,
inference(avatar_split_clause,[],[f369,f2232]) ).
fof(f2232,plain,
( spl0_306
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Ozero__class_Ozero(X3) != c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f369,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Ozero__class_Ozero(X3) != c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__iff__zero__nprt_1) ).
fof(f2224,plain,
spl0_305,
inference(avatar_split_clause,[],[f368,f2222]) ).
fof(f2222,plain,
( spl0_305
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f368,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
fof(f2220,plain,
spl0_304,
inference(avatar_split_clause,[],[f311,f2218]) ).
fof(f2218,plain,
( spl0_304
<=> ! [X4,X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X4,X5,X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Oinverse__class_Oinverse(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f311,axiom,
! [X3,X4,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Oinverse__class_Odivide(X4,X5,X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Oinverse__class_Oinverse(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
fof(f2216,plain,
spl0_303,
inference(avatar_split_clause,[],[f308,f2214]) ).
fof(f2214,plain,
( spl0_303
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f308,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Oplus__class_Oplus(X4,X5,X3),X3) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
fof(f2212,plain,
spl0_302,
inference(avatar_split_clause,[],[f307,f2210]) ).
fof(f2210,plain,
( spl0_302
<=> ! [X2,X3,X14] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X14,X3),c_HOL_Oplus__class_Oplus(X2,X14,X3),X3) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f307,axiom,
! [X2,X3,X14] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X14,X3),c_HOL_Oplus__class_Oplus(X2,X14,X3),X3) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
fof(f2208,plain,
spl0_301,
inference(avatar_split_clause,[],[f287,f2206]) ).
fof(f2206,plain,
( spl0_301
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f287,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nprt__neg_0) ).
fof(f2204,plain,
spl0_300,
inference(avatar_split_clause,[],[f266,f2202]) ).
fof(f2202,plain,
( spl0_300
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f266,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(X1,X3),X3) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pprt__neg_0) ).
fof(f2200,plain,
spl0_299,
inference(avatar_split_clause,[],[f232,f2198]) ).
fof(f2198,plain,
( spl0_299
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3),X3) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f232,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),X5,X3),X3) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
fof(f2196,plain,
spl0_298,
inference(avatar_split_clause,[],[f220,f2194]) ).
fof(f2194,plain,
( spl0_298
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f220,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
fof(f2192,plain,
spl0_297,
inference(avatar_split_clause,[],[f219,f2190]) ).
fof(f2190,plain,
( spl0_297
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f219,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
fof(f2188,plain,
spl0_296,
inference(avatar_split_clause,[],[f218,f2186]) ).
fof(f2186,plain,
( spl0_296
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f218,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
fof(f2184,plain,
( spl0_295
| ~ spl0_2
| ~ spl0_276 ),
inference(avatar_split_clause,[],[f2082,f1995,f602,f2182]) ).
fof(f2082,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_2
| ~ spl0_276 ),
inference(resolution,[],[f1996,f603]) ).
fof(f2180,plain,
spl0_294,
inference(avatar_split_clause,[],[f217,f2178]) ).
fof(f2178,plain,
( spl0_294
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f217,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
fof(f2176,plain,
spl0_293,
inference(avatar_split_clause,[],[f216,f2174]) ).
fof(f2174,plain,
( spl0_293
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f216,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
fof(f2172,plain,
spl0_292,
inference(avatar_split_clause,[],[f215,f2170]) ).
fof(f2170,plain,
( spl0_292
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f215,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
fof(f2168,plain,
spl0_291,
inference(avatar_split_clause,[],[f214,f2166]) ).
fof(f2166,plain,
( spl0_291
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f214,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
fof(f2164,plain,
spl0_290,
inference(avatar_split_clause,[],[f213,f2162]) ).
fof(f2162,plain,
( spl0_290
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f213,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
fof(f2160,plain,
spl0_289,
inference(avatar_split_clause,[],[f212,f2158]) ).
fof(f212,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ozero__class_Ozero(X3) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__zero__iff__zero__pprt_0) ).
fof(f2156,plain,
spl0_288,
inference(avatar_split_clause,[],[f211,f2154]) ).
fof(f2154,plain,
( spl0_288
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ozero__class_Ozero(X3) != c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f211,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_HOL_Ozero__class_Ozero(X3) != c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__zero__iff__zero__pprt_1) ).
fof(f2152,plain,
spl0_287,
inference(avatar_split_clause,[],[f144,f2150]) ).
fof(f2150,plain,
( spl0_287
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X4,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f144,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oplus__class_Oplus(X4,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
fof(f2148,plain,
spl0_286,
inference(avatar_split_clause,[],[f138,f2146]) ).
fof(f2146,plain,
( spl0_286
<=> ! [X6,X4,X3] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_Power_Opower__class_Opower(X4,X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f138,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_Power_Opower__class_Opower(X4,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
fof(f2144,plain,
spl0_285,
inference(avatar_split_clause,[],[f131,f2142]) ).
fof(f2142,plain,
( spl0_285
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X4,X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f131,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X4,X3),X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
fof(f2132,plain,
spl0_284,
inference(avatar_split_clause,[],[f119,f2130]) ).
fof(f2130,plain,
( spl0_284
<=> ! [X6,X3] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(X6,tc_nat),X3),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f119,axiom,
! [X3,X6] :
( ~ class_Ring__and__Field_Oordered__field(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oinverse__class_Oinverse(c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(X6,tc_nat),X3),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__of__nat__fact__ge__zero_0) ).
fof(f2128,plain,
spl0_283,
inference(avatar_split_clause,[],[f38,f2126]) ).
fof(f2126,plain,
( spl0_283
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f38,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X5,X4,X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
fof(f2124,plain,
spl0_282,
inference(avatar_split_clause,[],[f12,f2122]) ).
fof(f2122,plain,
( spl0_282
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) = c_HOL_Oplus__class_Oplus(X4,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f12,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) = c_HOL_Oplus__class_Oplus(X4,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
fof(f2120,plain,
spl0_281,
inference(avatar_split_clause,[],[f11,f2118]) ).
fof(f2118,plain,
( spl0_281
<=> ! [X2,X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f11,axiom,
! [X2,X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__def_0) ).
fof(f2116,plain,
spl0_280,
inference(avatar_split_clause,[],[f10,f2114]) ).
fof(f2114,plain,
( spl0_280
<=> ! [X2,X1,X3] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f10,axiom,
! [X2,X3,X1] :
( ~ class_Int_Onumber__ring(X3)
| c_HOL_Ominus__class_Ominus(X1,X2,X3) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
fof(f2112,plain,
spl0_279,
inference(avatar_split_clause,[],[f9,f2110]) ).
fof(f2110,plain,
( spl0_279
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f9,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X4,X5,X3) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X5,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus_0) ).
fof(f2044,plain,
( ~ spl0_43
| spl0_278
| ~ spl0_2
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f2009,f1951,f602,f2042,f806]) ).
fof(f2009,plain,
( ! [X0] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_x(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal)),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) )
| ~ spl0_2
| ~ spl0_266 ),
inference(resolution,[],[f1952,f603]) ).
fof(f2005,plain,
( spl0_277
| ~ spl0_57
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1569,f1484,f876,f2002]) ).
fof(f2002,plain,
( spl0_277
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f876,plain,
( spl0_57
<=> class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1484,plain,
( spl0_190
<=> ! [X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1569,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_57
| ~ spl0_190 ),
inference(resolution,[],[f1485,f878]) ).
fof(f878,plain,
( class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f876]) ).
fof(f1485,plain,
( ! [X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X3),X3) )
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f1484]) ).
fof(f1997,plain,
spl0_276,
inference(avatar_split_clause,[],[f412,f1995]) ).
fof(f412,axiom,
! [X36,X34,X35] :
( ~ c_lessequals(X34,X36,tc_RealDef_Oreal)
| ~ c_lessequals(X36,X35,tc_RealDef_Oreal)
| c_lessequals(X34,X35,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f1993,plain,
spl0_275,
inference(avatar_split_clause,[],[f389,f1991]) ).
fof(f1991,plain,
( spl0_275
<=> ! [X1,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(X3) = X1
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f389,axiom,
! [X3,X1] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(X3) = X1
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
fof(f1989,plain,
spl0_274,
inference(avatar_split_clause,[],[f367,f1987]) ).
