TSTP Solution File: ALG406-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG406-1 : 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 : n018.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 18:37:38 EDT 2024
% Result : Unsatisfiable 5.52s 1.20s
% Output : Refutation 5.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1312
% Syntax : Number of formulae : 2252 ( 748 unt; 0 def)
% Number of atoms : 5616 ( 676 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 5958 (2594 ~;2656 |; 0 &)
% ( 708 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 770 ( 768 usr; 709 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 5 con; 0-3 aty)
% Number of variables : 2849 (2849 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15232,plain,
$false,
inference(avatar_sat_refutation,[],[f687,f692,f697,f702,f707,f712,f717,f722,f727,f732,f737,f742,f747,f752,f757,f762,f767,f772,f777,f782,f787,f792,f797,f802,f807,f812,f817,f822,f827,f832,f837,f842,f847,f852,f857,f862,f867,f872,f877,f882,f887,f892,f897,f902,f907,f912,f917,f922,f927,f932,f937,f942,f947,f952,f957,f962,f967,f972,f977,f982,f987,f992,f997,f1002,f1007,f1012,f1017,f1022,f1027,f1032,f1037,f1042,f1047,f1052,f1057,f1062,f1067,f1072,f1077,f1082,f1087,f1092,f1097,f1102,f1107,f1112,f1117,f1122,f1127,f1132,f1137,f1142,f1147,f1152,f1157,f1162,f1167,f1172,f1177,f1182,f1187,f1192,f1197,f1202,f1207,f1212,f1217,f1222,f1227,f1232,f1237,f1242,f1247,f1252,f1257,f1262,f1267,f1272,f1277,f1282,f1288,f1292,f1296,f1301,f1306,f1311,f1316,f1321,f1326,f1331,f1335,f1339,f1343,f1347,f1351,f1355,f1359,f1365,f1369,f1373,f1378,f1382,f1387,f1391,f1395,f1399,f1403,f1407,f1411,f1415,f1428,f1437,f1441,f1445,f1449,f1453,f1457,f1461,f1465,f1469,f1474,f1478,f1482,f1486,f1490,f1494,f1498,f1502,f1506,f1510,f1514,f1518,f1522,f1526,f1530,f1534,f1538,f1542,f1546,f1550,f1554,f1559,f1563,f1567,f1571,f1575,f1579,f1583,f1587,f1591,f1636,f1652,f1672,f1676,f1680,f1684,f1688,f1692,f1696,f1700,f1704,f1708,f1712,f1716,f1720,f1724,f1728,f1732,f1736,f1740,f1744,f1748,f1752,f1756,f1760,f1764,f1768,f1772,f1776,f1780,f1785,f1789,f1793,f1797,f1801,f1805,f1809,f1813,f1817,f1825,f1905,f1991,f2013,f2017,f2021,f2025,f2029,f2033,f2037,f2041,f2045,f2049,f2053,f2057,f2061,f2065,f2069,f2073,f2077,f2081,f2085,f2089,f2093,f2097,f2101,f2105,f2109,f2113,f2117,f2121,f2129,f2133,f2137,f2141,f2145,f2149,f2167,f2208,f2274,f2355,f2360,f2364,f2368,f2372,f2376,f2380,f2384,f2388,f2392,f2396,f2400,f2405,f2409,f2413,f2417,f2421,f2425,f2429,f2433,f2441,f2522,f2600,f2604,f2608,f2612,f2616,f2620,f2624,f2628,f2632,f2636,f2640,f2644,f2648,f2652,f2656,f2660,f2671,f2675,f2679,f2683,f2687,f2691,f2695,f2699,f2703,f2707,f2711,f2715,f2720,f2724,f2999,f3128,f3132,f3136,f3140,f3144,f3148,f3152,f3156,f3160,f3165,f3169,f3173,f3177,f3181,f3185,f3189,f3193,f3197,f3201,f3205,f3217,f3221,f3225,f3229,f3233,f3237,f3241,f3245,f3249,f3253,f3258,f3262,f3266,f3270,f3274,f3278,f3282,f3286,f3290,f3294,f3298,f3308,f3312,f3316,f3404,f3863,f4082,f4086,f4090,f4094,f4098,f4102,f4106,f4110,f4114,f4118,f4122,f4126,f4130,f4134,f4138,f4142,f4156,f4160,f4164,f4168,f4172,f4176,f4180,f4184,f4188,f4192,f4196,f4200,f4204,f4208,f4212,f4216,f4220,f4224,f4325,f4349,f4478,f4497,f4501,f4505,f4509,f4513,f4517,f4521,f4525,f4529,f4533,f4560,f4564,f4568,f4572,f4576,f4580,f4584,f4588,f4592,f4596,f4601,f4605,f4609,f4613,f4617,f4621,f4625,f4629,f4633,f4637,f4641,f4649,f4653,f4657,f4661,f4665,f4718,f4976,f5107,f5111,f5115,f5119,f5123,f5127,f5131,f5135,f5139,f5143,f5147,f5151,f5155,f5159,f5163,f5167,f5171,f5175,f5179,f5183,f5187,f5191,f5195,f5199,f5203,f5207,f5211,f5271,f5317,f5321,f5325,f5329,f5333,f5337,f5341,f5345,f5349,f5375,f5379,f5383,f5387,f5391,f5395,f5399,f5403,f5407,f5411,f5415,f5616,f5833,f5867,f5871,f5875,f5879,f5883,f5887,f5891,f5895,f5899,f5903,f5907,f5911,f5915,f5919,f5923,f5927,f5931,f5935,f5939,f5943,f5947,f5977,f5981,f5985,f6106,f6388,f6392,f6396,f6414,f6418,f6422,f6426,f6430,f6434,f6438,f6442,f6446,f6450,f6454,f6458,f6462,f6466,f6470,f6474,f6478,f6482,f6486,f6490,f6494,f6523,f6527,f6531,f6535,f6539,f6543,f6547,f6551,f6555,f6559,f6563,f6567,f6571,f6575,f6579,f6583,f6587,f6591,f6595,f6599,f6603,f6632,f6636,f6640,f6644,f6648,f6652,f6656,f6660,f6664,f6668,f6672,f6676,f6680,f6684,f6688,f6692,f6696,f6700,f6987,f7189,f7707,f7788,f7792,f7796,f7800,f7804,f7808,f7812,f7816,f7820,f7824,f7828,f7832,f7836,f7840,f7844,f7848,f7861,f7865,f7869,f7873,f7877,f7881,f7885,f7889,f7893,f7897,f7902,f7906,f7910,f7914,f7918,f7922,f7926,f7930,f7934,f7938,f8334,f8952,f9114,f9118,f9122,f9126,f9241,f9245,f9249,f9253,f9257,f9261,f9265,f9270,f9385,f9389,f9463,f9467,f9471,f9489,f9493,f9497,f9521,f9554,f9558,f9562,f9566,f9744,f9795,f9799,f9803,f9807,f9811,f9815,f9916,f10086,f10141,f10145,f10176,f10181,f10186,f10191,f10196,f10201,f10207,f10360,f10472,f10478,f10549,f10554,f10559,f10564,f10568,f10572,f10576,f10581,f10675,f10679,f11139,f11301,f11773,f13270,f13279,f13289,f13293,f13298,f13645,f13649,f13654,f14005,f14009,f14013,f14017,f14021,f14025,f14692,f14980,f14984,f14988,f14992,f14996,f15017,f15027,f15031,f15036,f15165,f15169,f15174,f15231]) ).
fof(f15231,plain,
( ~ spl0_123
| spl0_680 ),
inference(avatar_contradiction_clause,[],[f15221]) ).
fof(f15221,plain,
( $false
| ~ spl0_123
| spl0_680 ),
inference(resolution,[],[f11300,f1295]) ).
fof(f1295,plain,
( ! [X13] : c_lessequals(X13,X13,tc_RealDef_Oreal)
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1294]) ).
fof(f1294,plain,
( spl0_123
<=> ! [X13] : c_lessequals(X13,X13,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f11300,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_680 ),
inference(avatar_component_clause,[],[f11298]) ).
fof(f11298,plain,
( spl0_680
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f15174,plain,
( spl0_708
| ~ spl0_54
| ~ spl0_65
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2183,f2043,f1004,f949,f15172]) ).
fof(f15172,plain,
( spl0_708
<=> ! [X0] : c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f949,plain,
( spl0_54
<=> class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1004,plain,
( spl0_65
<=> class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f2043,plain,
( spl0_241
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f2183,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 )
| ~ spl0_65
| ~ spl0_241 ),
inference(resolution,[],[f2044,f1006]) ).
fof(f1006,plain,
( class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal)
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1004]) ).
fof(f2044,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 )
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f2043]) ).
fof(f15169,plain,
( spl0_707
| ~ spl0_113
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2153,f2015,f1244,f15167]) ).
fof(f15167,plain,
( spl0_707
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f1244,plain,
( spl0_113
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f2015,plain,
( spl0_234
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f2153,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_113
| ~ spl0_234 ),
inference(resolution,[],[f2016,f1246]) ).
fof(f1246,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1244]) ).
fof(f2016,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) )
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2015]) ).
fof(f15165,plain,
( spl0_706
| ~ spl0_78
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2152,f2015,f1069,f15163]) ).
fof(f15163,plain,
( spl0_706
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f1069,plain,
( spl0_78
<=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f2152,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_78
| ~ spl0_234 ),
inference(resolution,[],[f2016,f1071]) ).
fof(f1071,plain,
( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1069]) ).
fof(f15036,plain,
( spl0_705
| ~ spl0_585
| ~ spl0_704 ),
inference(avatar_split_clause,[],[f15032,f15029,f7704,f15034]) ).
fof(f15034,plain,
( spl0_705
<=> ! [X0] : v_w____ = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f7704,plain,
( spl0_585
<=> v_w____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f15029,plain,
( spl0_704
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f15032,plain,
( ! [X0] : v_w____ = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_585
| ~ spl0_704 ),
inference(forward_demodulation,[],[f15030,f7706]) ).
fof(f7706,plain,
( v_w____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ spl0_585 ),
inference(avatar_component_clause,[],[f7704]) ).
fof(f15030,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_704 ),
inference(avatar_component_clause,[],[f15029]) ).
fof(f15031,plain,
( spl0_704
| ~ spl0_113
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2151,f2011,f1244,f15029]) ).
fof(f2011,plain,
( spl0_233
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f2151,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_113
| ~ spl0_233 ),
inference(resolution,[],[f2012,f1246]) ).
fof(f2012,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) )
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2011]) ).
fof(f15027,plain,
( spl0_703
| ~ spl0_78
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2150,f2011,f1069,f15025]) ).
fof(f15025,plain,
( spl0_703
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f2150,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_78
| ~ spl0_233 ),
inference(resolution,[],[f2012,f1071]) ).
fof(f15017,plain,
( ~ spl0_84
| spl0_702
| ~ spl0_140
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1863,f1686,f1371,f15015,f1099]) ).
fof(f1099,plain,
( spl0_84
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f15015,plain,
( spl0_702
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),c_Complex_ORe(X0),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f1371,plain,
( spl0_140
<=> ! [X3] : c_lessequals(c_Complex_ORe(X3),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1686,plain,
( spl0_197
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1863,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),c_Complex_ORe(X0),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_140
| ~ spl0_197 ),
inference(resolution,[],[f1687,f1372]) ).
fof(f1372,plain,
( ! [X3] : c_lessequals(c_Complex_ORe(X3),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1371]) ).
fof(f1687,plain,
( ! [X3,X0,X4] :
( ~ c_lessequals(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f1686]) ).
fof(f14996,plain,
( spl0_701
| ~ spl0_145
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1638,f1532,f1393,f14994]) ).
fof(f14994,plain,
( spl0_701
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(X1,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f1393,plain,
( spl0_145
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| c_lessequals(X3,X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1532,plain,
( spl0_176
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(X3,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1638,plain,
( ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(X1,X0),tc_RealDef_Oreal) )
| ~ spl0_145
| ~ spl0_176 ),
inference(resolution,[],[f1533,f1394]) ).
fof(f1394,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| c_lessequals(X3,X4,tc_RealDef_Oreal) )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1393]) ).
fof(f1533,plain,
( ! [X3,X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(X3,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X0) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1532]) ).
fof(f14992,plain,
( spl0_700
| ~ spl0_145
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1637,f1528,f1393,f14990]) ).
fof(f14990,plain,
( spl0_700
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(X1,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f1528,plain,
( spl0_175
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(X4,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1637,plain,
( ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(X1,X0),tc_RealDef_Oreal) )
| ~ spl0_145
| ~ spl0_175 ),
inference(resolution,[],[f1529,f1394]) ).
fof(f1529,plain,
( ! [X0,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(X4,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X0) )
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1528]) ).
fof(f14988,plain,
( spl0_699
| ~ spl0_139
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1629,f1520,f1367,f14986]) ).
fof(f14986,plain,
( spl0_699
<=> ! [X0] : c_Transcendental_Ocos(c_NthRoot_Osqrt(X0)) = c_Transcendental_Ocos(c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f1367,plain,
( spl0_139
<=> ! [X3] : c_Transcendental_Ocos(X3) = c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1520,plain,
( spl0_173
<=> ! [X3] : c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(X3),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1629,plain,
( ! [X0] : c_Transcendental_Ocos(c_NthRoot_Osqrt(X0)) = c_Transcendental_Ocos(c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal)))
| ~ spl0_139
| ~ spl0_173 ),
inference(superposition,[],[f1368,f1521]) ).
fof(f1521,plain,
( ! [X3] : c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(X3),tc_RealDef_Oreal)
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1520]) ).
fof(f1368,plain,
( ! [X3] : c_Transcendental_Ocos(X3) = c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal))
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1367]) ).
fof(f14984,plain,
( spl0_698
| ~ spl0_139
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1619,f1500,f1367,f14982]) ).
fof(f14982,plain,
( spl0_698
<=> ! [X0] : c_Transcendental_Ocos(c_Transcendental_Osin(X0)) = c_Transcendental_Ocos(c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f1500,plain,
( spl0_168
<=> ! [X3] : c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X3),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1619,plain,
( ! [X0] : c_Transcendental_Ocos(c_Transcendental_Osin(X0)) = c_Transcendental_Ocos(c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal)))
| ~ spl0_139
| ~ spl0_168 ),
inference(superposition,[],[f1368,f1501]) ).
fof(f1501,plain,
( ! [X3] : c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X3),tc_RealDef_Oreal)
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f1500]) ).
fof(f14980,plain,
( spl0_697
| ~ spl0_145
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1593,f1447,f1393,f14978]) ).
fof(f14978,plain,
( spl0_697
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(X1,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f1447,plain,
( spl0_155
<=> ! [X0,X10] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(X10,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1593,plain,
( ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(X1,X0),tc_RealDef_Oreal) )
| ~ spl0_145
| ~ spl0_155 ),
inference(resolution,[],[f1448,f1394]) ).
fof(f1448,plain,
( ! [X10,X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(X10,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X0) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f1447]) ).
fof(f14692,plain,
( spl0_696
| ~ spl0_41
| ~ spl0_206
| ~ spl0_231
| ~ spl0_665 ),
inference(avatar_split_clause,[],[f10263,f10204,f1902,f1722,f884,f14689]) ).
fof(f14689,plain,
( spl0_696
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f884,plain,
( spl0_41
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1722,plain,
( spl0_206
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1902,plain,
( spl0_231
<=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f10204,plain,
( spl0_665
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f10263,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_41
| ~ spl0_206
| ~ spl0_231
| ~ spl0_665 ),
inference(forward_demodulation,[],[f10210,f1908]) ).
fof(f1908,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_41
| ~ spl0_206 ),
inference(resolution,[],[f1723,f886]) ).
fof(f886,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f884]) ).
fof(f1723,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_206 ),
inference(avatar_component_clause,[],[f1722]) ).
fof(f10210,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_231
| ~ spl0_665 ),
inference(superposition,[],[f1904,f10206]) ).
fof(f10206,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex)
| ~ spl0_665 ),
inference(avatar_component_clause,[],[f10204]) ).
fof(f1904,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_231 ),
inference(avatar_component_clause,[],[f1902]) ).
fof(f14025,plain,
( spl0_695
| ~ spl0_205
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2461,f2374,f1718,f14023]) ).
fof(f14023,plain,
( spl0_695
<=> ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f1718,plain,
( spl0_205
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f2374,plain,
( spl0_275
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2461,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_205
| ~ spl0_275 ),
inference(duplicate_literal_removal,[],[f2449]) ).
fof(f2449,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_205
| ~ spl0_275 ),
inference(resolution,[],[f2375,f1719]) ).
fof(f1719,plain,
( ! [X0] :
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f1718]) ).
fof(f2375,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_lessequals(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_275 ),
inference(avatar_component_clause,[],[f2374]) ).
fof(f14021,plain,
( spl0_694
| ~ spl0_110
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1930,f1758,f1229,f14019]) ).
fof(f14019,plain,
( spl0_694
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f1229,plain,
( spl0_110
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1758,plain,
( spl0_215
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1930,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_110
| ~ spl0_215 ),
inference(resolution,[],[f1759,f1231]) ).
fof(f1231,plain,
( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1229]) ).
fof(f1759,plain,
( ! [X0,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X5,X0) )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f1758]) ).
fof(f14017,plain,
( spl0_693
| ~ spl0_75
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1929,f1758,f1054,f14015]) ).
fof(f14015,plain,
( spl0_693
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f1054,plain,
( spl0_75
<=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1929,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_75
| ~ spl0_215 ),
inference(resolution,[],[f1759,f1056]) ).
fof(f1056,plain,
( class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f1054]) ).
fof(f14013,plain,
( spl0_692
| ~ spl0_24
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1928,f1758,f799,f14011]) ).
fof(f14011,plain,
( spl0_692
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f799,plain,
( spl0_24
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1928,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ spl0_24
| ~ spl0_215 ),
inference(resolution,[],[f1759,f801]) ).
fof(f801,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f14009,plain,
( spl0_691
| ~ spl0_22
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1915,f1738,f789,f14007]) ).
fof(f14007,plain,
( spl0_691
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f789,plain,
( spl0_22
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1738,plain,
( spl0_210
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1915,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ spl0_22
| ~ spl0_210 ),
inference(resolution,[],[f1739,f791]) ).
fof(f791,plain,
( class_Ring__and__Field_Omult__zero(tc_nat)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f789]) ).
fof(f1739,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_210 ),
inference(avatar_component_clause,[],[f1738]) ).
fof(f14005,plain,
( spl0_690
| ~ spl0_22
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1912,f1730,f789,f14003]) ).
fof(f14003,plain,
( spl0_690
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f1730,plain,
( spl0_208
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1912,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_22
| ~ spl0_208 ),
inference(resolution,[],[f1731,f791]) ).
fof(f1731,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f1730]) ).
fof(f13654,plain,
( spl0_689
| ~ spl0_585
| ~ spl0_688 ),
inference(avatar_split_clause,[],[f13650,f13647,f7704,f13652]) ).
fof(f13652,plain,
( spl0_689
<=> ! [X0] : v_w____ = c_HOL_Otimes__class_Otimes(v_w____,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f13647,plain,
( spl0_688
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f13650,plain,
( ! [X0] : v_w____ = c_HOL_Otimes__class_Otimes(v_w____,X0,tc_Complex_Ocomplex)
| ~ spl0_585
| ~ spl0_688 ),
inference(forward_demodulation,[],[f13648,f7706]) ).
fof(f13648,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_688 ),
inference(avatar_component_clause,[],[f13647]) ).
fof(f13649,plain,
( spl0_688
| ~ spl0_90
| ~ spl0_207 ),
inference(avatar_split_clause,[],[f1911,f1726,f1129,f13647]) ).
fof(f1129,plain,
( spl0_90
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1726,plain,
( spl0_207
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1911,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_90
| ~ spl0_207 ),
inference(resolution,[],[f1727,f1131]) ).
fof(f1131,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex)
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1129]) ).
fof(f1727,plain,
( ! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) )
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f1726]) ).
fof(f13645,plain,
( spl0_687
| ~ spl0_41
| ~ spl0_207 ),
inference(avatar_split_clause,[],[f1910,f1726,f884,f13643]) ).
fof(f13643,plain,
( spl0_687
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f1910,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_41
| ~ spl0_207 ),
inference(resolution,[],[f1727,f886]) ).
fof(f13298,plain,
( spl0_686
| ~ spl0_585
| ~ spl0_685 ),
inference(avatar_split_clause,[],[f13294,f13291,f7704,f13296]) ).
fof(f13296,plain,
( spl0_686
<=> ! [X0] : v_w____ = c_HOL_Otimes__class_Otimes(X0,v_w____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f13291,plain,
( spl0_685
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f13294,plain,
( ! [X0] : v_w____ = c_HOL_Otimes__class_Otimes(X0,v_w____,tc_Complex_Ocomplex)
| ~ spl0_585
| ~ spl0_685 ),
inference(forward_demodulation,[],[f13292,f7706]) ).
fof(f13292,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_685 ),
inference(avatar_component_clause,[],[f13291]) ).
fof(f13293,plain,
( spl0_685
| ~ spl0_90
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f1909,f1722,f1129,f13291]) ).
fof(f1909,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_90
| ~ spl0_206 ),
inference(resolution,[],[f1723,f1131]) ).
fof(f13289,plain,
( spl0_684
| ~ spl0_41
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f1908,f1722,f884,f13287]) ).
fof(f13287,plain,
( spl0_684
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f13279,plain,
( ~ spl0_84
| spl0_683
| ~ spl0_135
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1862,f1686,f1349,f13277,f1099]) ).
fof(f13277,plain,
( spl0_683
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Ocos(X0),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f1349,plain,
( spl0_135
<=> ! [X3] : c_lessequals(c_Transcendental_Ocos(X3),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1862,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Ocos(X0),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_135
| ~ spl0_197 ),
inference(resolution,[],[f1687,f1350]) ).
fof(f1350,plain,
( ! [X3] : c_lessequals(c_Transcendental_Ocos(X3),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1349]) ).
fof(f13270,plain,
( ~ spl0_84
| spl0_682
| ~ spl0_134
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1861,f1686,f1345,f13268,f1099]) ).
fof(f13268,plain,
( spl0_682
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Osin(X0),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f1345,plain,
( spl0_134
<=> ! [X3] : c_lessequals(c_Transcendental_Osin(X3),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1861,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Osin(X0),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_134
| ~ spl0_197 ),
inference(resolution,[],[f1687,f1346]) ).
fof(f1346,plain,
( ! [X3] : c_lessequals(c_Transcendental_Osin(X3),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1345]) ).
fof(f11773,plain,
( spl0_681
| ~ spl0_291
| ~ spl0_585 ),
inference(avatar_split_clause,[],[f11448,f7704,f2519,f11770]) ).
fof(f11770,plain,
( spl0_681
<=> v_w____ = c_HOL_Oinverse__class_Oinverse(v_w____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f2519,plain,
( spl0_291
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f11448,plain,
( v_w____ = c_HOL_Oinverse__class_Oinverse(v_w____,tc_Complex_Ocomplex)
| ~ spl0_291
| ~ spl0_585 ),
inference(superposition,[],[f2521,f7706]) ).
fof(f2521,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f2519]) ).
fof(f11301,plain,
( ~ spl0_680
| ~ spl0_41
| spl0_121
| ~ spl0_206
| ~ spl0_665 ),
inference(avatar_split_clause,[],[f10261,f10204,f1722,f1285,f884,f11298]) ).
fof(f1285,plain,
( spl0_121
<=> c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f10261,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_41
| spl0_121
| ~ spl0_206
| ~ spl0_665 ),
inference(forward_demodulation,[],[f10208,f1908]) ).
fof(f10208,plain,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_121
| ~ spl0_665 ),
inference(superposition,[],[f1287,f10206]) ).
fof(f1287,plain,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| spl0_121 ),
inference(avatar_component_clause,[],[f1285]) ).
fof(f11139,plain,
( ~ spl0_679
| ~ spl0_86
| ~ spl0_126
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f1983,f1803,f1308,f1109,f11136]) ).
fof(f11136,plain,
( spl0_679
<=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f1109,plain,
( spl0_86
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1308,plain,
( spl0_126
<=> c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1803,plain,
( spl0_226
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1983,plain,
( ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal)
| ~ spl0_126
| ~ spl0_226 ),
inference(resolution,[],[f1804,f1310]) ).
fof(f1310,plain,
( c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f1308]) ).
fof(f1804,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) )
| ~ spl0_226 ),
inference(avatar_component_clause,[],[f1803]) ).
fof(f10679,plain,
( spl0_678
| ~ spl0_110
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1655,f1573,f1229,f10677]) ).
fof(f10677,plain,
( spl0_678
<=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f1573,plain,
( spl0_186
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f1655,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_110
| ~ spl0_186 ),
inference(resolution,[],[f1574,f1231]) ).
fof(f1574,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 )
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f1573]) ).
fof(f10675,plain,
( spl0_677
| ~ spl0_24
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1653,f1573,f799,f10673]) ).
fof(f10673,plain,
( spl0_677
<=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f1653,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0
| ~ spl0_24
| ~ spl0_186 ),
inference(resolution,[],[f1574,f801]) ).
fof(f10581,plain,
( spl0_676
| ~ spl0_140
| ~ spl0_665 ),
inference(avatar_split_clause,[],[f10238,f10204,f1371,f10578]) ).
fof(f10578,plain,
( spl0_676
<=> c_lessequals(c_Complex_ORe(v_w____),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f10238,plain,
( c_lessequals(c_Complex_ORe(v_w____),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_140
| ~ spl0_665 ),
inference(superposition,[],[f1372,f10206]) ).
fof(f10576,plain,
( spl0_675
| ~ spl0_110
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1648,f1569,f1229,f10574]) ).
fof(f10574,plain,
( spl0_675
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f1569,plain,
( spl0_185
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1648,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_110
| ~ spl0_185 ),
inference(resolution,[],[f1570,f1231]) ).
fof(f1570,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f1569]) ).
fof(f10572,plain,
( spl0_674
| ~ spl0_75
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1647,f1569,f1054,f10570]) ).
fof(f10570,plain,
( spl0_674
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f1647,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_75
| ~ spl0_185 ),
inference(resolution,[],[f1570,f1056]) ).
fof(f10568,plain,
( spl0_673
| ~ spl0_24
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1646,f1569,f799,f10566]) ).
fof(f10566,plain,
( spl0_673
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f1646,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_24
| ~ spl0_185 ),
inference(resolution,[],[f1570,f801]) ).
fof(f10564,plain,
( spl0_672
| ~ spl0_94
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1645,f1565,f1149,f10561]) ).
fof(f10561,plain,
( spl0_672
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f1149,plain,
( spl0_94
<=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1565,plain,
( spl0_184
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1645,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_94
| ~ spl0_184 ),
inference(resolution,[],[f1566,f1151]) ).
fof(f1151,plain,
( class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1149]) ).
fof(f1566,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1565]) ).
fof(f10559,plain,
( spl0_671
| ~ spl0_51
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1644,f1565,f934,f10556]) ).
fof(f10556,plain,
( spl0_671
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f934,plain,
( spl0_51
<=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1644,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_51
| ~ spl0_184 ),
inference(resolution,[],[f1566,f936]) ).
fof(f936,plain,
( class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal)
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f934]) ).
fof(f10554,plain,
( spl0_670
| ~ spl0_107
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1643,f1552,f1214,f10551]) ).
fof(f10551,plain,
( spl0_670
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f1214,plain,
( spl0_107
<=> class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1552,plain,
( spl0_181
<=> ! [X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1643,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_Complex_Ocomplex)
| ~ spl0_107
| ~ spl0_181 ),
inference(resolution,[],[f1553,f1216]) ).
fof(f1216,plain,
( class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1214]) ).
fof(f1553,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0) )
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f1552]) ).
fof(f10549,plain,
( spl0_669
| ~ spl0_71
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1642,f1552,f1034,f10546]) ).
fof(f10546,plain,
( spl0_669
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f1034,plain,
( spl0_71
<=> class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1642,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_71
| ~ spl0_181 ),
inference(resolution,[],[f1553,f1036]) ).
fof(f1036,plain,
( class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal)
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f1034]) ).
fof(f10478,plain,
( spl0_668
| ~ spl0_585
| ~ spl0_667 ),
inference(avatar_split_clause,[],[f10473,f10469,f7704,f10475]) ).
fof(f10475,plain,
( spl0_668
<=> v_w____ = c_HOL_Ouminus__class_Ouminus(v_w____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f10469,plain,
( spl0_667
<=> 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_667])]) ).
fof(f10473,plain,
( v_w____ = c_HOL_Ouminus__class_Ouminus(v_w____,tc_Complex_Ocomplex)
| ~ spl0_585
| ~ spl0_667 ),
inference(forward_demodulation,[],[f10471,f7706]) ).
fof(f10471,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_667 ),
inference(avatar_component_clause,[],[f10469]) ).
fof(f10472,plain,
( spl0_667
| ~ spl0_113
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1640,f1540,f1244,f10469]) ).
fof(f1540,plain,
( spl0_178
<=> ! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1640,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_113
| ~ spl0_178 ),
inference(resolution,[],[f1541,f1246]) ).
fof(f1541,plain,
( ! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1540]) ).
fof(f10360,plain,
( spl0_666
| ~ spl0_78
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1639,f1540,f1069,f10357]) ).
fof(f10357,plain,
( spl0_666
<=> 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_666])]) ).
fof(f1639,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_78
| ~ spl0_178 ),
inference(resolution,[],[f1541,f1071]) ).
fof(f10207,plain,
( spl0_665
| ~ spl0_585
| ~ spl0_664 ),
inference(avatar_split_clause,[],[f10202,f10198,f7704,f10204]) ).
fof(f10198,plain,
( spl0_664
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f10202,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex)
| ~ spl0_585
| ~ spl0_664 ),
inference(forward_demodulation,[],[f10200,f7706]) ).
fof(f10200,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_664 ),
inference(avatar_component_clause,[],[f10198]) ).
fof(f10201,plain,
( spl0_664
| ~ spl0_100
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1631,f1524,f1179,f10198]) ).
fof(f1179,plain,
( spl0_100
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1524,plain,
( spl0_174
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1631,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_100
| ~ spl0_174 ),
inference(resolution,[],[f1525,f1181]) ).
fof(f1181,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1179]) ).
fof(f1525,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f1524]) ).
fof(f10196,plain,
( spl0_663
| ~ spl0_59
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1630,f1524,f974,f10193]) ).
fof(f10193,plain,
( spl0_663
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f974,plain,
( spl0_59
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1630,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_59
| ~ spl0_174 ),
inference(resolution,[],[f1525,f976]) ).
fof(f976,plain,
( class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f10191,plain,
( spl0_662
| ~ spl0_69
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1622,f1508,f1024,f10188]) ).
fof(f10188,plain,
( spl0_662
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f1024,plain,
( spl0_69
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1508,plain,
( spl0_170
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1622,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_69
| ~ spl0_170 ),
inference(resolution,[],[f1509,f1026]) ).
fof(f1026,plain,
( class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal)
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f1024]) ).
fof(f1509,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1508]) ).
fof(f10186,plain,
( spl0_661
| ~ spl0_103
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f1621,f1504,f1194,f10183]) ).
fof(f10183,plain,
( spl0_661
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f1194,plain,
( spl0_103
<=> class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1504,plain,
( spl0_169
<=> ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1621,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_103
| ~ spl0_169 ),
inference(resolution,[],[f1505,f1196]) ).
fof(f1196,plain,
( class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex)
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1194]) ).
fof(f1505,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f1504]) ).
fof(f10181,plain,
( spl0_660
| ~ spl0_65
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f1620,f1504,f1004,f10178]) ).
fof(f10178,plain,
( spl0_660
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f1620,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_65
| ~ spl0_169 ),
inference(resolution,[],[f1505,f1006]) ).
fof(f10176,plain,
( ~ spl0_69
| ~ spl0_151
| ~ spl0_622
| ~ spl0_182
| spl0_121
| ~ spl0_637 ),
inference(avatar_split_clause,[],[f9421,f9387,f1285,f1556,f8331,f1425,f1024]) ).
fof(f1425,plain,
( spl0_151
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f8331,plain,
( spl0_622
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f1556,plain,
( spl0_182
<=> c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f9387,plain,
( spl0_637
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f9421,plain,
( ~ c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal)
| spl0_121
| ~ spl0_637 ),
inference(resolution,[],[f9388,f1287]) ).
fof(f9388,plain,
( ! [X3,X0,X4] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X0),X3,X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_637 ),
inference(avatar_component_clause,[],[f9387]) ).
fof(f10145,plain,
spl0_659,
inference(avatar_split_clause,[],[f230,f10143]) ).
fof(f10143,plain,
( spl0_659
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f230,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_division__ring__inverse__add_0) ).
fof(f10141,plain,
spl0_658,
inference(avatar_split_clause,[],[f229,f10139]) ).
fof(f10139,plain,
( spl0_658
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f229,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__add_0) ).
fof(f10086,plain,
spl0_657,
inference(avatar_split_clause,[],[f287,f10084]) ).
fof(f10084,plain,
( spl0_657
<=> ! [X4,X13,X0,X3,X8] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X3 = X13
| X4 = X8
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X13,X4,X0),c_HOL_Otimes__class_Otimes(X3,X8,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X13,X8,X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f287,axiom,
! [X3,X0,X8,X4,X13] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X3 = X13
| X4 = X8
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X13,X4,X0),c_HOL_Otimes__class_Otimes(X3,X8,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X13,X8,X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
fof(f9916,plain,
( ~ spl0_38
| spl0_656
| ~ spl0_242
| ~ spl0_612 ),
inference(avatar_split_clause,[],[f7958,f7899,f2047,f9913,f869]) ).
fof(f869,plain,
( spl0_38
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f9913,plain,
( spl0_656
<=> c_lessequals(c_HOL_Ouminus__class_Ouminus(v_t____,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f2047,plain,
( spl0_242
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f7899,plain,
( spl0_612
<=> v_t____ = c_HOL_Oabs__class_Oabs(v_t____,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f7958,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(v_t____,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_242
| ~ spl0_612 ),
inference(superposition,[],[f2048,f7901]) ).
fof(f7901,plain,
( v_t____ = c_HOL_Oabs__class_Oabs(v_t____,tc_RealDef_Oreal)
| ~ spl0_612 ),
inference(avatar_component_clause,[],[f7899]) ).
fof(f2048,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f2047]) ).
fof(f9815,plain,
spl0_655,
inference(avatar_split_clause,[],[f460,f9813]) ).
fof(f9813,plain,
( spl0_655
<=> ! [X0,X7,X6,X2,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X6,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f460,axiom,
! [X2,X0,X1,X6,X7] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X6,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
fof(f9811,plain,
spl0_654,
inference(avatar_split_clause,[],[f459,f9809]) ).
fof(f9809,plain,
( spl0_654
<=> ! [X0,X7,X6,X2,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X6,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f459,axiom,
! [X2,X0,X1,X6,X7] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X6,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
fof(f9807,plain,
spl0_653,
inference(avatar_split_clause,[],[f265,f9805]) ).
fof(f9805,plain,
( spl0_653
<=> ! [X0,X7,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f265,axiom,
! [X2,X0,X1,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
fof(f9803,plain,
spl0_652,
inference(avatar_split_clause,[],[f154,f9801]) ).
fof(f9801,plain,
( spl0_652
<=> ! [X0,X7,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f154,axiom,
! [X2,X0,X1,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
fof(f9799,plain,
spl0_651,
inference(avatar_split_clause,[],[f152,f9797]) ).
fof(f9797,plain,
( spl0_651
<=> ! [X1,X0,X6,X2,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f152,axiom,
! [X2,X0,X1,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
fof(f9795,plain,
spl0_650,
inference(avatar_split_clause,[],[f151,f9793]) ).
fof(f9793,plain,
( spl0_650
<=> ! [X0,X7,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X6,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f151,axiom,
! [X2,X0,X1,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X6,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
fof(f9744,plain,
spl0_649,
inference(avatar_split_clause,[],[f33,f9742]) ).
fof(f9742,plain,
( spl0_649
<=> ! [X2,X0,X6,X1,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f33,axiom,
! [X2,X0,X1,X6,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).
fof(f9566,plain,
spl0_648,
inference(avatar_split_clause,[],[f158,f9564]) ).
fof(f9564,plain,
( spl0_648
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f158,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_0) ).
fof(f9562,plain,
spl0_647,
inference(avatar_split_clause,[],[f157,f9560]) ).
fof(f9560,plain,
( spl0_647
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f157,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_1) ).
fof(f9558,plain,
spl0_646,
inference(avatar_split_clause,[],[f156,f9556]) ).