fof(f367,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
fof(f1985,plain,
spl0_273,
inference(avatar_split_clause,[],[f329,f1983]) ).
fof(f329,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__zero__iff__pprt__id_0) ).
fof(f1977,plain,
spl0_272,
inference(avatar_split_clause,[],[f328,f1975]) ).
fof(f1975,plain,
( spl0_272
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3) != X4
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f328,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3) != X4
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__zero__iff__pprt__id_1) ).
fof(f1973,plain,
spl0_271,
inference(avatar_split_clause,[],[f309,f1971]) ).
fof(f1971,plain,
( spl0_271
<=> ! [X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f309,axiom,
! [X3,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthetic__div__0_0) ).
fof(f1969,plain,
spl0_270,
inference(avatar_split_clause,[],[f234,f1967]) ).
fof(f1967,plain,
( spl0_270
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f234,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3),X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_prts_0) ).
fof(f1965,plain,
spl0_269,
inference(avatar_split_clause,[],[f223,f1963]) ).
fof(f1963,plain,
( spl0_269
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X4 = X5
| c_HOL_Ouminus__class_Ouminus(X5,X3) != c_HOL_Ouminus__class_Ouminus(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f223,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X4 = X5
| c_HOL_Ouminus__class_Ouminus(X5,X3) != c_HOL_Ouminus__class_Ouminus(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f1961,plain,
spl0_268,
inference(avatar_split_clause,[],[f203,f1959]) ).
fof(f1959,plain,
( spl0_268
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f203,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__iff__nprt__id_0) ).
fof(f1957,plain,
spl0_267,
inference(avatar_split_clause,[],[f202,f1955]) ).
fof(f1955,plain,
( spl0_267
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3) != X4
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f202,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3) != X4
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__iff__nprt__id_1) ).
fof(f1953,plain,
spl0_266,
inference(avatar_split_clause,[],[f189,f1951]) ).
fof(f189,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X4,X5,X3)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X3),X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
fof(f1949,plain,
spl0_265,
inference(avatar_split_clause,[],[f163,f1947]) ).
fof(f163,axiom,
! [X3,X6,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X4,X3),X6,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__abs_0) ).
fof(f1945,plain,
spl0_264,
inference(avatar_split_clause,[],[f149,f1943]) ).
fof(f1943,plain,
( spl0_264
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ouminus__class_Ouminus(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f149,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Ouminus__class_Ouminus(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
fof(f1941,plain,
spl0_263,
inference(avatar_split_clause,[],[f109,f1939]) ).
fof(f1939,plain,
( spl0_263
<=> ! [X22,X3,X6] :
( ~ class_Nat_Osemiring__char__0(X3)
| X6 = X22
| c_Nat_Osemiring__1__class_Oof__nat(X22,X3) != c_Nat_Osemiring__1__class_Oof__nat(X6,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f109,axiom,
! [X3,X6,X22] :
( ~ class_Nat_Osemiring__char__0(X3)
| X6 = X22
| c_Nat_Osemiring__1__class_Oof__nat(X22,X3) != c_Nat_Osemiring__1__class_Oof__nat(X6,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
fof(f1937,plain,
( spl0_262
| ~ spl0_2
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f1886,f1821,f602,f1935]) ).
fof(f1935,plain,
( spl0_262
<=> ! [X0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f1821,plain,
( spl0_253
<=> ! [X14,X15] :
( X14 = X15
| ~ c_lessequals(X14,X15,tc_RealDef_Oreal)
| ~ c_lessequals(X15,X14,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f1886,plain,
( ! [X0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(v_x(X0),tc_Complex_Ocomplex) = X0 )
| ~ spl0_2
| ~ spl0_253 ),
inference(resolution,[],[f1822,f603]) ).
fof(f1822,plain,
( ! [X14,X15] :
( ~ c_lessequals(X15,X14,tc_RealDef_Oreal)
| ~ c_lessequals(X14,X15,tc_RealDef_Oreal)
| X14 = X15 )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f1821]) ).
fof(f1933,plain,
spl0_261,
inference(avatar_split_clause,[],[f69,f1931]) ).
fof(f1931,plain,
( spl0_261
<=> ! [X5,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f69,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Ofield(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
fof(f1929,plain,
spl0_260,
inference(avatar_split_clause,[],[f68,f1927]) ).
fof(f1927,plain,
( spl0_260
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oabs__class_Oabs(X4,X3) != c_HOL_Ozero__class_Ozero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f68,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Oabs__class_Oabs(X4,X3) != c_HOL_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
fof(f1925,plain,
spl0_259,
inference(avatar_split_clause,[],[f65,f1923]) ).
fof(f1923,plain,
( spl0_259
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oinverse__class_Oinverse(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f65,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ozero__class_Ozero(X3) != c_HOL_Oinverse__class_Oinverse(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
fof(f1921,plain,
spl0_258,
inference(avatar_split_clause,[],[f45,f1919]) ).
fof(f1919,plain,
( spl0_258
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X4 = X5
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ozero__class_Ozero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f45,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| X4 = X5
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f1917,plain,
spl0_257,
inference(avatar_split_clause,[],[f44,f1915]) ).
fof(f1915,plain,
( spl0_257
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X4 = X5
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ozero__class_Ozero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f44,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X4 = X5
| c_HOL_Ominus__class_Ominus(X4,X5,X3) != c_HOL_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f1913,plain,
spl0_256,
inference(avatar_split_clause,[],[f1,f1911]) ).
fof(f1911,plain,
( spl0_256
<=> ! [X0,X1] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f1,axiom,
! [X0,X1] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__minus__mult__self__le_0) ).
fof(f1874,plain,
( spl0_255
| ~ spl0_118
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1567,f1480,f1181,f1872]) ).
fof(f1872,plain,
( spl0_255
<=> ! [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_255])]) ).
fof(f1181,plain,
( spl0_118
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1480,plain,
( spl0_189
<=> ! [X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,X3),X3) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1567,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_118
| ~ spl0_189 ),
inference(resolution,[],[f1481,f1183]) ).
fof(f1183,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1181]) ).
fof(f1481,plain,
( ! [X3,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,X3),X3) = X5 )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1480]) ).
fof(f1852,plain,
( spl0_254
| ~ spl0_82
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1566,f1480,f1001,f1850]) ).
fof(f1850,plain,
( spl0_254
<=> ! [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_254])]) ).
fof(f1001,plain,
( spl0_82
<=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f1566,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_82
| ~ spl0_189 ),
inference(resolution,[],[f1481,f1003]) ).
fof(f1003,plain,
( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f1001]) ).
fof(f1823,plain,
spl0_253,
inference(avatar_split_clause,[],[f420,f1821]) ).
fof(f420,axiom,
! [X14,X15] :
( X14 = X15
| ~ c_lessequals(X14,X15,tc_RealDef_Oreal)
| ~ c_lessequals(X15,X14,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f1819,plain,
spl0_252,
inference(avatar_split_clause,[],[f394,f1817]) ).
fof(f1817,plain,
( spl0_252
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f394,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__root_1) ).
fof(f1815,plain,
( spl0_251
| ~ spl0_118
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1562,f1472,f1181,f1812]) ).
fof(f1812,plain,
( spl0_251
<=> 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_251])]) ).
fof(f1472,plain,
( spl0_187
<=> ! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1562,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_118
| ~ spl0_187 ),
inference(resolution,[],[f1473,f1183]) ).
fof(f1473,plain,
( ! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f1472]) ).
fof(f1810,plain,
spl0_250,
inference(avatar_split_clause,[],[f393,f1808]) ).
fof(f1808,plain,
( spl0_250
<=> ! [X1,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f393,axiom,
! [X3,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__0_0) ).
fof(f1806,plain,
spl0_249,
inference(avatar_split_clause,[],[f292,f1804]) ).
fof(f1804,plain,
( spl0_249
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,X5,X3) = c_HOL_Oplus__class_Oplus(X5,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f292,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,X5,X3) = c_HOL_Oplus__class_Oplus(X5,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f1802,plain,
spl0_248,
inference(avatar_split_clause,[],[f290,f1800]) ).
fof(f1800,plain,
( spl0_248
<=> ! [X4,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,X8,X3) = c_HOL_Oplus__class_Oplus(X8,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f290,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,X8,X3) = c_HOL_Oplus__class_Oplus(X8,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f1798,plain,
spl0_247,
inference(avatar_split_clause,[],[f288,f1796]) ).