fof(f9556,plain,
( spl0_646
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f156,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_2) ).
fof(f9554,plain,
spl0_645,
inference(avatar_split_clause,[],[f155,f9552]) ).
fof(f9552,plain,
( spl0_645
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f155,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).
fof(f9521,plain,
( ~ spl0_84
| ~ spl0_644
| ~ spl0_224
| ~ spl0_583 ),
inference(avatar_split_clause,[],[f7853,f7182,f1795,f9518,f1099]) ).
fof(f9518,plain,
( spl0_644
<=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f1795,plain,
( spl0_224
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f7182,plain,
( spl0_583
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f7853,plain,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl0_224
| ~ spl0_583 ),
inference(resolution,[],[f7183,f1796]) ).
fof(f1796,plain,
( ! [X3,X0,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f1795]) ).
fof(f7183,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_583 ),
inference(avatar_component_clause,[],[f7182]) ).
fof(f9497,plain,
spl0_643,
inference(avatar_split_clause,[],[f511,f9495]) ).
fof(f9495,plain,
( spl0_643
<=> ! [X4,X11,X0,X3,X21] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X0),X11,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X0),X21,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0),c_HOL_Otimes__class_Otimes(X11,X21,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f511,axiom,
! [X21,X3,X0,X11,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X0),X11,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X0),X21,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0),c_HOL_Otimes__class_Otimes(X11,X21,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult__less_0) ).
fof(f9493,plain,
spl0_642,
inference(avatar_split_clause,[],[f318,f9491]) ).
fof(f9491,plain,
( spl0_642
<=> ! [X20,X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X20,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X20,X0),X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X20,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f318,axiom,
! [X2,X0,X1,X6,X20] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X20,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X20,X0),X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X20,X0),X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
fof(f9489,plain,
spl0_641,
inference(avatar_split_clause,[],[f204,f9487]) ).
fof(f9487,plain,
( spl0_641
<=> ! [X11,X0,X6,X3,X7] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X6 = X7
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X11,X6,X0),X0) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X11,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f204,axiom,
! [X3,X0,X11,X6,X7] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X6 = X7
| c_HOL_Ozero__class_Ozero(X0) = X11
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X11,X6,X0),X0) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X11,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(f9471,plain,
spl0_640,
inference(avatar_split_clause,[],[f316,f9469]) ).
fof(f9469,plain,
( spl0_640
<=> ! [X4,X0,X3,X8] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X3,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f316,axiom,
! [X3,X0,X8,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X3,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
fof(f9467,plain,
spl0_639,
inference(avatar_split_clause,[],[f243,f9465]) ).
fof(f9465,plain,
( spl0_639
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f243,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
fof(f9463,plain,
spl0_638,
inference(avatar_split_clause,[],[f222,f9461]) ).
fof(f9461,plain,
( spl0_638
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X5,X0),X0),c_Power_Opower__class_Opower(X1,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f222,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X5,X0),X0),c_Power_Opower__class_Opower(X1,X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
fof(f9389,plain,
spl0_637,
inference(avatar_split_clause,[],[f510,f9387]) ).
fof(f510,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
fof(f9385,plain,
spl0_636,
inference(avatar_split_clause,[],[f509,f9383]) ).
fof(f9383,plain,
( spl0_636
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f509,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X4,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
fof(f9270,plain,
( ~ spl0_84
| ~ spl0_635
| ~ spl0_197
| ~ spl0_623 ),
inference(avatar_split_clause,[],[f9205,f8949,f1686,f9267,f1099]) ).
fof(f9267,plain,
( spl0_635
<=> c_HOL_Oord__class_Oless(v_t____,c_HOL_Ouminus__class_Ouminus(v_t____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f8949,plain,
( spl0_623
<=> c_lessequals(c_HOL_Ouminus__class_Ouminus(v_t____,tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f9205,plain,
( ~ c_HOL_Oord__class_Oless(v_t____,c_HOL_Ouminus__class_Ouminus(v_t____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl0_197
| ~ spl0_623 ),
inference(resolution,[],[f8951,f1687]) ).
fof(f8951,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(v_t____,tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal)
| ~ spl0_623 ),
inference(avatar_component_clause,[],[f8949]) ).
fof(f9265,plain,
spl0_634,
inference(avatar_split_clause,[],[f682,f9263]) ).
fof(f9263,plain,
( spl0_634
<=> ! [X0,X10,X2,X1] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X0),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(X10,X0),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f682,plain,
! [X2,X10,X0,X1] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X0),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(X10,X0),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(forward_demodulation,[],[f515,f532]) ).
fof(f532,axiom,
! [X28,X29,X27] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X27,X28,tc_RealDef_Oreal),X29,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X27,c_HOL_Otimes__class_Otimes(X28,X29,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__assoc_0) ).
fof(f515,axiom,
! [X2,X10,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,X0),c_RealVector_Onorm__class_Onorm(X2,X0),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(X10,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Opos__bounded_1) ).
fof(f9261,plain,
spl0_633,
inference(avatar_split_clause,[],[f681,f9259]) ).
fof(f9259,plain,
( spl0_633
<=> ! [X0,X9,X2,X1] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X0),c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1(X9,X0),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f681,plain,
! [X2,X0,X1,X9] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X0),c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1(X9,X0),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(forward_demodulation,[],[f518,f532]) ).
fof(f518,axiom,
! [X2,X0,X1,X9] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,X0),c_RealVector_Onorm__class_Onorm(X2,X0),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1(X9,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ononneg__bounded_1) ).
fof(f9257,plain,
spl0_632,
inference(avatar_split_clause,[],[f680,f9255]) ).
fof(f9255,plain,
( spl0_632
<=> ! [X2,X0,X22,X1] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X0),c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1(X22,X0),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f680,plain,
! [X2,X0,X1,X22] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X0),c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1(X22,X0),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(forward_demodulation,[],[f512,f532]) ).
fof(f512,axiom,
! [X2,X0,X1,X22] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,X0),c_RealVector_Onorm__class_Onorm(X2,X0),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1(X22,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Obounded_0) ).
fof(f9253,plain,
spl0_631,
inference(avatar_split_clause,[],[f546,f9251]) ).
fof(f9251,plain,
( spl0_631
<=> ! [X31,X0,X33,X32,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X33,X0),c_HOL_Otimes__class_Otimes(X31,X32,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X0),c_HOL_Otimes__class_Otimes(X33,X32,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f546,axiom,
! [X31,X0,X32,X30,X33] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X33,X0),c_HOL_Otimes__class_Otimes(X31,X32,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X0),c_HOL_Otimes__class_Otimes(X33,X32,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f9249,plain,
spl0_630,
inference(avatar_split_clause,[],[f233,f9247]) ).
fof(f9247,plain,
( spl0_630
<=> ! [X1,X0,X6,X2,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f233,axiom,
! [X2,X0,X1,X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f9245,plain,
spl0_629,
inference(avatar_split_clause,[],[f48,f9243]) ).
fof(f9243,plain,
( spl0_629
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f48,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
fof(f9241,plain,
spl0_628,
inference(avatar_split_clause,[],[f47,f9239]) ).
fof(f9239,plain,
( spl0_628
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f47,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
fof(f9126,plain,
spl0_627,
inference(avatar_split_clause,[],[f351,f9124]) ).
fof(f9124,plain,
( spl0_627
<=> ! [X4,X0,X6,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X3,X0),c_HOL_Otimes__class_Otimes(X6,c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f351,axiom,
! [X3,X0,X6,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X3,X0),c_HOL_Otimes__class_Otimes(X6,c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ratiotest__lemma_0) ).
fof(f9122,plain,
spl0_626,
inference(avatar_split_clause,[],[f321,f9120]) ).
fof(f9120,plain,
( spl0_626
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X5,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X5,X0),c_Power_Opower__class_Opower(X1,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f321,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X5,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X5,X0),c_Power_Opower__class_Opower(X1,X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__minus_0) ).
fof(f9118,plain,
spl0_625,
inference(avatar_split_clause,[],[f225,f9116]) ).
fof(f9116,plain,
( spl0_625
<=> ! [X6,X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f225,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
fof(f9114,plain,
spl0_624,
inference(avatar_split_clause,[],[f224,f9112]) ).
fof(f9112,plain,
( spl0_624
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f224,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
fof(f8952,plain,
( ~ spl0_38
| spl0_623
| ~ spl0_222
| ~ spl0_612 ),
inference(avatar_split_clause,[],[f7957,f7899,f1787,f8949,f869]) ).
fof(f1787,plain,
( spl0_222
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f7957,plain,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(v_t____,tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ spl0_222
| ~ spl0_612 ),
inference(superposition,[],[f1788,f7901]) ).
fof(f1788,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f1787]) ).
fof(f8334,plain,
( spl0_622
| ~ spl0_145
| ~ spl0_583 ),
inference(avatar_split_clause,[],[f7850,f7182,f1393,f8331]) ).
fof(f7850,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_145
| ~ spl0_583 ),
inference(resolution,[],[f7183,f1394]) ).
fof(f7938,plain,
spl0_621,
inference(avatar_split_clause,[],[f476,f7936]) ).
fof(f7936,plain,
( spl0_621
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f476,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
fof(f7934,plain,
spl0_620,
inference(avatar_split_clause,[],[f475,f7932]) ).
fof(f7932,plain,
( spl0_620
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f475,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
fof(f7930,plain,
spl0_619,
inference(avatar_split_clause,[],[f474,f7928]) ).
fof(f7928,plain,
( spl0_619
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f474,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
fof(f7926,plain,
spl0_618,
inference(avatar_split_clause,[],[f473,f7924]) ).
fof(f7924,plain,
( spl0_618
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f473,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
fof(f7922,plain,
spl0_617,
inference(avatar_split_clause,[],[f472,f7920]) ).
fof(f7920,plain,
( spl0_617
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f472,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
fof(f7918,plain,
spl0_616,
inference(avatar_split_clause,[],[f446,f7916]) ).
fof(f7916,plain,
( spl0_616
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f446,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
fof(f7914,plain,
spl0_615,
inference(avatar_split_clause,[],[f445,f7912]) ).
fof(f7912,plain,
( spl0_615
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f445,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
fof(f7910,plain,
spl0_614,
inference(avatar_split_clause,[],[f444,f7908]) ).
fof(f7908,plain,
( spl0_614
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f444,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
fof(f7906,plain,
spl0_613,
inference(avatar_split_clause,[],[f443,f7904]) ).
fof(f7904,plain,
( spl0_613
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f443,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
fof(f7902,plain,
( ~ spl0_80
| spl0_612
| ~ spl0_285
| spl0_584 ),
inference(avatar_split_clause,[],[f7314,f7186,f2415,f7899,f1079]) ).
fof(f1079,plain,
( spl0_80
<=> class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f2415,plain,
( spl0_285
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f7186,plain,
( spl0_584
<=> c_HOL_Oord__class_Oless(v_t____,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f7314,plain,
( v_t____ = c_HOL_Oabs__class_Oabs(v_t____,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
| ~ spl0_285
| spl0_584 ),
inference(resolution,[],[f7188,f2416]) ).
fof(f2416,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| ~ class_Ring__and__Field_Oabs__if(X0) )
| ~ spl0_285 ),
inference(avatar_component_clause,[],[f2415]) ).
fof(f7188,plain,
( ~ c_HOL_Oord__class_Oless(v_t____,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_584 ),
inference(avatar_component_clause,[],[f7186]) ).
fof(f7897,plain,
spl0_611,
inference(avatar_split_clause,[],[f431,f7895]) ).
fof(f7895,plain,
( spl0_611
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f431,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
fof(f7893,plain,
spl0_610,
inference(avatar_split_clause,[],[f417,f7891]) ).
fof(f7891,plain,
( spl0_610
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f417,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).
fof(f7889,plain,
spl0_609,
inference(avatar_split_clause,[],[f320,f7887]) ).
fof(f7887,plain,
( spl0_609
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),X3,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f320,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),X3,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_0) ).
fof(f7885,plain,
spl0_608,
inference(avatar_split_clause,[],[f271,f7883]) ).
fof(f7883,plain,
( spl0_608
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f271,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
fof(f7881,plain,
spl0_607,
inference(avatar_split_clause,[],[f270,f7879]) ).
fof(f7879,plain,
( spl0_607
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f270,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
fof(f7877,plain,
spl0_606,
inference(avatar_split_clause,[],[f269,f7875]) ).
fof(f7875,plain,
( spl0_606
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f269,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
fof(f7873,plain,
spl0_605,
inference(avatar_split_clause,[],[f268,f7871]) ).
fof(f7871,plain,
( spl0_605
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f268,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
fof(f7869,plain,
spl0_604,
inference(avatar_split_clause,[],[f267,f7867]) ).
fof(f7867,plain,
( spl0_604
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f267,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
fof(f7865,plain,
spl0_603,
inference(avatar_split_clause,[],[f266,f7863]) ).
fof(f7863,plain,
( spl0_603
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f266,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
fof(f7861,plain,
spl0_602,
inference(avatar_split_clause,[],[f263,f7859]) ).
fof(f7859,plain,
( spl0_602
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f263,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
fof(f7848,plain,
spl0_601,
inference(avatar_split_clause,[],[f262,f7846]) ).
fof(f7846,plain,
( spl0_601
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f262,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
fof(f7844,plain,
spl0_600,
inference(avatar_split_clause,[],[f261,f7842]) ).
fof(f7842,plain,
( spl0_600
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f261,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
fof(f7840,plain,
spl0_599,
inference(avatar_split_clause,[],[f260,f7838]) ).
fof(f7838,plain,
( spl0_599
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f260,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
fof(f7836,plain,
spl0_598,
inference(avatar_split_clause,[],[f216,f7834]) ).
fof(f7834,plain,
( spl0_598
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X0),X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f216,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X0),X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_2) ).
fof(f7832,plain,
spl0_597,
inference(avatar_split_clause,[],[f159,f7830]) ).
fof(f7830,plain,
( spl0_597
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X5,X0),c_Power_Opower__class_Opower(X2,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f159,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X5,X0),c_Power_Opower__class_Opower(X2,X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
fof(f7828,plain,
spl0_596,
inference(avatar_split_clause,[],[f89,f7826]) ).
fof(f7826,plain,
( spl0_596
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f89,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
fof(f7824,plain,
spl0_595,
inference(avatar_split_clause,[],[f87,f7822]) ).
fof(f7822,plain,
( spl0_595
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f87,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
fof(f7820,plain,
spl0_594,
inference(avatar_split_clause,[],[f86,f7818]) ).
fof(f7818,plain,
( spl0_594
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f86,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
fof(f7816,plain,
spl0_593,
inference(avatar_split_clause,[],[f84,f7814]) ).
fof(f7814,plain,
( spl0_593
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f84,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
fof(f7812,plain,
spl0_592,
inference(avatar_split_clause,[],[f82,f7810]) ).
fof(f7810,plain,
( spl0_592
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f82,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
fof(f7808,plain,
spl0_591,
inference(avatar_split_clause,[],[f81,f7806]) ).
fof(f7806,plain,
( spl0_591
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f81,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
fof(f7804,plain,
spl0_590,
inference(avatar_split_clause,[],[f80,f7802]) ).
fof(f7802,plain,
( spl0_590
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f80,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
fof(f7800,plain,
spl0_589,
inference(avatar_split_clause,[],[f79,f7798]) ).
fof(f7798,plain,
( spl0_589
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f79,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
fof(f7796,plain,
spl0_588,
inference(avatar_split_clause,[],[f77,f7794]) ).
fof(f7794,plain,
( spl0_588
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f77,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
fof(f7792,plain,
spl0_587,
inference(avatar_split_clause,[],[f63,f7790]) ).
fof(f7790,plain,
( spl0_587
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f63,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_0) ).
fof(f7788,plain,
spl0_586,
inference(avatar_split_clause,[],[f11,f7786]) ).
fof(f7786,plain,
( spl0_586
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X5,X0),c_Power_Opower__class_Opower(X2,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f11,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X5,X0),c_Power_Opower__class_Opower(X2,X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
fof(f7707,plain,
( ~ spl0_100
| spl0_585
| ~ spl0_300
| spl0_583 ),
inference(avatar_split_clause,[],[f7478,f7182,f2630,f7704,f1179]) ).
fof(f2630,plain,
( spl0_300
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f7478,plain,
( v_w____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl0_300
| spl0_583 ),
inference(resolution,[],[f7184,f2631]) ).
fof(f2631,plain,
( ! [X3,X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X0),tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_300 ),
inference(avatar_component_clause,[],[f2630]) ).
fof(f7184,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| spl0_583 ),
inference(avatar_component_clause,[],[f7182]) ).
fof(f7189,plain,
( ~ spl0_36
| ~ spl0_583
| ~ spl0_584
| ~ spl0_442
| ~ spl0_538 ),
inference(avatar_split_clause,[],[f7144,f6476,f4716,f7186,f7182,f859]) ).
fof(f859,plain,
( spl0_36
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f4716,plain,
( spl0_442
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f6476,plain,
( spl0_538
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f7144,plain,
( ~ c_HOL_Oord__class_Oless(v_t____,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| ~ spl0_442
| ~ spl0_538 ),
inference(duplicate_literal_removal,[],[f7124]) ).
fof(f7124,plain,
( ~ c_HOL_Oord__class_Oless(v_t____,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ spl0_442
| ~ spl0_538 ),
inference(resolution,[],[f6477,f4717]) ).
fof(f4717,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_442 ),
inference(avatar_component_clause,[],[f4716]) ).
fof(f6477,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_538 ),
inference(avatar_component_clause,[],[f6476]) ).
fof(f6987,plain,
( ~ spl0_84
| spl0_582
| ~ spl0_197
| ~ spl0_553 ),
inference(avatar_split_clause,[],[f6607,f6561,f1686,f6985,f1099]) ).
fof(f6985,plain,
( spl0_582
<=> ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f6561,plain,
( spl0_553
<=> ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f6607,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_197
| ~ spl0_553 ),
inference(resolution,[],[f6562,f1687]) ).
fof(f6562,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_553 ),
inference(avatar_component_clause,[],[f6561]) ).
fof(f6700,plain,
spl0_581,
inference(avatar_split_clause,[],[f492,f6698]) ).
fof(f6698,plain,
( spl0_581
<=> ! [X5,X0,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X15,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X15,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f492,axiom,
! [X0,X15,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X15,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X5,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X15,X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
fof(f6696,plain,
spl0_580,
inference(avatar_split_clause,[],[f480,f6694]) ).
fof(f6694,plain,
( spl0_580
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f480,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
fof(f6692,plain,
spl0_579,
inference(avatar_split_clause,[],[f479,f6690]) ).
fof(f6690,plain,
( spl0_579
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f479,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
fof(f6688,plain,
spl0_578,
inference(avatar_split_clause,[],[f478,f6686]) ).
fof(f6686,plain,
( spl0_578
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f478,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
fof(f6684,plain,
spl0_577,
inference(avatar_split_clause,[],[f477,f6682]) ).
fof(f6682,plain,
( spl0_577
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f477,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
fof(f6680,plain,
spl0_576,
inference(avatar_split_clause,[],[f471,f6678]) ).
fof(f6678,plain,
( spl0_576
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f471,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
fof(f6676,plain,
spl0_575,
inference(avatar_split_clause,[],[f469,f6674]) ).
fof(f6674,plain,
( spl0_575
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f469,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
fof(f6672,plain,
( ~ spl0_84
| spl0_574
| ~ spl0_197
| ~ spl0_532 ),
inference(avatar_split_clause,[],[f6498,f6452,f1686,f6670,f1099]) ).
fof(f6670,plain,
( spl0_574
<=> ! [X0] :
( ~ c_lessequals(X0,c_Complex_ORe(v_w____),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f6452,plain,
( spl0_532
<=> ! [X0] :
( ~ c_lessequals(X0,c_Complex_ORe(v_w____),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f6498,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Complex_ORe(v_w____),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_197
| ~ spl0_532 ),
inference(resolution,[],[f6453,f1687]) ).
fof(f6453,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_Complex_ORe(v_w____),tc_RealDef_Oreal) )
| ~ spl0_532 ),
inference(avatar_component_clause,[],[f6452]) ).
fof(f6668,plain,
spl0_573,
inference(avatar_split_clause,[],[f467,f6666]) ).
fof(f6666,plain,
( spl0_573
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f467,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
fof(f6664,plain,
spl0_572,
inference(avatar_split_clause,[],[f466,f6662]) ).
fof(f6662,plain,
( spl0_572
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f466,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
fof(f6660,plain,
spl0_571,
inference(avatar_split_clause,[],[f465,f6658]) ).
fof(f6658,plain,
( spl0_571
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f465,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
fof(f6656,plain,
spl0_570,
inference(avatar_split_clause,[],[f464,f6654]) ).
fof(f6654,plain,
( spl0_570
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f464,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
fof(f6652,plain,
spl0_569,
inference(avatar_split_clause,[],[f463,f6650]) ).
fof(f6650,plain,
( spl0_569
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f463,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
fof(f6648,plain,
spl0_568,
inference(avatar_split_clause,[],[f462,f6646]) ).
fof(f6646,plain,
( spl0_568
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f462,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
fof(f6644,plain,
spl0_567,
inference(avatar_split_clause,[],[f461,f6642]) ).
fof(f6642,plain,
( spl0_567
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f461,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
fof(f6640,plain,
spl0_566,
inference(avatar_split_clause,[],[f440,f6638]) ).
fof(f6638,plain,
( spl0_566
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f440,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f6636,plain,
spl0_565,
inference(avatar_split_clause,[],[f414,f6634]) ).
fof(f6634,plain,
( spl0_565
<=> ! [X0,X7,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f414,axiom,
! [X2,X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f6632,plain,
spl0_564,
inference(avatar_split_clause,[],[f410,f6630]) ).
fof(f6630,plain,
( spl0_564
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f410,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f6603,plain,
spl0_563,
inference(avatar_split_clause,[],[f370,f6601]) ).
fof(f6601,plain,
( spl0_563
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f370,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
fof(f6599,plain,
spl0_562,
inference(avatar_split_clause,[],[f363,f6597]) ).
fof(f6597,plain,
( spl0_562
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f363,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f6595,plain,
spl0_561,
inference(avatar_split_clause,[],[f358,f6593]) ).
fof(f6593,plain,
( spl0_561
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f358,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
fof(f6591,plain,
spl0_560,
inference(avatar_split_clause,[],[f357,f6589]) ).
fof(f6589,plain,
( spl0_560
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f357,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
fof(f6587,plain,
spl0_559,
inference(avatar_split_clause,[],[f356,f6585]) ).
fof(f6585,plain,
( spl0_559
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f356,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
fof(f6583,plain,
spl0_558,
inference(avatar_split_clause,[],[f355,f6581]) ).
fof(f6581,plain,
( spl0_558
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f355,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
fof(f6579,plain,
spl0_557,
inference(avatar_split_clause,[],[f325,f6577]) ).
fof(f6577,plain,
( spl0_557
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X5,X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X5,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f325,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X5,X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X5,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
fof(f6575,plain,
spl0_556,
inference(avatar_split_clause,[],[f308,f6573]) ).
fof(f6573,plain,
( spl0_556
<=> ! [X4,X0,X3,X19] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X3,X4,X0),X19,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X3,X19,X0),c_Power_Opower__class_Opower(X4,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f308,axiom,
! [X3,X0,X19,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X3,X4,X0),X19,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X3,X19,X0),c_Power_Opower__class_Opower(X4,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
fof(f6571,plain,
spl0_555,
inference(avatar_split_clause,[],[f307,f6569]) ).
fof(f6569,plain,
( spl0_555
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X0),X5,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X5,X0),c_Power_Opower__class_Opower(X2,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f307,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X0),X5,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X5,X0),c_Power_Opower__class_Opower(X2,X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
fof(f6567,plain,
spl0_554,
inference(avatar_split_clause,[],[f306,f6565]) ).
fof(f6565,plain,
( spl0_554
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f306,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f6563,plain,
( ~ spl0_100
| spl0_553
| ~ spl0_183
| ~ spl0_491 ),
inference(avatar_split_clause,[],[f6400,f5413,f1561,f6561,f1179]) ).
fof(f1561,plain,
( spl0_183
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f5413,plain,
( spl0_491
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f6400,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) )
| ~ spl0_183
| ~ spl0_491 ),
inference(resolution,[],[f5414,f1562]) ).
fof(f1562,plain,
( ! [X3,X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1561]) ).
fof(f5414,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_491 ),
inference(avatar_component_clause,[],[f5413]) ).
fof(f6559,plain,
spl0_552,
inference(avatar_split_clause,[],[f305,f6557]) ).
fof(f6557,plain,
( spl0_552
<=> ! [X4,X0,X14,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X14,c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X3,X0),c_HOL_Otimes__class_Otimes(X14,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f305,axiom,
! [X3,X0,X14,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X14,c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X14,X3,X0),c_HOL_Otimes__class_Otimes(X14,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
fof(f6555,plain,
spl0_551,
inference(avatar_split_clause,[],[f303,f6553]) ).
fof(f6553,plain,
( spl0_551
<=> ! [X17,X4,X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,X0),X17,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X17,X0),c_HOL_Otimes__class_Otimes(X4,X17,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f303,axiom,
! [X3,X0,X4,X17] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,X0),X17,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X17,X0),c_HOL_Otimes__class_Otimes(X4,X17,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
fof(f6551,plain,
spl0_550,
inference(avatar_split_clause,[],[f301,f6549]) ).
fof(f6549,plain,
( spl0_550
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X3,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f301,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X3,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
fof(f6547,plain,
spl0_549,
inference(avatar_split_clause,[],[f300,f6545]) ).
fof(f6545,plain,
( spl0_549
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f300,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
fof(f6543,plain,
spl0_548,
inference(avatar_split_clause,[],[f292,f6541]) ).
fof(f6541,plain,
( spl0_548
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f292,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X6,X1,X0),c_HOL_Otimes__class_Otimes(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
fof(f6539,plain,
spl0_547,
inference(avatar_split_clause,[],[f291,f6537]) ).
fof(f6537,plain,
( spl0_547
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f291,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X6,X0),c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
fof(f6535,plain,
spl0_546,
inference(avatar_split_clause,[],[f273,f6533]) ).
fof(f6533,plain,
( spl0_546
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f273,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
fof(f6531,plain,
spl0_545,
inference(avatar_split_clause,[],[f272,f6529]) ).
fof(f6529,plain,
( spl0_545
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f272,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
fof(f6527,plain,
spl0_544,
inference(avatar_split_clause,[],[f259,f6525]) ).
fof(f6525,plain,
( spl0_544
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f259,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
fof(f6523,plain,
spl0_543,
inference(avatar_split_clause,[],[f256,f6521]) ).
fof(f6521,plain,
( spl0_543
<=> ! [X3,X4,X0,X12,X8] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X3,X8,X0) = X12
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) != c_HOL_Oplus__class_Oplus(X4,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f256,axiom,
! [X3,X0,X8,X4,X12] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X3,X8,X0) = X12
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) != c_HOL_Oplus__class_Oplus(X4,X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
fof(f6494,plain,
spl0_542,
inference(avatar_split_clause,[],[f246,f6492]) ).
fof(f6492,plain,
( spl0_542
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f246,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
fof(f6490,plain,
spl0_541,
inference(avatar_split_clause,[],[f245,f6488]) ).
fof(f6488,plain,
( spl0_541
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f245,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
fof(f6486,plain,
spl0_540,
inference(avatar_split_clause,[],[f218,f6484]) ).
fof(f6484,plain,
( spl0_540
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f218,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
fof(f6482,plain,
spl0_539,
inference(avatar_split_clause,[],[f209,f6480]) ).
fof(f6480,plain,
( spl0_539
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f209,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
fof(f6478,plain,
spl0_538,
inference(avatar_split_clause,[],[f195,f6476]) ).
fof(f195,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
fof(f6474,plain,
spl0_537,
inference(avatar_split_clause,[],[f194,f6472]) ).
fof(f6472,plain,
( spl0_537
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f194,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
fof(f6470,plain,
spl0_536,
inference(avatar_split_clause,[],[f166,f6468]) ).
fof(f6468,plain,
( spl0_536
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f166,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
fof(f6466,plain,
spl0_535,
inference(avatar_split_clause,[],[f165,f6464]) ).
fof(f6464,plain,
( spl0_535
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f165,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
fof(f6462,plain,
spl0_534,
inference(avatar_split_clause,[],[f153,f6460]) ).
fof(f6460,plain,
( spl0_534
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X0),X3,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f153,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X0),X3,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).
fof(f6458,plain,
spl0_533,
inference(avatar_split_clause,[],[f121,f6456]) ).
fof(f6456,plain,
( spl0_533
<=> ! [X0,X7,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X6,X7,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f121,axiom,
! [X2,X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X6,X7,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f6454,plain,
( spl0_532
| ~ spl0_140
| ~ spl0_491 ),
inference(avatar_split_clause,[],[f6402,f5413,f1371,f6452]) ).
fof(f6402,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Complex_ORe(v_w____),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_140
| ~ spl0_491 ),
inference(resolution,[],[f5414,f1372]) ).
fof(f6450,plain,
spl0_531,
inference(avatar_split_clause,[],[f114,f6448]) ).
fof(f6448,plain,
( spl0_531
<=> ! [X1,X0,X6,X2,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X6,X7,X0)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f114,axiom,
! [X2,X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X6,X7,X0)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
fof(f6446,plain,
spl0_530,
inference(avatar_split_clause,[],[f107,f6444]) ).
fof(f6444,plain,
( spl0_530
<=> ! [X1,X0,X6,X2,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f107,axiom,
! [X2,X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
fof(f6442,plain,
spl0_529,
inference(avatar_split_clause,[],[f106,f6440]) ).
fof(f6440,plain,
( spl0_529
<=> ! [X0,X7,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X6,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f106,axiom,
! [X2,X0,X1,X6,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X6,X7,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
fof(f6438,plain,
spl0_528,
inference(avatar_split_clause,[],[f72,f6436]) ).
fof(f6436,plain,
( spl0_528
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f72,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
fof(f6434,plain,
spl0_527,
inference(avatar_split_clause,[],[f71,f6432]) ).
fof(f6432,plain,
( spl0_527
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f71,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
fof(f6430,plain,
spl0_526,
inference(avatar_split_clause,[],[f58,f6428]) ).
fof(f6428,plain,
( spl0_526
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f58,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
fof(f6426,plain,
spl0_525,
inference(avatar_split_clause,[],[f57,f6424]) ).
fof(f6424,plain,
( spl0_525
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f57,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
fof(f6422,plain,
spl0_524,
inference(avatar_split_clause,[],[f56,f6420]) ).
fof(f6420,plain,
( spl0_524
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f56,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
fof(f6418,plain,
spl0_523,
inference(avatar_split_clause,[],[f55,f6416]) ).
fof(f6416,plain,
( spl0_523
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f55,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
fof(f6414,plain,
spl0_522,
inference(avatar_split_clause,[],[f41,f6412]) ).
fof(f6412,plain,
( spl0_522
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f41,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X6,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f6396,plain,
spl0_521,
inference(avatar_split_clause,[],[f40,f6394]) ).
fof(f6394,plain,
( spl0_521
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f40,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X2,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X2,c_HOL_Oplus__class_Oplus(X1,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f6392,plain,
spl0_520,
inference(avatar_split_clause,[],[f12,f6390]) ).
fof(f6390,plain,
( spl0_520
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f12,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X6,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
fof(f6388,plain,
spl0_519,
inference(avatar_split_clause,[],[f1,f6386]) ).
fof(f6386,plain,
( spl0_519
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f6106,plain,
( spl0_518
| ~ spl0_145
| ~ spl0_504 ),
inference(avatar_split_clause,[],[f5952,f5905,f1393,f6104]) ).
fof(f6104,plain,
( spl0_518
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f5905,plain,
( spl0_504
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f5952,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_145
| ~ spl0_504 ),
inference(resolution,[],[f5906,f1394]) ).
fof(f5906,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_504 ),
inference(avatar_component_clause,[],[f5905]) ).
fof(f5985,plain,
spl0_517,
inference(avatar_split_clause,[],[f442,f5983]) ).
fof(f5983,plain,
( spl0_517
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f442,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
fof(f5981,plain,
spl0_516,
inference(avatar_split_clause,[],[f424,f5979]) ).
fof(f5979,plain,
( spl0_516
<=> ! [X15,X0,X5,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X5 = X15
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_Power_Opower__class_Opower(X1,X5,X0) != c_Power_Opower__class_Opower(X1,X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f424,axiom,
! [X0,X1,X15,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X5 = X15
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_Power_Opower__class_Opower(X1,X5,X0) != c_Power_Opower__class_Opower(X1,X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
fof(f5977,plain,
spl0_515,
inference(avatar_split_clause,[],[f400,f5975]) ).
fof(f5975,plain,
( spl0_515
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X5,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f400,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X5,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
fof(f5947,plain,
spl0_514,
inference(avatar_split_clause,[],[f392,f5945]) ).
fof(f5945,plain,
( spl0_514
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f392,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le__neg_0) ).
fof(f5943,plain,
spl0_513,
inference(avatar_split_clause,[],[f391,f5941]) ).
fof(f5941,plain,
( spl0_513
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f391,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le__neg_0) ).
fof(f5939,plain,
spl0_512,
inference(avatar_split_clause,[],[f390,f5937]) ).
fof(f5937,plain,
( spl0_512
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f390,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le_0) ).
fof(f5935,plain,
spl0_511,
inference(avatar_split_clause,[],[f389,f5933]) ).
fof(f5933,plain,
( spl0_511
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f389,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le_0) ).
fof(f5931,plain,
spl0_510,
inference(avatar_split_clause,[],[f361,f5929]) ).
fof(f5929,plain,
( spl0_510
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f361,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).
fof(f5927,plain,
spl0_509,
inference(avatar_split_clause,[],[f360,f5925]) ).
fof(f5925,plain,
( spl0_509
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f360,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).
fof(f5923,plain,
spl0_508,
inference(avatar_split_clause,[],[f359,f5921]) ).
fof(f5921,plain,
( spl0_508
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f359,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).
fof(f5919,plain,
spl0_507,
inference(avatar_split_clause,[],[f341,f5917]) ).
fof(f5917,plain,
( spl0_507
<=> ! [X4,X8,X3] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f341,axiom,
! [X3,X8,X4] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_0) ).
fof(f5915,plain,
spl0_506,
inference(avatar_split_clause,[],[f340,f5913]) ).
fof(f5913,plain,
( spl0_506
<=> ! [X4,X8,X3] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f340,axiom,
! [X3,X8,X4] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_1) ).
fof(f5911,plain,
spl0_505,
inference(avatar_split_clause,[],[f339,f5909]) ).
fof(f5909,plain,
( spl0_505
<=> ! [X4,X8,X3] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X8,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f339,axiom,
! [X3,X8,X4] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X8,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_0) ).
fof(f5907,plain,
( ~ spl0_69
| spl0_504
| ~ spl0_283
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f3701,f3402,f2407,f5905,f1024]) ).
fof(f2407,plain,
( spl0_283
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f3402,plain,
( spl0_367
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f3701,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) )
| ~ spl0_283
| ~ spl0_367 ),
inference(resolution,[],[f3403,f2408]) ).
fof(f2408,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f2407]) ).
fof(f3403,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_367 ),
inference(avatar_component_clause,[],[f3402]) ).
fof(f5903,plain,
spl0_503,
inference(avatar_split_clause,[],[f338,f5901]) ).
fof(f5901,plain,
( spl0_503
<=> ! [X4,X8,X3] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X8,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f338,axiom,
! [X3,X8,X4] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X8,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_1) ).
fof(f5899,plain,
spl0_502,
inference(avatar_split_clause,[],[f315,f5897]) ).
fof(f5897,plain,
( spl0_502
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Otimes__class_Otimes(X1,X1,X0) != c_HOL_Otimes__class_Otimes(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f315,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Otimes__class_Otimes(X1,X1,X0) != c_HOL_Otimes__class_Otimes(X2,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
fof(f5895,plain,
spl0_501,
inference(avatar_split_clause,[],[f290,f5893]) ).
fof(f5893,plain,
( spl0_501
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f290,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
fof(f5891,plain,
spl0_500,
inference(avatar_split_clause,[],[f258,f5889]) ).
fof(f5889,plain,
( spl0_500
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f258,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).
fof(f5887,plain,
spl0_499,
inference(avatar_split_clause,[],[f206,f5885]) ).
fof(f5885,plain,
( spl0_499
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f206,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
fof(f5883,plain,
spl0_498,
inference(avatar_split_clause,[],[f205,f5881]) ).