fof(f1796,plain,
( spl0_247
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f288,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
fof(f1794,plain,
spl0_246,
inference(avatar_split_clause,[],[f276,f1792]) ).
fof(f276,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Oabs__class_Oabs(X4,X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
fof(f1790,plain,
spl0_245,
inference(avatar_split_clause,[],[f273,f1788]) ).
fof(f1788,plain,
( spl0_245
<=> ! [X6,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X6,X3) = c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f273,axiom,
! [X3,X6] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_Nat_Osemiring__1__class_Oof__nat(X6,X3) = c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X6,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nat_0) ).
fof(f1786,plain,
spl0_244,
inference(avatar_split_clause,[],[f194,f1784]) ).
fof(f1784,plain,
( spl0_244
<=> ! [X1,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f194,axiom,
! [X3,X1] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X1,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
fof(f1782,plain,
spl0_243,
inference(avatar_split_clause,[],[f172,f1780]) ).
fof(f172,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X4,X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
fof(f1778,plain,
spl0_242,
inference(avatar_split_clause,[],[f157,f1776]) ).
fof(f1776,plain,
( spl0_242
<=> ! [X1,X3] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X3),X3) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f157,axiom,
! [X3,X1] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X3),X3) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f1774,plain,
spl0_241,
inference(avatar_split_clause,[],[f147,f1772]) ).
fof(f1772,plain,
( spl0_241
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f147,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f1770,plain,
spl0_240,
inference(avatar_split_clause,[],[f133,f1768]) ).
fof(f1768,plain,
( spl0_240
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ouminus__class_Ouminus(X4,X3) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f133,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = X4
| c_HOL_Ouminus__class_Ouminus(X4,X3) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f1766,plain,
spl0_239,
inference(avatar_split_clause,[],[f104,f1764]) ).
fof(f1764,plain,
( spl0_239
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X4,X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f104,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X3)
| ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X4,X3),X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
fof(f1762,plain,
spl0_238,
inference(avatar_split_clause,[],[f103,f1760]) ).
fof(f1760,plain,
( spl0_238
<=> ! [X2,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f103,axiom,
! [X2,X3,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Otimes__class_Otimes(X1,X2,X3) = c_HOL_Otimes__class_Otimes(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
fof(f1758,plain,
spl0_237,
inference(avatar_split_clause,[],[f86,f1756]) ).
fof(f1756,plain,
( spl0_237
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f86,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
fof(f1754,plain,
spl0_236,
inference(avatar_split_clause,[],[f85,f1752]) ).
fof(f1752,plain,
( spl0_236
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f85,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
fof(f1750,plain,
spl0_235,
inference(avatar_split_clause,[],[f84,f1748]) ).
fof(f1748,plain,
( spl0_235
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f84,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X3),X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).
fof(f1746,plain,
spl0_234,
inference(avatar_split_clause,[],[f43,f1744]) ).
fof(f1744,plain,
( spl0_234
<=> ! [X1,X3] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ominus__class_Ominus(X1,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f43,axiom,
! [X3,X1] :
( ~ class_Int_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oidom(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ominus__class_Ominus(X1,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f1742,plain,
spl0_233,
inference(avatar_split_clause,[],[f37,f1740]) ).
fof(f1740,plain,
( spl0_233
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X5,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f37,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X5,X3),X5,X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f1738,plain,
spl0_232,
inference(avatar_split_clause,[],[f28,f1736]) ).
fof(f1736,plain,
( spl0_232
<=> ! [X4,X5,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,X5,X3),X5,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f28,axiom,
! [X3,X4,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,X5,X3),X5,X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f1734,plain,
spl0_231,
inference(avatar_split_clause,[],[f13,f1732]) ).
fof(f1732,plain,
( spl0_231
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = c_HOL_Ouminus__class_Ouminus(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f13,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = c_HOL_Ouminus__class_Ouminus(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
fof(f1730,plain,
( spl0_230
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f1726,f1686,f1728]) ).
fof(f1728,plain,
( spl0_230
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f1686,plain,
( spl0_228
<=> ! [X2,X1,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f1726,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_228 ),
inference(factoring,[],[f1687]) ).
fof(f1687,plain,
( ! [X2,X3,X1] :
( c_lessequals(X2,X1,X3)
| c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f1686]) ).
fof(f1711,plain,
( spl0_229
| ~ spl0_82
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1561,f1472,f1001,f1708]) ).
fof(f1561,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_82
| ~ spl0_187 ),
inference(resolution,[],[f1473,f1003]) ).
fof(f1688,plain,
spl0_228,
inference(avatar_split_clause,[],[f408,f1686]) ).
fof(f408,axiom,
! [X2,X3,X1] :
( ~ class_Orderings_Olinorder(X3)
| c_lessequals(X1,X2,X3)
| c_lessequals(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1684,plain,
( spl0_227
| spl0_1 ),
inference(avatar_split_clause,[],[f405,f597,f1682]) ).
fof(f405,axiom,
! [X28] :
( v_thesis____
| c_lessequals(X28,c_RealVector_Onorm__class_Onorm(v_sko__local__Xthat__1(v_c____,v_cs____,X28),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
fof(f1680,plain,
( spl0_226
| ~ spl0_118
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1556,f1464,f1181,f1678]) ).
fof(f1678,plain,
( spl0_226
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1464,plain,
( spl0_185
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1556,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_118
| ~ spl0_185 ),
inference(resolution,[],[f1465,f1183]) ).
fof(f1465,plain,
( ! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f1464]) ).
fof(f1676,plain,
spl0_225,
inference(avatar_split_clause,[],[f399,f1674]) ).
fof(f1674,plain,
( spl0_225
<=> ! [X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f399,axiom,
! [X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_1) ).
fof(f1672,plain,
spl0_224,
inference(avatar_split_clause,[],[f395,f1670]) ).
fof(f1670,plain,
( spl0_224
<=> ! [X1] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f395,axiom,
! [X1] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__mod__minus__le__complex__mod_0) ).
fof(f1668,plain,
spl0_223,
inference(avatar_split_clause,[],[f350,f1666]) ).
fof(f1666,plain,
( spl0_223
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f350,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Otimes__class_Otimes(X4,X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
fof(f1664,plain,
spl0_222,
inference(avatar_split_clause,[],[f332,f1662]) ).
fof(f1662,plain,
( spl0_222
<=> ! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f332,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
fof(f1660,plain,
spl0_221,
inference(avatar_split_clause,[],[f294,f1658]) ).
fof(f1658,plain,
( spl0_221
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f294,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
fof(f1656,plain,
spl0_220,
inference(avatar_split_clause,[],[f153,f1654]) ).
fof(f1654,plain,
( spl0_220
<=> ! [X2,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f153,axiom,
! [X2,X3] :
( ~ class_RealVector_Oreal__normed__field(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
fof(f1652,plain,
spl0_219,
inference(avatar_split_clause,[],[f150,f1650]) ).
fof(f1650,plain,
( spl0_219
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f150,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ofield(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
fof(f1648,plain,
spl0_218,
inference(avatar_split_clause,[],[f130,f1646]) ).
fof(f1646,plain,
( spl0_218
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f130,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f1644,plain,
spl0_217,
inference(avatar_split_clause,[],[f129,f1642]) ).
fof(f1642,plain,
( spl0_217
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f129,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f1640,plain,
spl0_216,
inference(avatar_split_clause,[],[f127,f1638]) ).
fof(f1638,plain,
( spl0_216
<=> ! [X5,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f127,axiom,
! [X3,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
fof(f1636,plain,
( spl0_215
| ~ spl0_82
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1555,f1464,f1001,f1634]) ).
fof(f1634,plain,
( spl0_215
<=> ! [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_215])]) ).
fof(f1555,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_82
| ~ spl0_185 ),
inference(resolution,[],[f1465,f1003]) ).
fof(f1632,plain,
spl0_214,
inference(avatar_split_clause,[],[f126,f1630]) ).
fof(f1630,plain,
( spl0_214
<=> ! [X4,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f126,axiom,
! [X3,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
fof(f1628,plain,
spl0_213,
inference(avatar_split_clause,[],[f123,f1626]) ).
fof(f1626,plain,
( spl0_213
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f123,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f1624,plain,
spl0_212,
inference(avatar_split_clause,[],[f122,f1622]) ).
fof(f1622,plain,
( spl0_212
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f122,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Omult__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f1620,plain,
spl0_211,
inference(avatar_split_clause,[],[f121,f1618]) ).
fof(f1618,plain,
( spl0_211
<=> ! [X5,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f121,axiom,
! [X3,X5] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X3),X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f1616,plain,
spl0_210,
inference(avatar_split_clause,[],[f62,f1614]) ).
fof(f1614,plain,
( spl0_210
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f62,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f1612,plain,
spl0_209,
inference(avatar_split_clause,[],[f7,f1610]) ).
fof(f1610,plain,
( spl0_209
<=> ! [X6,X3] :
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(X6,tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f7,axiom,
! [X3,X6] :
( ~ class_Nat_Osemiring__char__0(X3)
| c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(X6,tc_nat),X3) != c_HOL_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__fact__not__zero_0) ).
fof(f1606,plain,
( spl0_208
| ~ spl0_113
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1553,f1456,f1156,f1604]) ).
fof(f1604,plain,
( spl0_208
<=> ! [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_208])]) ).
fof(f1156,plain,
( spl0_113
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1456,plain,
( spl0_183
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ominus__class_Ominus(X1,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1553,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex)
| ~ spl0_113
| ~ spl0_183 ),
inference(resolution,[],[f1457,f1158]) ).
fof(f1158,plain,
( class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1156]) ).
fof(f1457,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ominus__class_Ominus(X1,X1,X3) )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1456]) ).
fof(f1575,plain,
( spl0_207
| ~ spl0_76
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1552,f1456,f971,f1573]) ).
fof(f1573,plain,
( spl0_207
<=> ! [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_207])]) ).
fof(f971,plain,
( spl0_76
<=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1552,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,X0,tc_RealDef_Oreal)
| ~ spl0_76
| ~ spl0_183 ),
inference(resolution,[],[f1457,f973]) ).
fof(f973,plain,
( class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f971]) ).
fof(f1551,plain,
spl0_206,
inference(avatar_split_clause,[],[f392,f1549]) ).
fof(f1549,plain,
( spl0_206
<=> ! [X1,X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f392,axiom,
! [X3,X1] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
fof(f1547,plain,
( spl0_205
| ~ spl0_176
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1439,f1436,f1423,f1544]) ).
fof(f1544,plain,
( spl0_205
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1423,plain,
( spl0_176
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1436,plain,
( spl0_179
<=> ! [X1] : c_lessequals(c_Complex_ORe(X1),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1439,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_176
| ~ spl0_179 ),
inference(superposition,[],[f1437,f1425]) ).
fof(f1425,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1423]) ).
fof(f1437,plain,
( ! [X1] : c_lessequals(c_Complex_ORe(X1),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1436]) ).
fof(f1542,plain,
spl0_204,
inference(avatar_split_clause,[],[f388,f1540]) ).
fof(f1540,plain,
( spl0_204
<=> ! [X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f388,axiom,
! [X3] :
( ~ class_RealVector_Oreal__normed__vector(X3)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__zero_0) ).
fof(f1538,plain,
spl0_203,
inference(avatar_split_clause,[],[f387,f1536]) ).
fof(f1536,plain,
( spl0_203
<=> ! [X6,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X6,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f387,axiom,
! [X3,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_Nat_Osemiring__1__class_Oof__nat(X6,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
fof(f1534,plain,
spl0_202,
inference(avatar_split_clause,[],[f340,f1532]) ).
fof(f1532,plain,
( spl0_202
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f340,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__pprt_0) ).
fof(f1530,plain,
spl0_201,
inference(avatar_split_clause,[],[f206,f1528]) ).
fof(f1528,plain,
( spl0_201
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f206,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_lessequals(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X4,X3),c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nprt__le__zero_0) ).
fof(f1526,plain,
spl0_200,
inference(avatar_split_clause,[],[f198,f1524]) ).
fof(f1524,plain,
( spl0_200
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f198,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(c_HOL_Ozero__class_Ozero(X3),c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
fof(f1522,plain,
spl0_199,
inference(avatar_split_clause,[],[f161,f1520]) ).
fof(f1520,plain,
( spl0_199
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f161,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f1518,plain,
spl0_198,
inference(avatar_split_clause,[],[f160,f1516]) ).
fof(f1516,plain,
( spl0_198
<=> ! [X4,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f160,axiom,
! [X3,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1514,plain,
spl0_197,
inference(avatar_split_clause,[],[f159,f1512]) ).
fof(f1512,plain,
( spl0_197
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f159,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1510,plain,
spl0_196,
inference(avatar_split_clause,[],[f156,f1508]) ).
fof(f1508,plain,
( spl0_196
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f156,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1506,plain,
spl0_195,
inference(avatar_split_clause,[],[f155,f1504]) ).
fof(f1504,plain,
( spl0_195
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f155,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X3),X4,X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1502,plain,
spl0_194,
inference(avatar_split_clause,[],[f154,f1500]) ).
fof(f1500,plain,
( spl0_194
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f154,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Omonoid__add(X3)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1498,plain,
spl0_193,
inference(avatar_split_clause,[],[f148,f1496]) ).
fof(f1496,plain,
( spl0_193
<=> ! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f148,axiom,
! [X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
fof(f1494,plain,
spl0_192,
inference(avatar_split_clause,[],[f146,f1492]) ).
fof(f1492,plain,
( spl0_192
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f146,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pprt__0_0) ).
fof(f1490,plain,
spl0_191,
inference(avatar_split_clause,[],[f137,f1488]) ).
fof(f1488,plain,
( spl0_191
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f137,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nprt__0_0) ).
fof(f1486,plain,
spl0_190,
inference(avatar_split_clause,[],[f134,f1484]) ).
fof(f134,axiom,
! [X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
fof(f1482,plain,
spl0_189,
inference(avatar_split_clause,[],[f74,f1480]) ).
fof(f74,axiom,
! [X3,X5] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,X3),X3) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
fof(f1478,plain,
spl0_188,
inference(avatar_split_clause,[],[f67,f1476]) ).
fof(f1476,plain,
( spl0_188
<=> ! [X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f67,axiom,
! [X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
fof(f1474,plain,
spl0_187,
inference(avatar_split_clause,[],[f66,f1472]) ).
fof(f66,axiom,
! [X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
fof(f1470,plain,
spl0_186,
inference(avatar_split_clause,[],[f42,f1468]) ).
fof(f1468,plain,
( spl0_186
<=> ! [X4,X3] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ominus__class_Ominus(X4,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f42,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ominus__class_Ominus(X4,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
fof(f1466,plain,
spl0_185,
inference(avatar_split_clause,[],[f41,f1464]) ).
fof(f41,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Ogroup__add(X3)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(X3),X3) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f1462,plain,
( spl0_184
| ~ spl0_175
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1448,f1445,f1419,f1460]) ).
fof(f1460,plain,
( spl0_184
<=> ! [X0] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1448,plain,
( ! [X0] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(X0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_175
| ~ spl0_181 ),
inference(resolution,[],[f1446,f1420]) ).
fof(f1458,plain,
spl0_183,
inference(avatar_split_clause,[],[f39,f1456]) ).
fof(f39,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_HOL_Ozero__class_Ozero(X3) = c_HOL_Ominus__class_Ominus(X1,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f1454,plain,
spl0_182,
inference(avatar_split_clause,[],[f29,f1452]) ).
fof(f1452,plain,
( spl0_182
<=> ! [X14,X15] : c_HOL_Otimes__class_Otimes(X14,X15,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X15,X14,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f29,axiom,
! [X14,X15] : c_HOL_Otimes__class_Otimes(X14,X15,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X15,X14,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
fof(f1447,plain,
spl0_181,
inference(avatar_split_clause,[],[f407,f1445]) ).
fof(f407,axiom,
! [X14,X15] :
( c_lessequals(X14,X15,tc_RealDef_Oreal)
| c_lessequals(X15,X14,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
fof(f1443,plain,
spl0_180,
inference(avatar_split_clause,[],[f179,f1441]) ).
fof(f179,axiom,
! [X3,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X3)
| c_lessequals(X4,c_HOL_Oabs__class_Oabs(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
fof(f1438,plain,
spl0_179,
inference(avatar_split_clause,[],[f396,f1436]) ).