fof(f5881,plain,
( spl0_498
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f205,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
fof(f5879,plain,
spl0_497,
inference(avatar_split_clause,[],[f187,f5877]) ).
fof(f5877,plain,
( spl0_497
<=> ! [X5,X0,X1] :
( ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f187,axiom,
! [X0,X1,X5] :
( ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
fof(f5875,plain,
spl0_496,
inference(avatar_split_clause,[],[f92,f5873]) ).
fof(f5873,plain,
( spl0_496
<=> ! [X4,X8,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f92,axiom,
! [X3,X8,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__iff1_0) ).
fof(f5871,plain,
spl0_495,
inference(avatar_split_clause,[],[f91,f5869]) ).
fof(f5869,plain,
( spl0_495
<=> ! [X4,X8,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f91,axiom,
! [X3,X8,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X8,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__iff1_1) ).
fof(f5867,plain,
spl0_494,
inference(avatar_split_clause,[],[f90,f5865]) ).
fof(f5865,plain,
( spl0_494
<=> ! [X4,X8,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X8,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f90,axiom,
! [X3,X8,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X8,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X8,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__mono2_0) ).
fof(f5833,plain,
spl0_493,
inference(avatar_split_clause,[],[f9,f5831]) ).
fof(f5831,plain,
( spl0_493
<=> ! [X5,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f9,axiom,
! [X3,X0,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X3,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
fof(f5616,plain,
( ~ spl0_38
| spl0_492
| ~ spl0_275
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f2667,f2618,f2374,f5614,f869]) ).
fof(f5614,plain,
( spl0_492
<=> ! [X0] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f2618,plain,
( spl0_297
<=> ! [X0] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f2667,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) )
| ~ spl0_275
| ~ spl0_297 ),
inference(resolution,[],[f2619,f2375]) ).
fof(f2619,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_297 ),
inference(avatar_component_clause,[],[f2618]) ).
fof(f5415,plain,
( spl0_491
| ~ spl0_289
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f2661,f2618,f2431,f5413]) ).
fof(f2431,plain,
( spl0_289
<=> ! [X25,X24,X26] :
( ~ c_lessequals(X24,X26,tc_RealDef_Oreal)
| ~ c_lessequals(X26,X25,tc_RealDef_Oreal)
| c_lessequals(X24,X25,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f2661,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_lessequals(X1,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_289
| ~ spl0_297 ),
inference(resolution,[],[f2619,f2432]) ).
fof(f2432,plain,
( ! [X26,X24,X25] :
( ~ c_lessequals(X26,X25,tc_RealDef_Oreal)
| ~ c_lessequals(X24,X26,tc_RealDef_Oreal)
| c_lessequals(X24,X25,tc_RealDef_Oreal) )
| ~ spl0_289 ),
inference(avatar_component_clause,[],[f2431]) ).
fof(f5411,plain,
spl0_490,
inference(avatar_split_clause,[],[f547,f5409]) ).
fof(f5409,plain,
( spl0_490
<=> ! [X4,X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X3,X0),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f547,axiom,
! [X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X3,X0),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult__ineq_0) ).
fof(f5407,plain,
spl0_489,
inference(avatar_split_clause,[],[f520,f5405]) ).
fof(f5405,plain,
( spl0_489
<=> ! [X4,X0,X23] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X23,X4,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X23,X0),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f520,axiom,
! [X0,X4,X23] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X23,X4,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X23,X0),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Opos__bounded_1) ).
fof(f5403,plain,
spl0_488,
inference(avatar_split_clause,[],[f519,f5401]) ).
fof(f5401,plain,
( spl0_488
<=> ! [X0,X23,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X23,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X23,X0),c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1(X3,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f519,axiom,
! [X3,X0,X23] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X23,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X23,X0),c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1(X3,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ononneg__bounded_1) ).
fof(f5399,plain,
spl0_487,
inference(avatar_split_clause,[],[f517,f5397]) ).
fof(f5397,plain,
( spl0_487
<=> ! [X0,X23,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X23,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X23,X0),c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1(X3,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f517,axiom,
! [X3,X0,X23] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X23,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X23,X0),c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1(X3,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Obounded_0) ).
fof(f5395,plain,
spl0_486,
inference(avatar_split_clause,[],[f516,f5393]) ).
fof(f5393,plain,
( spl0_486
<=> ! [X4,X0,X23] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X23,X4,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X23,X0),c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f516,axiom,
! [X0,X4,X23] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X23,X4,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X23,X0),c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ononneg__bounded_1) ).
fof(f5391,plain,
spl0_485,
inference(avatar_split_clause,[],[f514,f5389]) ).
fof(f5389,plain,
( spl0_485
<=> ! [X0,X23,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X23,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X23,X0),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(X3,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f514,axiom,
! [X3,X0,X23] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X23,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X23,X0),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(X3,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Opos__bounded_1) ).
fof(f5387,plain,
spl0_484,
inference(avatar_split_clause,[],[f513,f5385]) ).
fof(f5385,plain,
( spl0_484
<=> ! [X4,X0,X23] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X23,X4,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X23,X0),c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f513,axiom,
! [X0,X4,X23] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X23,X4,X0),X0),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X23,X0),c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1(X4,X0),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Obounded_0) ).
fof(f5383,plain,
spl0_483,
inference(avatar_split_clause,[],[f488,f5381]) ).
fof(f5381,plain,
( spl0_483
<=> ! [X0,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X15,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X15,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f488,axiom,
! [X0,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X15,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X15,X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(f5379,plain,
spl0_482,
inference(avatar_split_clause,[],[f487,f5377]) ).
fof(f5377,plain,
( spl0_482
<=> ! [X0,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X15,c_HOL_Otimes__class_Otimes(X1,X15,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f487,axiom,
! [X0,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X15,c_HOL_Otimes__class_Otimes(X1,X15,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(f5375,plain,
spl0_481,
inference(avatar_split_clause,[],[f481,f5373]) ).
fof(f5373,plain,
( spl0_481
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Olordered__ring(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f481,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Olordered__ring(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).
fof(f5349,plain,
spl0_480,
inference(avatar_split_clause,[],[f326,f5347]) ).
fof(f5347,plain,
( spl0_480
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X5,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f326,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X5,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
fof(f5345,plain,
spl0_479,
inference(avatar_split_clause,[],[f255,f5343]) ).
fof(f5343,plain,
( spl0_479
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f255,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).
fof(f5341,plain,
spl0_478,
inference(avatar_split_clause,[],[f235,f5339]) ).
fof(f5339,plain,
( spl0_478
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f235,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__leI_0) ).
fof(f5337,plain,
spl0_477,
inference(avatar_split_clause,[],[f203,f5335]) ).
fof(f5335,plain,
( spl0_477
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f203,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).
fof(f5333,plain,
spl0_476,
inference(avatar_split_clause,[],[f201,f5331]) ).
fof(f5331,plain,
( spl0_476
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f201,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,X6,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f5329,plain,
spl0_475,
inference(avatar_split_clause,[],[f192,f5327]) ).
fof(f5327,plain,
( spl0_475
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f192,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
fof(f5325,plain,
spl0_474,
inference(avatar_split_clause,[],[f173,f5323]) ).
fof(f5323,plain,
( spl0_474
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),X6,X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X6,c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f173,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),X6,X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X6,c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).
fof(f5321,plain,
spl0_473,
inference(avatar_split_clause,[],[f54,f5319]) ).
fof(f5319,plain,
( spl0_473
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f54,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__order_0) ).
fof(f5317,plain,
spl0_472,
inference(avatar_split_clause,[],[f13,f5315]) ).
fof(f5315,plain,
( spl0_472
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f13,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
fof(f5271,plain,
( ~ spl0_55
| ~ spl0_471
| ~ spl0_56
| ~ spl0_203
| ~ spl0_257
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f4863,f4716,f2107,f1710,f959,f5268,f954]) ).
fof(f954,plain,
( spl0_55
<=> class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f5268,plain,
( spl0_471
<=> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f959,plain,
( spl0_56
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f1710,plain,
( spl0_203
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2107,plain,
( spl0_257
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,X4,X0) = c_HOL_Oplus__class_Oplus(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f4863,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal)
| ~ spl0_56
| ~ spl0_203
| ~ spl0_257
| ~ spl0_442 ),
inference(forward_demodulation,[],[f4854,f2269]) ).
fof(f2269,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal)
| ~ spl0_56
| ~ spl0_257 ),
inference(resolution,[],[f2108,f961]) ).
fof(f961,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f959]) ).
fof(f2108,plain,
( ! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,X4,X0) = c_HOL_Oplus__class_Oplus(X4,X3,X0) )
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f2107]) ).
fof(f4854,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal)
| ~ spl0_203
| ~ spl0_442 ),
inference(resolution,[],[f4717,f1711]) ).
fof(f1711,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f1710]) ).
fof(f5211,plain,
spl0_470,
inference(avatar_split_clause,[],[f679,f5209]) ).
fof(f5209,plain,
( spl0_470
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f679,plain,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
inference(duplicate_literal_removal,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f5207,plain,
spl0_469,
inference(avatar_split_clause,[],[f537,f5205]) ).
fof(f5205,plain,
( spl0_469
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X6,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f537,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X6,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f5203,plain,
spl0_468,
inference(avatar_split_clause,[],[f536,f5201]) ).
fof(f5201,plain,
( spl0_468
<=> ! [X31,X33,X0,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X33,X0),X31,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X0),X33,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f536,axiom,
! [X31,X0,X30,X33] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X33,X0),X31,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X30,X31,X0),X33,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f5199,plain,
spl0_467,
inference(avatar_split_clause,[],[f533,f5197]) ).
fof(f5197,plain,
( spl0_467
<=> ! [X31,X0,X30,X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X30,c_HOL_Otimes__class_Otimes(X31,X32,X0),X0) = c_HOL_Otimes__class_Otimes(X31,c_HOL_Otimes__class_Otimes(X30,X32,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f533,axiom,
! [X31,X0,X32,X30] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X30,c_HOL_Otimes__class_Otimes(X31,X32,X0),X0) = c_HOL_Otimes__class_Otimes(X31,c_HOL_Otimes__class_Otimes(X30,X32,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f5195,plain,
spl0_466,
inference(avatar_split_clause,[],[f531,f5193]) ).
fof(f5193,plain,
( spl0_466
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X4,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f531,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X4,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
fof(f5191,plain,
spl0_465,
inference(avatar_split_clause,[],[f529,f5189]) ).
fof(f5189,plain,
( spl0_465
<=> ! [X4,X0,X3] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X3,X0),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f529,axiom,
! [X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X3,X0),c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult_0) ).
fof(f5187,plain,
( ~ spl0_84
| spl0_464
| ~ spl0_197
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f4537,f4323,f1686,f5185,f1099]) ).
fof(f5185,plain,
( spl0_464
<=> ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f4323,plain,
( spl0_403
<=> ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f4537,plain,
( ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_197
| ~ spl0_403 ),
inference(resolution,[],[f4324,f1687]) ).
fof(f4324,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),X0,tc_RealDef_Oreal) )
| ~ spl0_403 ),
inference(avatar_component_clause,[],[f4323]) ).
fof(f5183,plain,
spl0_463,
inference(avatar_split_clause,[],[f505,f5181]) ).
fof(f5181,plain,
( spl0_463
<=> ! [X3] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X3
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X3
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f505,axiom,
! [X3] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X3
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X3
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__is__one_0) ).
fof(f5179,plain,
spl0_462,
inference(avatar_split_clause,[],[f493,f5177]) ).
fof(f5177,plain,
( spl0_462
<=> ! [X4,X0,X3] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(c_HOL_Otimes__class_Otimes(X3,X4,tc_RealDef_Oreal),X0) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X3,X0),c_RealVector_Oof__real(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f493,axiom,
! [X3,X0,X4] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(c_HOL_Otimes__class_Otimes(X3,X4,tc_RealDef_Oreal),X0) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X3,X0),c_RealVector_Oof__real(X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__mult_0) ).
fof(f5175,plain,
spl0_461,
inference(avatar_split_clause,[],[f454,f5173]) ).
fof(f5173,plain,
( spl0_461
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f454,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
fof(f5171,plain,
spl0_460,
inference(avatar_split_clause,[],[f453,f5169]) ).
fof(f5169,plain,
( spl0_460
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f453,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add_0) ).
fof(f5167,plain,
spl0_459,
inference(avatar_split_clause,[],[f402,f5165]) ).
fof(f5165,plain,
( spl0_459
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X5,X0),X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f402,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X5,X0),X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).
fof(f5163,plain,
spl0_458,
inference(avatar_split_clause,[],[f401,f5161]) ).
fof(f5161,plain,
( spl0_458
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f401,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
fof(f5159,plain,
spl0_457,
inference(avatar_split_clause,[],[f314,f5157]) ).
fof(f5157,plain,
( spl0_457
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f314,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
fof(f5155,plain,
spl0_456,
inference(avatar_split_clause,[],[f312,f5153]) ).
fof(f5153,plain,
( spl0_456
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f312,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
fof(f5151,plain,
spl0_455,
inference(avatar_split_clause,[],[f311,f5149]) ).
fof(f5149,plain,
( spl0_455
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f311,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult_0) ).
fof(f5147,plain,
spl0_454,
inference(avatar_split_clause,[],[f289,f5145]) ).
fof(f5145,plain,
( spl0_454
<=> ! [X5,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X5,X0),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X5,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f289,axiom,
! [X0,X1,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X5,X0),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X5,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).
fof(f5143,plain,
( spl0_453
| ~ spl0_289
| ~ spl0_404 ),
inference(avatar_split_clause,[],[f4479,f4346,f2431,f5141]) ).
fof(f5141,plain,
( spl0_453
<=> ! [X0] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f4346,plain,
( spl0_404
<=> c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f4479,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_289
| ~ spl0_404 ),
inference(resolution,[],[f4348,f2432]) ).
fof(f4348,plain,
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_404 ),
inference(avatar_component_clause,[],[f4346]) ).
fof(f5139,plain,
spl0_452,
inference(avatar_split_clause,[],[f254,f5137]) ).
fof(f5137,plain,
( spl0_452
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f254,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__abs__inverse_0) ).
fof(f5135,plain,
spl0_451,
inference(avatar_split_clause,[],[f212,f5133]) ).
fof(f5133,plain,
( spl0_451
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X5,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f212,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X5,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inverse_0) ).
fof(f5131,plain,
spl0_450,
inference(avatar_split_clause,[],[f23,f5129]) ).
fof(f5129,plain,
( spl0_450
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f23,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f5127,plain,
spl0_449,
inference(avatar_split_clause,[],[f22,f5125]) ).
fof(f5125,plain,
( spl0_449
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X6,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f22,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X6,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f5123,plain,
spl0_448,
inference(avatar_split_clause,[],[f21,f5121]) ).
fof(f5121,plain,
( spl0_448
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f21,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
fof(f5119,plain,
spl0_447,
inference(avatar_split_clause,[],[f20,f5117]) ).
fof(f5117,plain,
( spl0_447
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f20,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X8,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f5115,plain,
spl0_446,
inference(avatar_split_clause,[],[f19,f5113]) ).
fof(f5113,plain,
( spl0_446
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X6,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f19,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X6,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f5111,plain,
spl0_445,
inference(avatar_split_clause,[],[f17,f5109]) ).
fof(f5109,plain,
( spl0_445
<=> ! [X0,X6,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X6,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f17,axiom,
! [X2,X0,X1,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X6,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f5107,plain,
spl0_444,
inference(avatar_split_clause,[],[f16,f5105]) ).
fof(f5105,plain,
( spl0_444
<=> ! [X0,X6,X1,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X1,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f16,axiom,
! [X0,X1,X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X1,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f4976,plain,
( ~ spl0_85
| spl0_443
| ~ spl0_199
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f4266,f4194,f1694,f4974,f1104]) ).
fof(f1104,plain,
( spl0_85
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f4974,plain,
( spl0_443
<=> ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f1694,plain,
( spl0_199
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f4194,plain,
( spl0_395
<=> ! [X0] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f4266,plain,
( ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
| ~ spl0_199
| ~ spl0_395 ),
inference(resolution,[],[f4195,f1695]) ).
fof(f1695,plain,
( ! [X3,X0,X4] :
( c_lessequals(X4,X3,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f1694]) ).
fof(f4195,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),X0,tc_RealDef_Oreal) )
| ~ spl0_395 ),
inference(avatar_component_clause,[],[f4194]) ).
fof(f4718,plain,
( ~ spl0_84
| spl0_442
| ~ spl0_224
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f3694,f3402,f1795,f4716,f1099]) ).
fof(f3694,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_224
| ~ spl0_367 ),
inference(resolution,[],[f3403,f1796]) ).
fof(f4665,plain,
spl0_441,
inference(avatar_split_clause,[],[f489,f4663]) ).
fof(f4663,plain,
( spl0_441
<=> ! [X0,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X15,X15,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f489,axiom,
! [X0,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X15,X15,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X15,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(f4661,plain,
spl0_440,
inference(avatar_split_clause,[],[f485,f4659]) ).
fof(f4659,plain,
( spl0_440
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X3,X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f485,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X3,X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_2) ).
fof(f4657,plain,
spl0_439,
inference(avatar_split_clause,[],[f483,f4655]) ).
fof(f4655,plain,
( spl0_439
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X3,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f483,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X3,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_1) ).
fof(f4653,plain,
spl0_438,
inference(avatar_split_clause,[],[f441,f4651]) ).
fof(f4651,plain,
( spl0_438
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f441,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).
fof(f4649,plain,
spl0_437,
inference(avatar_split_clause,[],[f439,f4647]) ).
fof(f4647,plain,
( spl0_437
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f439,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f4641,plain,
spl0_436,
inference(avatar_split_clause,[],[f438,f4639]) ).
fof(f4639,plain,
( spl0_436
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f438,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f4637,plain,
spl0_435,
inference(avatar_split_clause,[],[f437,f4635]) ).
fof(f4635,plain,
( spl0_435
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f437,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f4633,plain,
spl0_434,
inference(avatar_split_clause,[],[f436,f4631]) ).
fof(f4631,plain,
( spl0_434
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X1,X0),c_HOL_Oplus__class_Oplus(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f436,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X1,X0),c_HOL_Oplus__class_Oplus(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f4629,plain,
spl0_433,
inference(avatar_split_clause,[],[f435,f4627]) ).