fof(f396,axiom,
! [X1] : c_lessequals(c_Complex_ORe(X1),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__Re__le__cmod_0) ).
fof(f1434,plain,
spl0_178,
inference(avatar_split_clause,[],[f414,f1432]) ).
fof(f1432,plain,
( spl0_178
<=> ! [X1,X3] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X1,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f414,axiom,
! [X3,X1] :
( ~ class_Orderings_Opreorder(X3)
| c_lessequals(X1,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1430,plain,
spl0_177,
inference(avatar_split_clause,[],[f413,f1428]) ).
fof(f1428,plain,
( spl0_177
<=> ! [X1,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X1,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f413,axiom,
! [X3,X1] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X1,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1426,plain,
spl0_176,
inference(avatar_split_clause,[],[f92,f1423]) ).
fof(f92,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Ozero_0) ).
fof(f1421,plain,
( spl0_175
| spl0_1 ),
inference(avatar_split_clause,[],[f424,f597,f1419]) ).
fof(f424,axiom,
! [X18] :
( v_thesis____
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_x(X18),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1417,plain,
spl0_174,
inference(avatar_split_clause,[],[f594,f1415]) ).
fof(f1415,plain,
( spl0_174
<=> ! [X37] :
( ~ class_HOL_Ozero(X37)
| class_HOL_Ozero(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f594,axiom,
! [X37] :
( ~ class_HOL_Ozero(X37)
| class_HOL_Ozero(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).
fof(f1413,plain,
spl0_173,
inference(avatar_split_clause,[],[f593,f1411]) ).
fof(f1411,plain,
( spl0_173
<=> ! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| class_Power_Opower(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f593,axiom,
! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| class_Power_Opower(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).
fof(f1409,plain,
spl0_172,
inference(avatar_split_clause,[],[f592,f1407]) ).
fof(f1407,plain,
( spl0_172
<=> ! [X37] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X37)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f592,axiom,
! [X37] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X37)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(f1405,plain,
spl0_171,
inference(avatar_split_clause,[],[f591,f1403]) ).
fof(f1403,plain,
( spl0_171
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f591,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Oorder) ).
fof(f1401,plain,
spl0_170,
inference(avatar_split_clause,[],[f590,f1399]) ).
fof(f1399,plain,
( spl0_170
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f590,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(f1397,plain,
spl0_169,
inference(avatar_split_clause,[],[f589,f1395]) ).
fof(f1395,plain,
( spl0_169
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f589,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(f1393,plain,
spl0_168,
inference(avatar_split_clause,[],[f588,f1391]) ).
fof(f1391,plain,
( spl0_168
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f588,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Nat_Osemiring__char__0) ).
fof(f1389,plain,
spl0_167,
inference(avatar_split_clause,[],[f587,f1387]) ).
fof(f1387,plain,
( spl0_167
<=> ! [X37] :
( ~ class_Ring__and__Field_Oidom(X37)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f587,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oidom(X37)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
fof(f1385,plain,
spl0_166,
inference(avatar_split_clause,[],[f586,f1383]) ).
fof(f1383,plain,
( spl0_166
<=> ! [X37] :
( ~ class_Ring__and__Field_Ocomm__ring(X37)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f586,axiom,
! [X37] :
( ~ class_Ring__and__Field_Ocomm__ring(X37)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
fof(f1381,plain,
spl0_165,
inference(avatar_split_clause,[],[f585,f1379]) ).
fof(f1379,plain,
( spl0_165
<=> ! [X37] :
( ~ class_OrderedGroup_Oab__group__add(X37)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f585,axiom,
! [X37] :
( ~ class_OrderedGroup_Oab__group__add(X37)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
fof(f1377,plain,
spl0_164,
inference(avatar_split_clause,[],[f584,f1375]) ).
fof(f1375,plain,
( spl0_164
<=> ! [X37] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X37)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f584,axiom,
! [X37] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X37)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
fof(f1373,plain,
spl0_163,
inference(avatar_split_clause,[],[f583,f1371]) ).
fof(f1371,plain,
( spl0_163
<=> ! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X37)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f583,axiom,
! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X37)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
fof(f1369,plain,
spl0_162,
inference(avatar_split_clause,[],[f582,f1367]) ).
fof(f1367,plain,
( spl0_162
<=> ! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f582,axiom,
! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
fof(f1365,plain,
spl0_161,
inference(avatar_split_clause,[],[f581,f1363]) ).
fof(f1363,plain,
( spl0_161
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f581,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).
fof(f1361,plain,
spl0_160,
inference(avatar_split_clause,[],[f580,f1359]) ).
fof(f1359,plain,
( spl0_160
<=> ! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X37)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f580,axiom,
! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X37)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
fof(f1357,plain,
spl0_159,
inference(avatar_split_clause,[],[f579,f1355]) ).
fof(f1355,plain,
( spl0_159
<=> ! [X37] :
( ~ class_OrderedGroup_Oab__group__add(X37)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f579,axiom,
! [X37] :
( ~ class_OrderedGroup_Oab__group__add(X37)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
fof(f1353,plain,
spl0_158,
inference(avatar_split_clause,[],[f578,f1351]) ).
fof(f1351,plain,
( spl0_158
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f578,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).
fof(f1349,plain,
spl0_157,
inference(avatar_split_clause,[],[f577,f1347]) ).
fof(f1347,plain,
( spl0_157
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f577,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
fof(f1345,plain,
spl0_156,
inference(avatar_split_clause,[],[f576,f1343]) ).
fof(f1343,plain,
( spl0_156
<=> ! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f576,axiom,
! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
fof(f1341,plain,
spl0_155,
inference(avatar_split_clause,[],[f575,f1339]) ).
fof(f1339,plain,
( spl0_155
<=> ! [X37] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X37)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f575,axiom,
! [X37] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X37)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
fof(f1337,plain,
spl0_154,
inference(avatar_split_clause,[],[f574,f1335]) ).
fof(f1335,plain,
( spl0_154
<=> ! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X37)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f574,axiom,
! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X37)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
fof(f1333,plain,
spl0_153,
inference(avatar_split_clause,[],[f573,f1331]) ).
fof(f1331,plain,
( spl0_153
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f573,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).
fof(f1329,plain,
spl0_152,
inference(avatar_split_clause,[],[f572,f1327]) ).
fof(f1327,plain,
( spl0_152
<=> ! [X37] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X37)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f572,axiom,
! [X37] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X37)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
fof(f1325,plain,
spl0_151,
inference(avatar_split_clause,[],[f571,f1323]) ).
fof(f1323,plain,
( spl0_151
<=> ! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f571,axiom,
! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1321,plain,
spl0_150,
inference(avatar_split_clause,[],[f570,f1319]) ).
fof(f1319,plain,
( spl0_150
<=> ! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X37)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f570,axiom,
! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X37)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
fof(f1317,plain,
spl0_149,
inference(avatar_split_clause,[],[f569,f1315]) ).
fof(f1315,plain,
( spl0_149
<=> ! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X37)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f569,axiom,
! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X37)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1313,plain,
spl0_148,
inference(avatar_split_clause,[],[f568,f1311]) ).
fof(f1311,plain,
( spl0_148
<=> ! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f568,axiom,
! [X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X37)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1309,plain,
spl0_147,
inference(avatar_split_clause,[],[f567,f1307]) ).
fof(f1307,plain,
( spl0_147
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f567,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).
fof(f1305,plain,
spl0_146,
inference(avatar_split_clause,[],[f566,f1303]) ).
fof(f1303,plain,
( spl0_146
<=> ! [X37] :
( ~ class_Ring__and__Field_Oidom(X37)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f566,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oidom(X37)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
fof(f1301,plain,
spl0_145,
inference(avatar_split_clause,[],[f565,f1299]) ).
fof(f1299,plain,
( spl0_145
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f565,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs) ).
fof(f1297,plain,
spl0_144,
inference(avatar_split_clause,[],[f564,f1295]) ).
fof(f1295,plain,
( spl0_144
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f564,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).
fof(f1293,plain,
spl0_143,
inference(avatar_split_clause,[],[f563,f1291]) ).
fof(f1291,plain,
( spl0_143
<=> ! [X37] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X37)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f563,axiom,
! [X37] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X37)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1289,plain,
spl0_142,
inference(avatar_split_clause,[],[f562,f1287]) ).
fof(f1287,plain,
( spl0_142
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f562,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
fof(f1285,plain,
spl0_141,
inference(avatar_split_clause,[],[f561,f1283]) ).
fof(f1283,plain,
( spl0_141
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f561,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
fof(f1281,plain,
spl0_140,
inference(avatar_split_clause,[],[f560,f1279]) ).
fof(f1279,plain,
( spl0_140
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f560,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
fof(f1277,plain,
spl0_139,
inference(avatar_split_clause,[],[f559,f1275]) ).
fof(f1275,plain,
( spl0_139
<=> ! [X37] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X37)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f559,axiom,
! [X37] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X37)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1273,plain,
spl0_138,
inference(avatar_split_clause,[],[f558,f1271]) ).
fof(f1271,plain,
( spl0_138
<=> ! [X37] :
( ~ class_Ring__and__Field_Oidom(X37)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f558,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oidom(X37)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1269,plain,
spl0_137,
inference(avatar_split_clause,[],[f557,f1267]) ).
fof(f1267,plain,
( spl0_137
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f557,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1265,plain,
spl0_136,
inference(avatar_split_clause,[],[f556,f1263]) ).
fof(f1263,plain,
( spl0_136
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f556,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f1261,plain,
spl0_135,
inference(avatar_split_clause,[],[f555,f1259]) ).
fof(f1259,plain,
( spl0_135
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f555,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1257,plain,
spl0_134,
inference(avatar_split_clause,[],[f554,f1255]) ).
fof(f1255,plain,
( spl0_134
<=> ! [X37] :
( ~ class_Ring__and__Field_Oidom(X37)
| class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f554,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oidom(X37)
| class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f1253,plain,
spl0_133,
inference(avatar_split_clause,[],[f553,f1251]) ).
fof(f1251,plain,
( spl0_133
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f553,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1249,plain,
spl0_132,
inference(avatar_split_clause,[],[f552,f1247]) ).
fof(f1247,plain,
( spl0_132
<=> ! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f552,axiom,
! [X37] :
( ~ class_Ring__and__Field_Oordered__idom(X37)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1245,plain,
spl0_131,
inference(avatar_split_clause,[],[f427,f1243]) ).
fof(f1243,plain,
( spl0_131
<=> ! [X37] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X37)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f427,axiom,
! [X37] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X37)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
fof(f1241,plain,
spl0_130,
inference(avatar_split_clause,[],[f426,f1239]) ).
fof(f1239,plain,
( spl0_130
<=> ! [X37] :
( ~ class_Ring__and__Field_Ocomm__ring(X37)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f426,axiom,
! [X37] :
( ~ class_Ring__and__Field_Ocomm__ring(X37)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
fof(f1237,plain,
spl0_129,
inference(avatar_split_clause,[],[f425,f1235]) ).
fof(f1235,plain,
( spl0_129
<=> ! [X37] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X37)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f425,axiom,
! [X37] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X37)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f1233,plain,
~ spl0_128,
inference(avatar_split_clause,[],[f197,f1230]) ).
fof(f1230,plain,
( spl0_128
<=> v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f197,axiom,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cs0_0) ).
fof(f1228,plain,
spl0_127,
inference(avatar_split_clause,[],[f411,f1226]) ).
fof(f1226,plain,
( spl0_127
<=> ! [X15] : c_lessequals(X15,X15,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f411,axiom,
! [X15] : c_lessequals(X15,X15,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
fof(f1224,plain,
spl0_126,
inference(avatar_split_clause,[],[f551,f1221]) ).
fof(f1221,plain,
( spl0_126
<=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f551,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
fof(f1219,plain,
spl0_125,
inference(avatar_split_clause,[],[f550,f1216]) ).
fof(f1216,plain,
( spl0_125
<=> class_Power_Opower(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f550,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
fof(f1214,plain,
spl0_124,
inference(avatar_split_clause,[],[f549,f1211]) ).
fof(f1211,plain,
( spl0_124
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f549,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f1209,plain,
spl0_123,
inference(avatar_split_clause,[],[f548,f1206]) ).
fof(f1206,plain,
( spl0_123
<=> class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f548,axiom,
class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) ).
fof(f1204,plain,
spl0_122,
inference(avatar_split_clause,[],[f547,f1201]) ).
fof(f1201,plain,
( spl0_122
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f547,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f1199,plain,
spl0_121,
inference(avatar_split_clause,[],[f546,f1196]) ).
fof(f1196,plain,
( spl0_121
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f546,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(f1194,plain,
spl0_120,
inference(avatar_split_clause,[],[f545,f1191]) ).
fof(f1191,plain,
( spl0_120
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f545,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f1189,plain,
spl0_119,
inference(avatar_split_clause,[],[f544,f1186]) ).
fof(f1186,plain,
( spl0_119
<=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f544,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(f1184,plain,
spl0_118,
inference(avatar_split_clause,[],[f543,f1181]) ).
fof(f543,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(f1179,plain,
spl0_117,
inference(avatar_split_clause,[],[f542,f1176]) ).
fof(f1176,plain,
( spl0_117
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f542,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(f1174,plain,
spl0_116,
inference(avatar_split_clause,[],[f541,f1171]) ).
fof(f1171,plain,
( spl0_116
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f541,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(f1169,plain,
spl0_115,
inference(avatar_split_clause,[],[f540,f1166]) ).
fof(f1166,plain,
( spl0_115
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f540,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f1164,plain,
spl0_114,
inference(avatar_split_clause,[],[f539,f1161]) ).
fof(f1161,plain,
( spl0_114
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f539,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(f1159,plain,
spl0_113,
inference(avatar_split_clause,[],[f538,f1156]) ).
fof(f538,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f1154,plain,
spl0_112,
inference(avatar_split_clause,[],[f537,f1151]) ).
fof(f1151,plain,
( spl0_112
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f537,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(f1149,plain,
spl0_111,
inference(avatar_split_clause,[],[f536,f1146]) ).
fof(f1146,plain,
( spl0_111
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f536,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f1144,plain,
spl0_110,
inference(avatar_split_clause,[],[f535,f1141]) ).
fof(f1141,plain,
( spl0_110
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f535,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f1139,plain,
spl0_109,
inference(avatar_split_clause,[],[f534,f1136]) ).
fof(f1136,plain,
( spl0_109
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f534,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(f1134,plain,
spl0_108,
inference(avatar_split_clause,[],[f533,f1131]) ).
fof(f1131,plain,
( spl0_108
<=> class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f533,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
fof(f1129,plain,
spl0_107,
inference(avatar_split_clause,[],[f532,f1126]) ).
fof(f1126,plain,
( spl0_107
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f532,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(f1124,plain,
spl0_106,
inference(avatar_split_clause,[],[f531,f1121]) ).
fof(f1121,plain,
( spl0_106
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f531,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1119,plain,
spl0_105,
inference(avatar_split_clause,[],[f530,f1116]) ).
fof(f1116,plain,
( spl0_105
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f530,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1114,plain,
spl0_104,
inference(avatar_split_clause,[],[f529,f1111]) ).
fof(f1111,plain,
( spl0_104
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f529,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f1109,plain,
spl0_103,
inference(avatar_split_clause,[],[f528,f1106]) ).
fof(f1106,plain,
( spl0_103
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f528,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1104,plain,
spl0_102,
inference(avatar_split_clause,[],[f527,f1101]) ).
fof(f1101,plain,
( spl0_102
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f527,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1099,plain,
spl0_101,
inference(avatar_split_clause,[],[f526,f1096]) ).
fof(f1096,plain,
( spl0_101
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f526,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(f1094,plain,
spl0_100,
inference(avatar_split_clause,[],[f525,f1091]) ).
fof(f1091,plain,
( spl0_100
<=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f525,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(f1089,plain,
spl0_99,
inference(avatar_split_clause,[],[f524,f1086]) ).
fof(f1086,plain,
( spl0_99
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f524,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(f1084,plain,
spl0_98,
inference(avatar_split_clause,[],[f523,f1081]) ).
fof(f1081,plain,
( spl0_98
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f523,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1079,plain,
spl0_97,
inference(avatar_split_clause,[],[f522,f1076]) ).
fof(f1076,plain,
( spl0_97
<=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f522,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(f1074,plain,
spl0_96,
inference(avatar_split_clause,[],[f521,f1071]) ).