fof(f4627,plain,
( spl0_433
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X1,X0),c_HOL_Oplus__class_Oplus(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f435,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X1,X0),c_HOL_Oplus__class_Oplus(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f4625,plain,
spl0_432,
inference(avatar_split_clause,[],[f434,f4623]) ).
fof(f4623,plain,
( spl0_432
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X1,X0),c_HOL_Oplus__class_Oplus(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f434,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X1,X0),c_HOL_Oplus__class_Oplus(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f4621,plain,
spl0_431,
inference(avatar_split_clause,[],[f411,f4619]) ).
fof(f4619,plain,
( spl0_431
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f411,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).
fof(f4617,plain,
spl0_430,
inference(avatar_split_clause,[],[f365,f4615]) ).
fof(f4615,plain,
( spl0_430
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f365,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).
fof(f4613,plain,
spl0_429,
inference(avatar_split_clause,[],[f364,f4611]) ).
fof(f4611,plain,
( spl0_429
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f364,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).
fof(f4609,plain,
spl0_428,
inference(avatar_split_clause,[],[f345,f4607]) ).
fof(f4607,plain,
( spl0_428
<=> ! [X6,X2,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Otimes__class_Otimes(X6,X1,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X6,X2,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f345,axiom,
! [X2,X1,X6] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Otimes__class_Otimes(X6,X1,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X6,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__left__cancel_0) ).
fof(f4605,plain,
spl0_427,
inference(avatar_split_clause,[],[f344,f4603]) ).
fof(f4603,plain,
( spl0_427
<=> ! [X6,X2,X1] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Otimes__class_Otimes(X1,X6,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X2,X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f344,axiom,
! [X2,X1,X6] :
( X1 = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Otimes__class_Otimes(X1,X6,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X2,X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__right__cancel_0) ).
fof(f4601,plain,
( ~ spl0_84
| ~ spl0_426
| ~ spl0_197
| ~ spl0_404 ),
inference(avatar_split_clause,[],[f4482,f4346,f1686,f4598,f1099]) ).
fof(f4598,plain,
( spl0_426
<=> c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f4482,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl0_197
| ~ spl0_404 ),
inference(resolution,[],[f4348,f1687]) ).
fof(f4596,plain,
spl0_425,
inference(avatar_split_clause,[],[f319,f4594]) ).
fof(f4594,plain,
( spl0_425
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f319,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_1) ).
fof(f4592,plain,
spl0_424,
inference(avatar_split_clause,[],[f264,f4590]) ).
fof(f4590,plain,
( spl0_424
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f264,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
fof(f4588,plain,
spl0_423,
inference(avatar_split_clause,[],[f238,f4586]) ).
fof(f4586,plain,
( spl0_423
<=> ! [X4,X0,X3,X8] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X4 = X8
| c_HOL_Oplus__class_Oplus(X3,X8,X0) != c_HOL_Oplus__class_Oplus(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f238,axiom,
! [X3,X0,X8,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X4 = X8
| c_HOL_Oplus__class_Oplus(X3,X8,X0) != c_HOL_Oplus__class_Oplus(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f4584,plain,
spl0_422,
inference(avatar_split_clause,[],[f228,f4582]) ).
fof(f4582,plain,
( spl0_422
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f228,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).
fof(f4580,plain,
spl0_421,
inference(avatar_split_clause,[],[f186,f4578]) ).
fof(f4578,plain,
( spl0_421
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f186,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).
fof(f4576,plain,
spl0_420,
inference(avatar_split_clause,[],[f184,f4574]) ).
fof(f4574,plain,
( spl0_420
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f184,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
fof(f4572,plain,
spl0_419,
inference(avatar_split_clause,[],[f183,f4570]) ).
fof(f4570,plain,
( spl0_419
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f183,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
fof(f4568,plain,
spl0_418,
inference(avatar_split_clause,[],[f171,f4566]) ).
fof(f4566,plain,
( spl0_418
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f171,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_1) ).
fof(f4564,plain,
spl0_417,
inference(avatar_split_clause,[],[f161,f4562]) ).
fof(f4562,plain,
( spl0_417
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f161,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
fof(f4560,plain,
spl0_416,
inference(avatar_split_clause,[],[f135,f4558]) ).
fof(f4558,plain,
( spl0_416
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X6,X1,X0),c_HOL_Oplus__class_Oplus(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f135,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X6,X1,X0),c_HOL_Oplus__class_Oplus(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f4533,plain,
spl0_415,
inference(avatar_split_clause,[],[f134,f4531]) ).
fof(f4531,plain,
( spl0_415
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f134,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f4529,plain,
spl0_414,
inference(avatar_split_clause,[],[f133,f4527]) ).
fof(f4527,plain,
( spl0_414
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X6,X1,X0),c_HOL_Oplus__class_Oplus(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f133,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X6,X1,X0),c_HOL_Oplus__class_Oplus(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f4525,plain,
spl0_413,
inference(avatar_split_clause,[],[f132,f4523]) ).
fof(f4523,plain,
( spl0_413
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X6,X1,X0),c_HOL_Oplus__class_Oplus(X6,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f132,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X6,X1,X0),c_HOL_Oplus__class_Oplus(X6,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f4521,plain,
spl0_412,
inference(avatar_split_clause,[],[f131,f4519]) ).
fof(f4519,plain,
( spl0_412
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f131,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f4517,plain,
spl0_411,
inference(avatar_split_clause,[],[f130,f4515]) ).
fof(f4515,plain,
( spl0_411
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f130,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X6,X0),c_HOL_Oplus__class_Oplus(X2,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f4513,plain,
spl0_410,
inference(avatar_split_clause,[],[f73,f4511]) ).
fof(f4511,plain,
( spl0_410
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X8,X0) = X3
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f73,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X8,X0) = X3
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
fof(f4509,plain,
spl0_409,
inference(avatar_split_clause,[],[f69,f4507]) ).
fof(f4507,plain,
( spl0_409
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f69,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).
fof(f4505,plain,
spl0_408,
inference(avatar_split_clause,[],[f60,f4503]) ).
fof(f4503,plain,
( spl0_408
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f60,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).
fof(f4501,plain,
spl0_407,
inference(avatar_split_clause,[],[f59,f4499]) ).
fof(f4499,plain,
( spl0_407
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f59,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_1) ).
fof(f4497,plain,
spl0_406,
inference(avatar_split_clause,[],[f43,f4495]) ).
fof(f4495,plain,
( spl0_406
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f43,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).
fof(f4478,plain,
spl0_405,
inference(avatar_split_clause,[],[f6,f4476]) ).
fof(f4476,plain,
( spl0_405
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f6,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_0) ).
fof(f4349,plain,
( ~ spl0_38
| spl0_404
| ~ spl0_143
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f4261,f4194,f1385,f4346,f869]) ).
fof(f1385,plain,
( spl0_143
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f4261,plain,
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ spl0_143
| ~ spl0_395 ),
inference(resolution,[],[f4195,f1386]) ).
fof(f1386,plain,
( ! [X0,X1] :
( c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1385]) ).
fof(f4325,plain,
( spl0_403
| ~ spl0_150
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f4254,f4194,f1413,f4323]) ).
fof(f1413,plain,
( spl0_150
<=> ! [X13,X8] :
( c_lessequals(X8,X13,tc_RealDef_Oreal)
| c_lessequals(X13,X8,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f4254,plain,
( ! [X0] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_150
| ~ spl0_395 ),
inference(resolution,[],[f4195,f1414]) ).
fof(f1414,plain,
( ! [X8,X13] :
( c_lessequals(X8,X13,tc_RealDef_Oreal)
| c_lessequals(X13,X8,tc_RealDef_Oreal) )
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1413]) ).
fof(f4224,plain,
spl0_402,
inference(avatar_split_clause,[],[f532,f4222]) ).
fof(f4222,plain,
( spl0_402
<=> ! [X29,X27,X28] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X27,X28,tc_RealDef_Oreal),X29,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X27,c_HOL_Otimes__class_Otimes(X28,X29,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f4220,plain,
spl0_401,
inference(avatar_split_clause,[],[f486,f4218]) ).
fof(f4218,plain,
( spl0_401
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f486,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
fof(f4216,plain,
spl0_400,
inference(avatar_split_clause,[],[f428,f4214]) ).
fof(f4214,plain,
( spl0_400
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f428,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f4212,plain,
spl0_399,
inference(avatar_split_clause,[],[f427,f4210]) ).
fof(f4210,plain,
( spl0_399
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f427,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f4208,plain,
spl0_398,
inference(avatar_split_clause,[],[f394,f4206]) ).
fof(f4206,plain,
( spl0_398
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f394,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
fof(f4204,plain,
spl0_397,
inference(avatar_split_clause,[],[f372,f4202]) ).
fof(f4202,plain,
( spl0_397
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f372,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
fof(f4200,plain,
spl0_396,
inference(avatar_split_clause,[],[f371,f4198]) ).
fof(f4198,plain,
( spl0_396
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f371,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).
fof(f4196,plain,
( ~ spl0_86
| spl0_395
| ~ spl0_161
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f4025,f3310,f1471,f4194,f1109]) ).
fof(f1471,plain,
( spl0_161
<=> c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f3310,plain,
( spl0_365
<=> ! [X4,X0,X3,X8] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ c_lessequals(X8,X4,X0)
| c_lessequals(X8,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f4025,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),X0,tc_RealDef_Oreal) )
| ~ spl0_161
| ~ spl0_365 ),
inference(resolution,[],[f3311,f1473]) ).
fof(f1473,plain,
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1471]) ).
fof(f3311,plain,
( ! [X3,X0,X8,X4] :
( ~ c_lessequals(X8,X4,X0)
| ~ c_lessequals(X4,X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X8,X3,X0) )
| ~ spl0_365 ),
inference(avatar_component_clause,[],[f3310]) ).
fof(f4192,plain,
spl0_394,
inference(avatar_split_clause,[],[f367,f4190]) ).
fof(f4190,plain,
( spl0_394
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f367,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f4188,plain,
spl0_393,
inference(avatar_split_clause,[],[f366,f4186]) ).
fof(f4186,plain,
( spl0_393
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f366,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f4184,plain,
spl0_392,
inference(avatar_split_clause,[],[f324,f4182]) ).
fof(f4182,plain,
( spl0_392
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f324,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__inverse_0) ).
fof(f4180,plain,
spl0_391,
inference(avatar_split_clause,[],[f323,f4178]) ).
fof(f4178,plain,
( spl0_391
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f323,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__inverse_0) ).
fof(f4176,plain,
spl0_390,
inference(avatar_split_clause,[],[f322,f4174]) ).
fof(f4174,plain,
( spl0_390
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f322,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse_0) ).
fof(f4172,plain,
spl0_389,
inference(avatar_split_clause,[],[f310,f4170]) ).
fof(f4170,plain,
( spl0_389
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f310,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
fof(f4168,plain,
spl0_388,
inference(avatar_split_clause,[],[f309,f4166]) ).
fof(f4166,plain,
( spl0_388
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f309,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
fof(f4164,plain,
spl0_387,
inference(avatar_split_clause,[],[f297,f4162]) ).
fof(f4162,plain,
( spl0_387
<=> ! [X4,X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f297,axiom,
! [X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
fof(f4160,plain,
spl0_386,
inference(avatar_split_clause,[],[f296,f4158]) ).
fof(f4158,plain,
( spl0_386
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f296,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
fof(f4156,plain,
spl0_385,
inference(avatar_split_clause,[],[f294,f4154]) ).
fof(f4154,plain,
( spl0_385
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Otimes__class_Otimes(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f294,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Otimes__class_Otimes(X2,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
fof(f4142,plain,
spl0_384,
inference(avatar_split_clause,[],[f293,f4140]) ).
fof(f4140,plain,
( spl0_384
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f293,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
fof(f4138,plain,
spl0_383,
inference(avatar_split_clause,[],[f286,f4136]) ).
fof(f4136,plain,
( spl0_383
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(X1,X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f286,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(X1,X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
fof(f4134,plain,
spl0_382,
inference(avatar_split_clause,[],[f274,f4132]) ).
fof(f4132,plain,
( spl0_382
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f274,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
fof(f4130,plain,
spl0_381,
inference(avatar_split_clause,[],[f232,f4128]) ).
fof(f4128,plain,
( spl0_381
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f232,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_1) ).
fof(f4126,plain,
spl0_380,
inference(avatar_split_clause,[],[f231,f4124]) ).
fof(f4124,plain,
( spl0_380
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f231,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_0) ).
fof(f4122,plain,
spl0_379,
inference(avatar_split_clause,[],[f215,f4120]) ).
fof(f4120,plain,
( spl0_379
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f215,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(f4118,plain,
spl0_378,
inference(avatar_split_clause,[],[f214,f4116]) ).
fof(f4116,plain,
( spl0_378
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f214,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(f4114,plain,
spl0_377,
inference(avatar_split_clause,[],[f213,f4112]) ).
fof(f4112,plain,
( spl0_377
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f213,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
fof(f4110,plain,
spl0_376,
inference(avatar_split_clause,[],[f65,f4108]) ).
fof(f4108,plain,
( spl0_376
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f65,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__inverse_0) ).
fof(f4106,plain,
spl0_375,
inference(avatar_split_clause,[],[f64,f4104]) ).
fof(f4104,plain,
( spl0_375
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X5,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f64,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X5,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__abs_0) ).
fof(f4102,plain,
( ~ spl0_86
| spl0_374
| ~ spl0_231
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f3363,f3130,f1902,f4100,f1109]) ).
fof(f4100,plain,
( spl0_374
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f3130,plain,
( spl0_324
<=> ! [X4,X0,X3,X8] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X8,X4,X0)
| c_HOL_Oord__class_Oless(X8,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f3363,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),X0,tc_RealDef_Oreal) )
| ~ spl0_231
| ~ spl0_324 ),
inference(resolution,[],[f3131,f1904]) ).
fof(f3131,plain,
( ! [X3,X0,X8,X4] :
( ~ c_HOL_Oord__class_Oless(X8,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X8,X3,X0) )
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f3130]) ).
fof(f4098,plain,
spl0_373,
inference(avatar_split_clause,[],[f53,f4096]) ).
fof(f4096,plain,
( spl0_373
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f53,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(f4094,plain,
spl0_372,
inference(avatar_split_clause,[],[f52,f4092]) ).
fof(f4092,plain,
( spl0_372
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f52,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(f4090,plain,
spl0_371,
inference(avatar_split_clause,[],[f51,f4088]) ).
fof(f4088,plain,
( spl0_371
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f51,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
fof(f4086,plain,
spl0_370,
inference(avatar_split_clause,[],[f50,f4084]) ).
fof(f4084,plain,
( spl0_370
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f50,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
fof(f4082,plain,
spl0_369,
inference(avatar_split_clause,[],[f10,f4080]) ).
fof(f4080,plain,
( spl0_369
<=> ! [X5,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f10,axiom,
! [X3,X0,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X3,X5,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
fof(f3863,plain,
( spl0_368
| ~ spl0_145
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f3691,f3402,f1393,f3861]) ).
fof(f3861,plain,
( spl0_368
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f3691,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_145
| ~ spl0_367 ),
inference(resolution,[],[f3403,f1394]) ).
fof(f3404,plain,
( ~ spl0_84
| spl0_367
| ~ spl0_231
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f3339,f3126,f1902,f3402,f1099]) ).
fof(f3126,plain,
( spl0_323
<=> ! [X4,X0,X3,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X8,X0)
| c_HOL_Oord__class_Oless(X3,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f3339,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_231
| ~ spl0_323 ),
inference(resolution,[],[f3127,f1904]) ).
fof(f3127,plain,
( ! [X3,X0,X8,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X8,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X3,X8,X0) )
| ~ spl0_323 ),
inference(avatar_component_clause,[],[f3126]) ).
fof(f3316,plain,
spl0_366,
inference(avatar_split_clause,[],[f524,f3314]) ).
fof(f3314,plain,
( spl0_366
<=> ! [X4,X0,X3,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X8,X0)
| c_lessequals(X3,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f524,axiom,
! [X3,X0,X8,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X8,X0)
| c_lessequals(X3,X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f3312,plain,
spl0_365,
inference(avatar_split_clause,[],[f523,f3310]) ).
fof(f523,axiom,
! [X3,X0,X8,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ c_lessequals(X8,X4,X0)
| c_lessequals(X8,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f3308,plain,
spl0_364,
inference(avatar_split_clause,[],[f491,f3306]) ).
fof(f3306,plain,
( spl0_364
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = X2
| c_HOL_Oone__class_Oone(X0) != c_HOL_Otimes__class_Otimes(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f491,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = X2
| c_HOL_Oone__class_Oone(X0) != c_HOL_Otimes__class_Otimes(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
fof(f3298,plain,
spl0_363,
inference(avatar_split_clause,[],[f449,f3296]) ).
fof(f3296,plain,
( spl0_363
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f449,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
fof(f3294,plain,
spl0_362,
inference(avatar_split_clause,[],[f448,f3292]) ).
fof(f3292,plain,
( spl0_362
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f448,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
fof(f3290,plain,
spl0_361,
inference(avatar_split_clause,[],[f429,f3288]) ).
fof(f3288,plain,
( spl0_361
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f429,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
fof(f3286,plain,
spl0_360,
inference(avatar_split_clause,[],[f413,f3284]) ).
fof(f3284,plain,
( spl0_360
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f413,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_negative__imp__inverse__negative_0) ).
fof(f3282,plain,
spl0_359,
inference(avatar_split_clause,[],[f396,f3280]) ).
fof(f3280,plain,
( spl0_359
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f396,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
fof(f3278,plain,
spl0_358,
inference(avatar_split_clause,[],[f395,f3276]) ).
fof(f3276,plain,
( spl0_358
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = X2
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f395,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = X2
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__unique_0) ).
fof(f3274,plain,
spl0_357,
inference(avatar_split_clause,[],[f333,f3272]) ).
fof(f3272,plain,
( spl0_357
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = X3
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Oinverse(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f333,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = X3
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Oinverse(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
fof(f3270,plain,
spl0_356,
inference(avatar_split_clause,[],[f253,f3268]) ).
fof(f3268,plain,
( spl0_356
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f253,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
fof(f3266,plain,
spl0_355,
inference(avatar_split_clause,[],[f252,f3264]) ).
fof(f3264,plain,
( spl0_355
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f252,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
fof(f3262,plain,
spl0_354,
inference(avatar_split_clause,[],[f241,f3260]) ).