fof(f1071,plain,
( spl0_96
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f521,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(f1069,plain,
spl0_95,
inference(avatar_split_clause,[],[f520,f1066]) ).
fof(f1066,plain,
( spl0_95
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f520,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(f1064,plain,
spl0_94,
inference(avatar_split_clause,[],[f519,f1061]) ).
fof(f1061,plain,
( spl0_94
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f519,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f1059,plain,
spl0_93,
inference(avatar_split_clause,[],[f518,f1056]) ).
fof(f1056,plain,
( spl0_93
<=> class_HOL_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f518,axiom,
class_HOL_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Ozero) ).
fof(f1054,plain,
spl0_92,
inference(avatar_split_clause,[],[f517,f1051]) ).
fof(f1051,plain,
( spl0_92
<=> class_Power_Opower(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f517,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Power_Opower) ).
fof(f1049,plain,
spl0_91,
inference(avatar_split_clause,[],[f516,f1046]) ).
fof(f1046,plain,
( spl0_91
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f516,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f1044,plain,
spl0_90,
inference(avatar_split_clause,[],[f515,f1041]) ).
fof(f515,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
fof(f1039,plain,
spl0_89,
inference(avatar_split_clause,[],[f514,f1036]) ).
fof(f1036,plain,
( spl0_89
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f514,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f1034,plain,
spl0_88,
inference(avatar_split_clause,[],[f513,f1031]) ).
fof(f1031,plain,
( spl0_88
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f513,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f1029,plain,
spl0_87,
inference(avatar_split_clause,[],[f512,f1026]) ).
fof(f1026,plain,
( spl0_87
<=> class_Nat_Osemiring__char__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f512,axiom,
class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Nat_Osemiring__char__0) ).
fof(f1024,plain,
spl0_86,
inference(avatar_split_clause,[],[f511,f1021]) ).
fof(f1021,plain,
( spl0_86
<=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f511,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
fof(f1019,plain,
spl0_85,
inference(avatar_split_clause,[],[f510,f1016]) ).
fof(f1016,plain,
( spl0_85
<=> class_Ring__and__Field_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f510,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
fof(f1014,plain,
spl0_84,
inference(avatar_split_clause,[],[f509,f1011]) ).
fof(f1011,plain,
( spl0_84
<=> class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f509,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
fof(f1009,plain,
spl0_83,
inference(avatar_split_clause,[],[f508,f1006]) ).
fof(f1006,plain,
( spl0_83
<=> class_RealVector_Oreal__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f508,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__field) ).
fof(f1004,plain,
spl0_82,
inference(avatar_split_clause,[],[f507,f1001]) ).
fof(f507,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f999,plain,
spl0_81,
inference(avatar_split_clause,[],[f506,f996]) ).
fof(f996,plain,
( spl0_81
<=> class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f506,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
fof(f994,plain,
spl0_80,
inference(avatar_split_clause,[],[f505,f991]) ).
fof(f991,plain,
( spl0_80
<=> class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f505,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
fof(f989,plain,
spl0_79,
inference(avatar_split_clause,[],[f504,f986]) ).
fof(f986,plain,
( spl0_79
<=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f504,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
fof(f984,plain,
spl0_78,
inference(avatar_split_clause,[],[f503,f981]) ).
fof(f981,plain,
( spl0_78
<=> class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f503,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(f979,plain,
spl0_77,
inference(avatar_split_clause,[],[f502,f976]) ).
fof(f976,plain,
( spl0_77
<=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f502,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(f974,plain,
spl0_76,
inference(avatar_split_clause,[],[f501,f971]) ).
fof(f501,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
fof(f969,plain,
spl0_75,
inference(avatar_split_clause,[],[f500,f966]) ).
fof(f966,plain,
( spl0_75
<=> class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f500,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(f964,plain,
spl0_74,
inference(avatar_split_clause,[],[f499,f961]) ).
fof(f499,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(f959,plain,
spl0_73,
inference(avatar_split_clause,[],[f498,f956]) ).
fof(f956,plain,
( spl0_73
<=> class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f498,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(f954,plain,
spl0_72,
inference(avatar_split_clause,[],[f497,f951]) ).
fof(f951,plain,
( spl0_72
<=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f497,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
fof(f949,plain,
spl0_71,
inference(avatar_split_clause,[],[f496,f946]) ).
fof(f946,plain,
( spl0_71
<=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f496,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(f944,plain,
spl0_70,
inference(avatar_split_clause,[],[f495,f941]) ).
fof(f941,plain,
( spl0_70
<=> class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f495,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(f939,plain,
spl0_69,
inference(avatar_split_clause,[],[f494,f936]) ).
fof(f936,plain,
( spl0_69
<=> class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f494,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).
fof(f934,plain,
spl0_68,
inference(avatar_split_clause,[],[f493,f931]) ).
fof(f931,plain,
( spl0_68
<=> class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f493,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) ).
fof(f929,plain,
spl0_67,
inference(avatar_split_clause,[],[f492,f926]) ).
fof(f926,plain,
( spl0_67
<=> class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f492,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(f924,plain,
spl0_66,
inference(avatar_split_clause,[],[f491,f921]) ).
fof(f921,plain,
( spl0_66
<=> class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f491,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(f919,plain,
spl0_65,
inference(avatar_split_clause,[],[f490,f916]) ).
fof(f916,plain,
( spl0_65
<=> class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f490,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
fof(f914,plain,
spl0_64,
inference(avatar_split_clause,[],[f489,f911]) ).
fof(f911,plain,
( spl0_64
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f489,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).
fof(f909,plain,
spl0_63,
inference(avatar_split_clause,[],[f488,f906]) ).
fof(f906,plain,
( spl0_63
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f488,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f904,plain,
spl0_62,
inference(avatar_split_clause,[],[f487,f901]) ).
fof(f901,plain,
( spl0_62
<=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f487,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
fof(f899,plain,
spl0_61,
inference(avatar_split_clause,[],[f486,f896]) ).
fof(f896,plain,
( spl0_61
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f486,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f894,plain,
spl0_60,
inference(avatar_split_clause,[],[f485,f891]) ).
fof(f891,plain,
( spl0_60
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f485,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0) ).
fof(f889,plain,
spl0_59,
inference(avatar_split_clause,[],[f484,f886]) ).
fof(f886,plain,
( spl0_59
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f484,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(f884,plain,
spl0_58,
inference(avatar_split_clause,[],[f483,f881]) ).
fof(f881,plain,
( spl0_58
<=> class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f483,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(f879,plain,
spl0_57,
inference(avatar_split_clause,[],[f482,f876]) ).
fof(f482,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(f874,plain,
spl0_56,
inference(avatar_split_clause,[],[f481,f871]) ).
fof(f871,plain,
( spl0_56
<=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f481,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(f869,plain,
spl0_55,
inference(avatar_split_clause,[],[f480,f866]) ).
fof(f866,plain,
( spl0_55
<=> class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f480,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) ).
fof(f864,plain,
spl0_54,
inference(avatar_split_clause,[],[f479,f861]) ).
fof(f861,plain,
( spl0_54
<=> class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f479,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(f859,plain,
spl0_53,
inference(avatar_split_clause,[],[f478,f856]) ).
fof(f856,plain,
( spl0_53
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f478,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
fof(f854,plain,
spl0_52,
inference(avatar_split_clause,[],[f477,f851]) ).
fof(f851,plain,
( spl0_52
<=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f477,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(f849,plain,
spl0_51,
inference(avatar_split_clause,[],[f476,f846]) ).
fof(f476,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(f844,plain,
spl0_50,
inference(avatar_split_clause,[],[f475,f841]) ).
fof(f475,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(f839,plain,
spl0_49,
inference(avatar_split_clause,[],[f474,f836]) ).
fof(f836,plain,
( spl0_49
<=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f474,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(f834,plain,
spl0_48,
inference(avatar_split_clause,[],[f473,f831]) ).
fof(f831,plain,
( spl0_48
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f473,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(f829,plain,
spl0_47,
inference(avatar_split_clause,[],[f472,f826]) ).
fof(f826,plain,
( spl0_47
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f472,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(f824,plain,
spl0_46,
inference(avatar_split_clause,[],[f471,f821]) ).