fof(f3260,plain,
( spl0_354
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X6
| c_HOL_Oplus__class_Oplus(X6,X1,X0) != c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f241,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X6
| c_HOL_Oplus__class_Oplus(X6,X1,X0) != c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f3258,plain,
( ~ spl0_85
| spl0_353
| ~ spl0_199
| spl0_322 ),
inference(avatar_split_clause,[],[f3082,f2996,f1694,f3255,f1104]) ).
fof(f3255,plain,
( spl0_353
<=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f2996,plain,
( spl0_322
<=> c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f3082,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ spl0_199
| spl0_322 ),
inference(resolution,[],[f2998,f1695]) ).
fof(f2998,plain,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| spl0_322 ),
inference(avatar_component_clause,[],[f2996]) ).
fof(f3253,plain,
spl0_352,
inference(avatar_split_clause,[],[f240,f3251]) ).
fof(f3251,plain,
( spl0_352
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X6
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f240,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X6
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f3249,plain,
spl0_351,
inference(avatar_split_clause,[],[f239,f3247]) ).
fof(f3247,plain,
( spl0_351
<=> ! [X0,X6,X2,X1] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X2 = X6
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f239,axiom,
! [X2,X0,X1,X6] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X2 = X6
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f3245,plain,
spl0_350,
inference(avatar_split_clause,[],[f208,f3243]) ).
fof(f3243,plain,
( spl0_350
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| X1 = X2
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f208,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| X1 = X2
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
fof(f3241,plain,
spl0_349,
inference(avatar_split_clause,[],[f196,f3239]) ).
fof(f3239,plain,
( spl0_349
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f196,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
fof(f3237,plain,
spl0_348,
inference(avatar_split_clause,[],[f190,f3235]) ).
fof(f3235,plain,
( spl0_348
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f190,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
fof(f3233,plain,
spl0_347,
inference(avatar_split_clause,[],[f189,f3231]) ).
fof(f3231,plain,
( spl0_347
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f189,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
fof(f3229,plain,
spl0_346,
inference(avatar_split_clause,[],[f164,f3227]) ).
fof(f3227,plain,
( spl0_346
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f164,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
fof(f3225,plain,
spl0_345,
inference(avatar_split_clause,[],[f163,f3223]) ).
fof(f3223,plain,
( spl0_345
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f163,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
fof(f3221,plain,
spl0_344,
inference(avatar_split_clause,[],[f160,f3219]) ).
fof(f3219,plain,
( spl0_344
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f160,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
fof(f3217,plain,
spl0_343,
inference(avatar_split_clause,[],[f150,f3215]) ).
fof(f3215,plain,
( spl0_343
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f150,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
fof(f3205,plain,
spl0_342,
inference(avatar_split_clause,[],[f148,f3203]) ).
fof(f3203,plain,
( spl0_342
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f148,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
fof(f3201,plain,
spl0_341,
inference(avatar_split_clause,[],[f137,f3199]) ).
fof(f3199,plain,
( spl0_341
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f137,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
fof(f3197,plain,
spl0_340,
inference(avatar_split_clause,[],[f136,f3195]) ).
fof(f3195,plain,
( spl0_340
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f136,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
fof(f3193,plain,
spl0_339,
inference(avatar_split_clause,[],[f119,f3191]) ).
fof(f3191,plain,
( spl0_339
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X4,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f119,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X3,X4,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f3189,plain,
spl0_338,
inference(avatar_split_clause,[],[f116,f3187]) ).
fof(f3187,plain,
( spl0_338
<=> ! [X4,X0,X3,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X8,X0)
| ~ c_lessequals(X3,X4,X0)
| c_HOL_Oord__class_Oless(X3,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f116,axiom,
! [X3,X0,X8,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X8,X0)
| ~ c_lessequals(X3,X4,X0)
| c_HOL_Oord__class_Oless(X3,X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f3185,plain,
spl0_337,
inference(avatar_split_clause,[],[f115,f3183]) ).
fof(f3183,plain,
( spl0_337
<=> ! [X4,X0,X3,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(X4,X8,X0)
| c_HOL_Oord__class_Oless(X3,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f115,axiom,
! [X3,X0,X8,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(X4,X8,X0)
| c_HOL_Oord__class_Oless(X3,X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f3181,plain,
spl0_336,
inference(avatar_split_clause,[],[f113,f3179]) ).
fof(f3179,plain,
( spl0_336
<=> ! [X4,X0,X3,X8] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X8,X4,X0)
| ~ c_lessequals(X4,X3,X0)
| c_HOL_Oord__class_Oless(X8,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f113,axiom,
! [X3,X0,X8,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X8,X4,X0)
| ~ c_lessequals(X4,X3,X0)
| c_HOL_Oord__class_Oless(X8,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f3177,plain,
spl0_335,
inference(avatar_split_clause,[],[f112,f3175]) ).
fof(f3175,plain,
( spl0_335
<=> ! [X4,X0,X3,X8] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_lessequals(X8,X4,X0)
| c_HOL_Oord__class_Oless(X8,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f112,axiom,
! [X3,X0,X8,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_lessequals(X8,X4,X0)
| c_HOL_Oord__class_Oless(X8,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f3173,plain,
spl0_334,
inference(avatar_split_clause,[],[f111,f3171]) ).
fof(f3171,plain,
( spl0_334
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f111,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
fof(f3169,plain,
spl0_333,
inference(avatar_split_clause,[],[f108,f3167]) ).
fof(f3167,plain,
( spl0_333
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f108,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
fof(f3165,plain,
( spl0_332
| ~ spl0_150
| spl0_322 ),
inference(avatar_split_clause,[],[f3078,f2996,f1413,f3162]) ).
fof(f3162,plain,
( spl0_332
<=> c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f3078,plain,
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_150
| spl0_322 ),
inference(resolution,[],[f2998,f1414]) ).
fof(f3160,plain,
spl0_331,
inference(avatar_split_clause,[],[f76,f3158]) ).
fof(f3158,plain,
( spl0_331
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f76,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).
fof(f3156,plain,
spl0_330,
inference(avatar_split_clause,[],[f67,f3154]) ).
fof(f3154,plain,
( spl0_330
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f67,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).
fof(f3152,plain,
spl0_329,
inference(avatar_split_clause,[],[f45,f3150]) ).
fof(f3150,plain,
( spl0_329
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f45,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).
fof(f3148,plain,
spl0_328,
inference(avatar_split_clause,[],[f44,f3146]) ).
fof(f3146,plain,
( spl0_328
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f44,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_0) ).
fof(f3144,plain,
spl0_327,
inference(avatar_split_clause,[],[f42,f3142]) ).
fof(f3142,plain,
( spl0_327
<=> ! [X0,X1,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oplus__class_Oplus(X3,X1,X0) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f42,axiom,
! [X3,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oplus__class_Oplus(X3,X1,X0) != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f3140,plain,
spl0_326,
inference(avatar_split_clause,[],[f35,f3138]) ).
fof(f3138,plain,
( spl0_326
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f35,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
fof(f3136,plain,
spl0_325,
inference(avatar_split_clause,[],[f34,f3134]) ).
fof(f3134,plain,
( spl0_325
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f34,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
fof(f3132,plain,
spl0_324,
inference(avatar_split_clause,[],[f26,f3130]) ).
fof(f26,axiom,
! [X3,X0,X8,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X8,X4,X0)
| c_HOL_Oord__class_Oless(X8,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f3128,plain,
spl0_323,
inference(avatar_split_clause,[],[f25,f3126]) ).
fof(f25,axiom,
! [X3,X0,X8,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X8,X0)
| c_HOL_Oord__class_Oless(X3,X8,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f2999,plain,
( ~ spl0_55
| ~ spl0_322
| ~ spl0_56
| ~ spl0_203
| ~ spl0_257
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f2923,f2709,f2107,f1710,f959,f2996,f954]) ).
fof(f2709,plain,
( spl0_318
<=> ! [X0] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f2923,plain,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal)
| ~ spl0_56
| ~ spl0_203
| ~ spl0_257
| ~ spl0_318 ),
inference(forward_demodulation,[],[f2917,f2269]) ).
fof(f2917,plain,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal)
| ~ spl0_203
| ~ spl0_318 ),
inference(resolution,[],[f2710,f1711]) ).
fof(f2710,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) )
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f2709]) ).
fof(f2724,plain,
spl0_321,
inference(avatar_split_clause,[],[f542,f2722]) ).
fof(f2722,plain,
( spl0_321
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f542,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
fof(f2720,plain,
spl0_320,
inference(avatar_split_clause,[],[f504,f2717]) ).
fof(f2717,plain,
( spl0_320
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f504,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__is__one_2) ).
fof(f2715,plain,
spl0_319,
inference(avatar_split_clause,[],[f490,f2713]) ).
fof(f2713,plain,
( spl0_319
<=> ! [X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f490,axiom,
! [X3,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
fof(f2711,plain,
( ~ spl0_85
| spl0_318
| ~ spl0_200
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f2664,f2618,f1698,f2709,f1104]) ).
fof(f1698,plain,
( spl0_200
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_lessequals(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f2664,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) )
| ~ spl0_200
| ~ spl0_297 ),
inference(resolution,[],[f2619,f1699]) ).
fof(f1699,plain,
( ! [X3,X0,X4] :
( ~ c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f1698]) ).
fof(f2707,plain,
spl0_317,
inference(avatar_split_clause,[],[f451,f2705]) ).
fof(f2705,plain,
( spl0_317
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f451,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
fof(f2703,plain,
spl0_316,
inference(avatar_split_clause,[],[f450,f2701]) ).
fof(f2701,plain,
( spl0_316
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f450,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
fof(f2699,plain,
spl0_315,
inference(avatar_split_clause,[],[f416,f2697]) ).
fof(f2697,plain,
( spl0_315
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f416,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
fof(f2695,plain,
spl0_314,
inference(avatar_split_clause,[],[f415,f2693]) ).
fof(f2693,plain,
( spl0_314
<=> ! [X4,X0,X8] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f415,axiom,
! [X0,X8,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
fof(f2691,plain,
spl0_313,
inference(avatar_split_clause,[],[f382,f2689]) ).
fof(f2689,plain,
( spl0_313
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f382,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
fof(f2687,plain,
spl0_312,
inference(avatar_split_clause,[],[f380,f2685]) ).
fof(f2685,plain,
( spl0_312
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f380,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
fof(f2683,plain,
spl0_311,
inference(avatar_split_clause,[],[f379,f2681]) ).
fof(f2681,plain,
( spl0_311
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f379,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
fof(f2679,plain,
spl0_310,
inference(avatar_split_clause,[],[f378,f2677]) ).
fof(f2677,plain,
( spl0_310
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f378,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
fof(f2675,plain,
spl0_309,
inference(avatar_split_clause,[],[f377,f2673]) ).
fof(f2673,plain,
( spl0_309
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f377,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
fof(f2671,plain,
spl0_308,
inference(avatar_split_clause,[],[f376,f2669]) ).
fof(f2669,plain,
( spl0_308
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f376,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
fof(f2660,plain,
spl0_307,
inference(avatar_split_clause,[],[f375,f2658]) ).
fof(f2658,plain,
( spl0_307
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f375,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
fof(f2656,plain,
spl0_306,
inference(avatar_split_clause,[],[f374,f2654]) ).
fof(f2654,plain,
( spl0_306
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f374,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
fof(f2652,plain,
spl0_305,
inference(avatar_split_clause,[],[f373,f2650]) ).
fof(f2650,plain,
( spl0_305
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f373,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
fof(f2648,plain,
spl0_304,
inference(avatar_split_clause,[],[f343,f2646]) ).
fof(f2646,plain,
( spl0_304
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X3,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f343,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X3,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_0) ).
fof(f2644,plain,
spl0_303,
inference(avatar_split_clause,[],[f247,f2642]) ).
fof(f2642,plain,
( spl0_303
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f247,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
fof(f2640,plain,
spl0_302,
inference(avatar_split_clause,[],[f220,f2638]) ).
fof(f2638,plain,
( spl0_302
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f220,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__minus_0) ).
fof(f2636,plain,
spl0_301,
inference(avatar_split_clause,[],[f197,f2634]) ).
fof(f2634,plain,
( spl0_301
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f197,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
fof(f2632,plain,
spl0_300,
inference(avatar_split_clause,[],[f191,f2630]) ).
fof(f191,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__norm__iff_1) ).
fof(f2628,plain,
spl0_299,
inference(avatar_split_clause,[],[f188,f2626]) ).
fof(f2626,plain,
( spl0_299
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f188,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
fof(f2624,plain,
spl0_298,
inference(avatar_split_clause,[],[f181,f2622]) ).
fof(f2622,plain,
( spl0_298
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f181,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f2620,plain,
( spl0_297
| ~ spl0_161
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f2577,f2431,f1471,f2618]) ).
fof(f2577,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_161
| ~ spl0_289 ),
inference(resolution,[],[f2432,f1473]) ).
fof(f2616,plain,
spl0_296,
inference(avatar_split_clause,[],[f177,f2614]) ).
fof(f2614,plain,
( spl0_296
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f177,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
fof(f2612,plain,
spl0_295,
inference(avatar_split_clause,[],[f172,f2610]) ).
fof(f2610,plain,
( spl0_295
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f172,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
fof(f2608,plain,
spl0_294,
inference(avatar_split_clause,[],[f126,f2606]) ).
fof(f2606,plain,
( spl0_294
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f126,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
fof(f2604,plain,
spl0_293,
inference(avatar_split_clause,[],[f124,f2602]) ).
fof(f2602,plain,
( spl0_293
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| ~ c_lessequals(X3,X4,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f124,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| ~ c_lessequals(X3,X4,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f2600,plain,
spl0_292,
inference(avatar_split_clause,[],[f46,f2598]) ).
fof(f2598,plain,
( spl0_292
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f46,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
fof(f2522,plain,
( spl0_291
| ~ spl0_96
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1617,f1492,f1159,f2519]) ).
fof(f1159,plain,
( spl0_96
<=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1492,plain,
( spl0_166
<=> ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1617,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_96
| ~ spl0_166 ),
inference(resolution,[],[f1493,f1161]) ).
fof(f1161,plain,
( class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f1493,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1492]) ).
fof(f2441,plain,
( spl0_290
| ~ spl0_54
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1616,f1492,f949,f2438]) ).
fof(f2438,plain,
( spl0_290
<=> 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_290])]) ).
fof(f1616,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_54
| ~ spl0_166 ),
inference(resolution,[],[f1493,f951]) ).
fof(f951,plain,
( class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f949]) ).
fof(f2433,plain,
spl0_289,
inference(avatar_split_clause,[],[f526,f2431]) ).
fof(f526,axiom,
! [X26,X24,X25] :
( ~ c_lessequals(X24,X26,tc_RealDef_Oreal)
| ~ c_lessequals(X26,X25,tc_RealDef_Oreal)
| c_lessequals(X24,X25,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f2429,plain,
spl0_288,
inference(avatar_split_clause,[],[f495,f2427]) ).
fof(f2427,plain,
( spl0_288
<=> ! [X12,X3] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X12,X12,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f495,axiom,
! [X3,X12] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X12,X12,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__minus__mult__self__le_0) ).
fof(f2425,plain,
spl0_287,
inference(avatar_split_clause,[],[f447,f2423]) ).
fof(f2423,plain,
( spl0_287
<=> ! [X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f447,axiom,
! [X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_0) ).
fof(f2421,plain,
spl0_286,
inference(avatar_split_clause,[],[f432,f2419]) ).
fof(f2419,plain,
( spl0_286
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f432,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
fof(f2417,plain,
spl0_285,
inference(avatar_split_clause,[],[f430,f2415]) ).
fof(f430,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_1) ).
fof(f2413,plain,
spl0_284,
inference(avatar_split_clause,[],[f423,f2411]) ).
fof(f2411,plain,
( spl0_284
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oinverse__class_Oinverse(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f423,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oinverse__class_Oinverse(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
fof(f2409,plain,
spl0_283,
inference(avatar_split_clause,[],[f398,f2407]) ).
fof(f398,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
fof(f2405,plain,
( spl0_282
| ~ spl0_107
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1615,f1488,f1214,f2402]) ).
fof(f2402,plain,
( spl0_282
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f1488,plain,
( spl0_165
<=> ! [X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1615,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Complex_Ocomplex)
| ~ spl0_107
| ~ spl0_165 ),
inference(resolution,[],[f1489,f1216]) ).
fof(f1489,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0) )
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1488]) ).
fof(f2400,plain,
spl0_281,
inference(avatar_split_clause,[],[f362,f2398]) ).
fof(f2398,plain,
( spl0_281
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f362,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X5,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__abs_0) ).
fof(f2396,plain,
spl0_280,
inference(avatar_split_clause,[],[f346,f2394]) ).
fof(f2394,plain,
( spl0_280
<=> ! [X4,X3] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X3,X4,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f346,axiom,
! [X3,X4] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X3,X4,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__mult_0) ).
fof(f2392,plain,
spl0_279,
inference(avatar_split_clause,[],[f219,f2390]) ).
fof(f2390,plain,
( spl0_279
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f219,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f2388,plain,
spl0_278,
inference(avatar_split_clause,[],[f207,f2386]) ).
fof(f2386,plain,
( spl0_278
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_RealVector_Oof__real(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f207,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_RealVector_Oof__real(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).
fof(f2384,plain,
spl0_277,
inference(avatar_split_clause,[],[f182,f2382]) ).
fof(f2382,plain,
( spl0_277
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f182,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
fof(f2380,plain,
spl0_276,
inference(avatar_split_clause,[],[f175,f2378]) ).
fof(f2378,plain,
( spl0_276
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f175,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f2376,plain,
spl0_275,
inference(avatar_split_clause,[],[f138,f2374]) ).
fof(f138,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
fof(f2372,plain,
spl0_274,
inference(avatar_split_clause,[],[f66,f2370]) ).
fof(f2370,plain,
( spl0_274
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f66,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
fof(f2368,plain,
spl0_273,
inference(avatar_split_clause,[],[f39,f2366]) ).
fof(f2366,plain,
( spl0_273
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f39,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
fof(f2364,plain,
spl0_272,
inference(avatar_split_clause,[],[f37,f2362]) ).
fof(f2362,plain,
( spl0_272
<=> ! [X4,X0,X3] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| X3 = X4
| c_RealVector_Oof__real(X3,X0) != c_RealVector_Oof__real(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f37,axiom,
! [X3,X0,X4] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| X3 = X4
| c_RealVector_Oof__real(X3,X0) != c_RealVector_Oof__real(X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__iff_0) ).