fof(f821,plain,
( spl0_46
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f471,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(f819,plain,
spl0_45,
inference(avatar_split_clause,[],[f470,f816]) ).
fof(f816,plain,
( spl0_45
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f470,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(f814,plain,
spl0_44,
inference(avatar_split_clause,[],[f469,f811]) ).
fof(f811,plain,
( spl0_44
<=> class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f469,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).
fof(f809,plain,
spl0_43,
inference(avatar_split_clause,[],[f468,f806]) ).
fof(f468,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f804,plain,
spl0_42,
inference(avatar_split_clause,[],[f467,f801]) ).
fof(f801,plain,
( spl0_42
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f467,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(f799,plain,
spl0_41,
inference(avatar_split_clause,[],[f466,f796]) ).
fof(f796,plain,
( spl0_41
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f466,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f794,plain,
spl0_40,
inference(avatar_split_clause,[],[f465,f791]) ).
fof(f791,plain,
( spl0_40
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f465,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(f789,plain,
spl0_39,
inference(avatar_split_clause,[],[f464,f786]) ).
fof(f786,plain,
( spl0_39
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f464,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(f784,plain,
spl0_38,
inference(avatar_split_clause,[],[f463,f781]) ).
fof(f781,plain,
( spl0_38
<=> class_HOL_Ozero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f463,axiom,
class_HOL_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Ozero) ).
fof(f779,plain,
spl0_37,
inference(avatar_split_clause,[],[f462,f776]) ).
fof(f776,plain,
( spl0_37
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f462,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f774,plain,
spl0_36,
inference(avatar_split_clause,[],[f461,f771]) ).
fof(f771,plain,
( spl0_36
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f461,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f769,plain,
spl0_35,
inference(avatar_split_clause,[],[f460,f766]) ).
fof(f766,plain,
( spl0_35
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f460,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f764,plain,
spl0_34,
inference(avatar_split_clause,[],[f459,f761]) ).
fof(f761,plain,
( spl0_34
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f459,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f759,plain,
spl0_33,
inference(avatar_split_clause,[],[f458,f756]) ).
fof(f756,plain,
( spl0_33
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f458,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f754,plain,
spl0_32,
inference(avatar_split_clause,[],[f457,f751]) ).
fof(f751,plain,
( spl0_32
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f457,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f749,plain,
spl0_31,
inference(avatar_split_clause,[],[f456,f746]) ).
fof(f746,plain,
( spl0_31
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f456,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f744,plain,
spl0_30,
inference(avatar_split_clause,[],[f455,f741]) ).
fof(f741,plain,
( spl0_30
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f455,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f739,plain,
spl0_29,
inference(avatar_split_clause,[],[f454,f736]) ).
fof(f736,plain,
( spl0_29
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f454,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f734,plain,
spl0_28,
inference(avatar_split_clause,[],[f453,f731]) ).
fof(f731,plain,
( spl0_28
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f453,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f729,plain,
spl0_27,
inference(avatar_split_clause,[],[f452,f726]) ).
fof(f726,plain,
( spl0_27
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f452,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f724,plain,
spl0_26,
inference(avatar_split_clause,[],[f451,f721]) ).
fof(f721,plain,
( spl0_26
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f451,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(f719,plain,
spl0_25,
inference(avatar_split_clause,[],[f450,f716]) ).
fof(f716,plain,
( spl0_25
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f450,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f714,plain,
spl0_24,
inference(avatar_split_clause,[],[f449,f711]) ).
fof(f711,plain,
( spl0_24
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f449,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f709,plain,
spl0_23,
inference(avatar_split_clause,[],[f448,f706]) ).
fof(f706,plain,
( spl0_23
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f448,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f704,plain,
spl0_22,
inference(avatar_split_clause,[],[f447,f701]) ).
fof(f701,plain,
( spl0_22
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f447,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f699,plain,
spl0_21,
inference(avatar_split_clause,[],[f446,f696]) ).
fof(f696,plain,
( spl0_21
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f446,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f694,plain,
spl0_20,
inference(avatar_split_clause,[],[f445,f691]) ).
fof(f691,plain,
( spl0_20
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f445,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).
fof(f689,plain,
spl0_19,
inference(avatar_split_clause,[],[f444,f686]) ).
fof(f686,plain,
( spl0_19
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f444,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(f684,plain,
spl0_18,
inference(avatar_split_clause,[],[f443,f681]) ).
fof(f681,plain,
( spl0_18
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f443,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f679,plain,
spl0_17,
inference(avatar_split_clause,[],[f442,f676]) ).
fof(f676,plain,
( spl0_17
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f442,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(f674,plain,
spl0_16,
inference(avatar_split_clause,[],[f441,f671]) ).
fof(f671,plain,
( spl0_16
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f441,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f669,plain,
spl0_15,
inference(avatar_split_clause,[],[f440,f666]) ).
fof(f666,plain,
( spl0_15
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f440,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f664,plain,
spl0_14,
inference(avatar_split_clause,[],[f439,f661]) ).
fof(f661,plain,
( spl0_14
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f439,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f659,plain,
spl0_13,
inference(avatar_split_clause,[],[f438,f656]) ).
fof(f656,plain,
( spl0_13
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f438,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f654,plain,
spl0_12,
inference(avatar_split_clause,[],[f437,f651]) ).
fof(f651,plain,
( spl0_12
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f437,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f649,plain,
spl0_11,
inference(avatar_split_clause,[],[f436,f646]) ).
fof(f646,plain,
( spl0_11
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f436,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(f644,plain,
spl0_10,
inference(avatar_split_clause,[],[f435,f641]) ).
fof(f641,plain,
( spl0_10
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f435,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(f639,plain,
spl0_9,
inference(avatar_split_clause,[],[f434,f636]) ).
fof(f636,plain,
( spl0_9
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f434,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f634,plain,
spl0_8,
inference(avatar_split_clause,[],[f433,f631]) ).
fof(f631,plain,
( spl0_8
<=> class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f433,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) ).
fof(f629,plain,
spl0_7,
inference(avatar_split_clause,[],[f432,f626]) ).
fof(f626,plain,
( spl0_7
<=> class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f432,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring) ).
fof(f624,plain,
spl0_6,
inference(avatar_split_clause,[],[f431,f621]) ).
fof(f621,plain,
( spl0_6
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f431,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f619,plain,
spl0_5,
inference(avatar_split_clause,[],[f430,f616]) ).
fof(f616,plain,
( spl0_5
<=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f430,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
fof(f614,plain,
spl0_4,
inference(avatar_split_clause,[],[f429,f611]) ).
fof(f611,plain,
( spl0_4
<=> class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f429,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
fof(f609,plain,
spl0_3,
inference(avatar_split_clause,[],[f428,f606]) ).
fof(f606,plain,
( spl0_3
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f428,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f604,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f423,f597,f602]) ).
fof(f423,axiom,
! [X18] :
( v_thesis____
| c_lessequals(X18,c_RealVector_Onorm__class_Onorm(v_x(X18),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f600,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f422,f597]) ).
fof(f422,axiom,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ALG386-1 : TPTP v8.2.0. Released v4.1.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37 % Computer : n006.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat May 18 22:44:53 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % (15487)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.41 % (15490)WARNING: value z3 for option sas not known
% 0.15/0.42 % (15491)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.42 % (15488)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.42 % (15489)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.42 % (15493)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)
% 0.15/0.42 % (15492)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)
% 0.15/0.42 % (15494)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)
% 0.15/0.42 % (15490)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)
% 0.22/0.47 TRYING [1]
% 0.22/0.49 TRYING [2]
% 1.78/0.64 % (15492)First to succeed.
% 1.88/0.67 % (15492)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15487"
% 1.88/0.67 % (15492)Refutation found. Thanks to Tanya!
% 1.88/0.67 % SZS status Unsatisfiable for theBenchmark
% 1.88/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 1.88/0.69 % (15492)------------------------------
% 1.88/0.69 % (15492)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.88/0.69 % (15492)Termination reason: Refutation
% 1.88/0.69
% 1.88/0.69 % (15492)Memory used [KB]: 4043
% 1.88/0.69 % (15492)Time elapsed: 0.254 s
% 1.88/0.69 % (15492)Instructions burned: 368 (million)
% 1.88/0.69 % (15487)Success in time 0.296 s
%------------------------------------------------------------------------------