fof(f2360,plain,
( spl0_271
| ~ spl0_71
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1614,f1488,f1034,f2357]) ).
fof(f2357,plain,
( spl0_271
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f1614,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_71
| ~ spl0_165 ),
inference(resolution,[],[f1489,f1036]) ).
fof(f2355,plain,
spl0_270,
inference(avatar_split_clause,[],[f14,f2353]) ).
fof(f2353,plain,
( spl0_270
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f14,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
fof(f2274,plain,
( spl0_269
| ~ spl0_113
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1613,f1480,f1244,f2272]) ).
fof(f2272,plain,
( spl0_269
<=> ! [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_269])]) ).
fof(f1480,plain,
( spl0_163
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1613,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_113
| ~ spl0_163 ),
inference(resolution,[],[f1481,f1246]) ).
fof(f1481,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f1480]) ).
fof(f2208,plain,
( spl0_268
| ~ spl0_78
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1612,f1480,f1069,f2206]) ).
fof(f2206,plain,
( spl0_268
<=> ! [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_268])]) ).
fof(f1612,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_78
| ~ spl0_163 ),
inference(resolution,[],[f1481,f1071]) ).
fof(f2167,plain,
( spl0_267
| ~ spl0_112
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1599,f1455,f1239,f2165]) ).
fof(f2165,plain,
( spl0_267
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f1239,plain,
( spl0_112
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1455,plain,
( spl0_157
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1599,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_112
| ~ spl0_157 ),
inference(resolution,[],[f1456,f1241]) ).
fof(f1241,plain,
( class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1239]) ).
fof(f1456,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1455]) ).
fof(f2149,plain,
spl0_266,
inference(avatar_split_clause,[],[f555,f2147]) ).
fof(f2147,plain,
( spl0_266
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X4,X3,X0) = c_HOL_Otimes__class_Otimes(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f555,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X4,X3,X0) = c_HOL_Otimes__class_Otimes(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
fof(f2145,plain,
spl0_265,
inference(avatar_split_clause,[],[f543,f2143]) ).
fof(f2143,plain,
( spl0_265
<=> ! [X13,X8] :
( X8 = X13
| ~ c_lessequals(X8,X13,tc_RealDef_Oreal)
| ~ c_lessequals(X13,X8,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f543,axiom,
! [X8,X13] :
( X8 = X13
| ~ c_lessequals(X8,X13,tc_RealDef_Oreal)
| ~ c_lessequals(X13,X8,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f2141,plain,
spl0_264,
inference(avatar_split_clause,[],[f500,f2139]) ).
fof(f2139,plain,
( spl0_264
<=> ! [X3] :
( ~ c_lessequals(X3,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X3),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f500,axiom,
! [X3] :
( ~ c_lessequals(X3,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X3),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__1__iff_1) ).
fof(f2137,plain,
spl0_263,
inference(avatar_split_clause,[],[f499,f2135]) ).
fof(f2135,plain,
( spl0_263
<=> ! [X3] :
( c_lessequals(X3,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X3),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f499,axiom,
! [X3] :
( c_lessequals(X3,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X3),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__1__iff_0) ).
fof(f2133,plain,
spl0_262,
inference(avatar_split_clause,[],[f498,f2131]) ).
fof(f2131,plain,
( spl0_262
<=> ! [X4] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f498,axiom,
! [X4] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__1__iff_1) ).
fof(f2129,plain,
spl0_261,
inference(avatar_split_clause,[],[f497,f2127]) ).
fof(f2127,plain,
( spl0_261
<=> ! [X4] :
( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f497,axiom,
! [X4] :
( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__1__iff_0) ).
fof(f2121,plain,
spl0_260,
inference(avatar_split_clause,[],[f404,f2119]) ).
fof(f2119,plain,
( spl0_260
<=> ! [X3] :
( c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f404,axiom,
! [X3] :
( c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__1__iff_0) ).
fof(f2117,plain,
spl0_259,
inference(avatar_split_clause,[],[f403,f2115]) ).
fof(f2115,plain,
( spl0_259
<=> ! [X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f403,axiom,
! [X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__1__iff_1) ).
fof(f2113,plain,
spl0_258,
inference(avatar_split_clause,[],[f387,f2111]) ).
fof(f2111,plain,
( spl0_258
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f387,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f2109,plain,
spl0_257,
inference(avatar_split_clause,[],[f386,f2107]) ).
fof(f386,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,X4,X0) = c_HOL_Oplus__class_Oplus(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
fof(f2105,plain,
spl0_256,
inference(avatar_split_clause,[],[f381,f2103]) ).
fof(f2103,plain,
( spl0_256
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f381,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
fof(f2101,plain,
spl0_255,
inference(avatar_split_clause,[],[f350,f2099]) ).
fof(f2099,plain,
( spl0_255
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X3,X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f350,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X3,X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
fof(f2097,plain,
spl0_254,
inference(avatar_split_clause,[],[f337,f2095]) ).
fof(f2095,plain,
( spl0_254
<=> ! [X4,X3] :
( X3 = X4
| ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f337,axiom,
! [X3,X4] :
( X3 = X4
| ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_2) ).
fof(f2093,plain,
spl0_253,
inference(avatar_split_clause,[],[f328,f2091]) ).
fof(f2091,plain,
( spl0_253
<=> ! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f328,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
fof(f2089,plain,
spl0_252,
inference(avatar_split_clause,[],[f251,f2087]) ).
fof(f2087,plain,
( spl0_252
<=> ! [X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X3),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f251,axiom,
! [X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X3),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__zero_0) ).
fof(f2085,plain,
spl0_251,
inference(avatar_split_clause,[],[f250,f2083]) ).
fof(f2083,plain,
( spl0_251
<=> ! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f250,axiom,
! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__0__iff_0) ).
fof(f2081,plain,
( spl0_250
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2007,f1815,f2079]) ).
fof(f2079,plain,
( spl0_250
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f1815,plain,
( spl0_229
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X4,X0)
| c_lessequals(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2007,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_229 ),
inference(factoring,[],[f1816]) ).
fof(f1816,plain,
( ! [X3,X0,X4] :
( c_lessequals(X4,X3,X0)
| c_lessequals(X3,X4,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f1815]) ).
fof(f2077,plain,
spl0_249,
inference(avatar_split_clause,[],[f237,f2075]) ).
fof(f2075,plain,
( spl0_249
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f237,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
fof(f2073,plain,
spl0_248,
inference(avatar_split_clause,[],[f217,f2071]) ).
fof(f2071,plain,
( spl0_248
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f217,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f2069,plain,
spl0_247,
inference(avatar_split_clause,[],[f199,f2067]) ).
fof(f2067,plain,
( spl0_247
<=> ! [X4] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f199,axiom,
! [X4] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__0__iff_0) ).
fof(f2065,plain,
spl0_246,
inference(avatar_split_clause,[],[f198,f2063]) ).
fof(f2063,plain,
( spl0_246
<=> ! [X4] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f198,axiom,
! [X4] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__0__iff_1) ).
fof(f2061,plain,
spl0_245,
inference(avatar_split_clause,[],[f96,f2059]) ).
fof(f2059,plain,
( spl0_245
<=> ! [X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f96,axiom,
! [X3,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f2057,plain,
spl0_244,
inference(avatar_split_clause,[],[f62,f2055]) ).
fof(f2055,plain,
( spl0_244
<=> ! [X3] :
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f62,axiom,
! [X3] :
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_1) ).
fof(f2053,plain,
spl0_243,
inference(avatar_split_clause,[],[f61,f2051]) ).
fof(f2051,plain,
( spl0_243
<=> ! [X3] :
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f61,axiom,
! [X3] :
( c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_0) ).
fof(f2049,plain,
spl0_242,
inference(avatar_split_clause,[],[f38,f2047]) ).
fof(f38,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
fof(f2045,plain,
spl0_241,
inference(avatar_split_clause,[],[f32,f2043]) ).
fof(f32,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
fof(f2041,plain,
spl0_240,
inference(avatar_split_clause,[],[f31,f2039]) ).
fof(f2039,plain,
( spl0_240
<=> ! [X3] :
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f31,axiom,
! [X3] :
( c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_0) ).
fof(f2037,plain,
spl0_239,
inference(avatar_split_clause,[],[f30,f2035]) ).
fof(f2035,plain,
( spl0_239
<=> ! [X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f30,axiom,
! [X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_1) ).
fof(f2033,plain,
spl0_238,
inference(avatar_split_clause,[],[f28,f2031]) ).
fof(f2031,plain,
( spl0_238
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f28,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f2029,plain,
spl0_237,
inference(avatar_split_clause,[],[f8,f2027]) ).
fof(f2027,plain,
( spl0_237
<=> ! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f8,axiom,
! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__1__iff_0) ).
fof(f2025,plain,
spl0_236,
inference(avatar_split_clause,[],[f7,f2023]) ).
fof(f2023,plain,
( spl0_236
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f7,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__1__iff_1) ).
fof(f2021,plain,
spl0_235,
inference(avatar_split_clause,[],[f4,f2019]) ).
fof(f2019,plain,
( spl0_235
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f4,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
fof(f2017,plain,
spl0_234,
inference(avatar_split_clause,[],[f3,f2015]) ).
fof(f3,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
fof(f2013,plain,
spl0_233,
inference(avatar_split_clause,[],[f2,f2011]) ).
fof(f2,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).
fof(f1991,plain,
( ~ spl0_84
| ~ spl0_232
| ~ spl0_161
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1860,f1686,f1471,f1988,f1099]) ).
fof(f1988,plain,
( spl0_232
<=> c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f1860,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ spl0_161
| ~ spl0_197 ),
inference(resolution,[],[f1687,f1473]) ).
fof(f1905,plain,
( ~ spl0_85
| spl0_231
| spl0_121
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1870,f1694,f1285,f1902,f1104]) ).
fof(f1870,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| spl0_121
| ~ spl0_199 ),
inference(resolution,[],[f1695,f1287]) ).
fof(f1825,plain,
( spl0_230
| ~ spl0_77
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1598,f1455,f1064,f1823]) ).
fof(f1823,plain,
( spl0_230
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f1064,plain,
( spl0_77
<=> class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1598,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
| ~ spl0_77
| ~ spl0_157 ),
inference(resolution,[],[f1456,f1066]) ).
fof(f1066,plain,
( class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal)
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1064]) ).
fof(f1817,plain,
spl0_229,
inference(avatar_split_clause,[],[f522,f1815]) ).
fof(f522,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X4,X0)
| c_lessequals(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1813,plain,
spl0_228,
inference(avatar_split_clause,[],[f506,f1811]) ).
fof(f1811,plain,
( spl0_228
<=> ! [X3] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f506,axiom,
! [X3] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__mod__minus__le__complex__mod_0) ).
fof(f1809,plain,
spl0_227,
inference(avatar_split_clause,[],[f468,f1807]) ).
fof(f1807,plain,
( spl0_227
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f468,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
fof(f1805,plain,
spl0_226,
inference(avatar_split_clause,[],[f458,f1803]) ).
fof(f458,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f1801,plain,
spl0_225,
inference(avatar_split_clause,[],[f457,f1799]) ).
fof(f1799,plain,
( spl0_225
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f457,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f1797,plain,
spl0_224,
inference(avatar_split_clause,[],[f456,f1795]) ).
fof(f456,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f1793,plain,
spl0_223,
inference(avatar_split_clause,[],[f433,f1791]) ).
fof(f1791,plain,
( spl0_223
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f433,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
fof(f1789,plain,
spl0_222,
inference(avatar_split_clause,[],[f393,f1787]) ).
fof(f393,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
fof(f1785,plain,
~ spl0_221,
inference(avatar_split_clause,[],[f384,f1782]) ).
fof(f1782,plain,
( spl0_221
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f384,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_1) ).
fof(f1780,plain,
( spl0_220
| ~ spl0_26
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1597,f1455,f809,f1778]) ).
fof(f1778,plain,
( spl0_220
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f809,plain,
( spl0_26
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1597,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0
| ~ spl0_26
| ~ spl0_157 ),
inference(resolution,[],[f1456,f811]) ).
fof(f811,plain,
( class_OrderedGroup_Omonoid__add(tc_nat)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f809]) ).
fof(f1776,plain,
spl0_219,
inference(avatar_split_clause,[],[f368,f1774]) ).
fof(f1774,plain,
( spl0_219
<=> ! [X3] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(X3)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f368,axiom,
! [X3] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_Transcendental_Ocos(X3)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__one__sin__zero_0) ).
fof(f1772,plain,
spl0_218,
inference(avatar_split_clause,[],[f342,f1770]) ).
fof(f1770,plain,
( spl0_218
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f342,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_1) ).
fof(f1768,plain,
spl0_217,
inference(avatar_split_clause,[],[f336,f1766]) ).
fof(f1766,plain,
( spl0_217
<=> ! [X4,X3] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f336,axiom,
! [X3,X4] :
( ~ c_lessequals(X3,X4,tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_1) ).
fof(f1764,plain,
spl0_216,
inference(avatar_split_clause,[],[f335,f1762]) ).
fof(f1762,plain,
( spl0_216
<=> ! [X4,X3] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f335,axiom,
! [X3,X4] :
( c_lessequals(X3,X4,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_0) ).
fof(f1760,plain,
spl0_215,
inference(avatar_split_clause,[],[f329,f1758]) ).
fof(f329,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X5,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f1756,plain,
spl0_214,
inference(avatar_split_clause,[],[f285,f1754]) ).
fof(f1754,plain,
( spl0_214
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f285,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f1752,plain,
spl0_213,
inference(avatar_split_clause,[],[f284,f1750]) ).
fof(f1750,plain,
( spl0_213
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f284,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f1748,plain,
spl0_212,
inference(avatar_split_clause,[],[f283,f1746]) ).
fof(f1746,plain,
( spl0_212
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f283,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
fof(f1744,plain,
spl0_211,
inference(avatar_split_clause,[],[f280,f1742]) ).
fof(f1742,plain,
( spl0_211
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f280,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
fof(f1740,plain,
spl0_210,
inference(avatar_split_clause,[],[f278,f1738]) ).
fof(f278,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f1736,plain,
( spl0_209
| ~ spl0_112
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1596,f1451,f1239,f1734]) ).
fof(f1734,plain,
( spl0_209
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1451,plain,
( spl0_156
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1596,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_112
| ~ spl0_156 ),
inference(resolution,[],[f1452,f1241]) ).
fof(f1452,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1451]) ).
fof(f1732,plain,
spl0_208,
inference(avatar_split_clause,[],[f277,f1730]) ).
fof(f277,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f1728,plain,
spl0_207,
inference(avatar_split_clause,[],[f276,f1726]) ).
fof(f276,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f1724,plain,
spl0_206,
inference(avatar_split_clause,[],[f275,f1722]) ).
fof(f275,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f1720,plain,
spl0_205,
inference(avatar_split_clause,[],[f244,f1718]) ).
fof(f244,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
fof(f1716,plain,
spl0_204,
inference(avatar_split_clause,[],[f242,f1714]) ).
fof(f1714,plain,
( spl0_204
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f242,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f1712,plain,
spl0_203,
inference(avatar_split_clause,[],[f185,f1710]) ).
fof(f185,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f1708,plain,
spl0_202,
inference(avatar_split_clause,[],[f174,f1706]) ).
fof(f1706,plain,
( spl0_202
<=> ! [X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f174,axiom,
! [X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__not__eq__zero_0) ).
fof(f1704,plain,
spl0_201,
inference(avatar_split_clause,[],[f170,f1702]) ).
fof(f1702,plain,
( spl0_201
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f170,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__norm__iff_0) ).
fof(f1700,plain,
spl0_200,
inference(avatar_split_clause,[],[f146,f1698]) ).
fof(f146,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_lessequals(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f1696,plain,
spl0_199,
inference(avatar_split_clause,[],[f140,f1694]) ).
fof(f140,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f1692,plain,
( spl0_198
| ~ spl0_77
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1595,f1451,f1064,f1690]) ).
fof(f1690,plain,
( spl0_198
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f1595,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_77
| ~ spl0_156 ),
inference(resolution,[],[f1452,f1066]) ).
fof(f1688,plain,
spl0_197,
inference(avatar_split_clause,[],[f139,f1686]) ).
fof(f139,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(X4,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1684,plain,
spl0_196,
inference(avatar_split_clause,[],[f118,f1682]) ).
fof(f1682,plain,
( spl0_196
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f118,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1680,plain,
spl0_195,
inference(avatar_split_clause,[],[f117,f1678]) ).
fof(f1678,plain,
( spl0_195
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f117,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_lessequals(X3,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1676,plain,
spl0_194,
inference(avatar_split_clause,[],[f75,f1674]) ).
fof(f1674,plain,
( spl0_194
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f75,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_1) ).
fof(f1672,plain,
spl0_193,
inference(avatar_split_clause,[],[f74,f1670]) ).
fof(f1670,plain,
( spl0_193
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f74,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X3),c_NthRoot_Osqrt(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_0) ).
fof(f1652,plain,
( spl0_192
| ~ spl0_26
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1594,f1451,f809,f1650]) ).
fof(f1650,plain,
( spl0_192
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1594,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_26
| ~ spl0_156 ),
inference(resolution,[],[f1452,f811]) ).
fof(f1636,plain,
( spl0_191
| ~ spl0_38
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1592,f1435,f869,f1633]) ).
fof(f1633,plain,
( spl0_191
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1435,plain,
( spl0_152
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1592,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_38
| ~ spl0_152 ),
inference(resolution,[],[f1436,f871]) ).
fof(f871,plain,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f869]) ).
fof(f1436,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f1435]) ).
fof(f1591,plain,
spl0_190,
inference(avatar_split_clause,[],[f556,f1589]) ).
fof(f1589,plain,
( spl0_190
<=> ! [X13,X8] : c_HOL_Otimes__class_Otimes(X8,X13,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X13,X8,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f556,axiom,
! [X8,X13] : c_HOL_Otimes__class_Otimes(X8,X13,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X13,X8,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
fof(f1587,plain,
spl0_189,
inference(avatar_split_clause,[],[f554,f1585]) ).
fof(f1585,plain,
( spl0_189
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f554,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
fof(f1583,plain,
spl0_188,
inference(avatar_split_clause,[],[f553,f1581]) ).
fof(f1581,plain,
( spl0_188
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f553,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(f1579,plain,
spl0_187,
inference(avatar_split_clause,[],[f550,f1577]) ).
fof(f1577,plain,
( spl0_187
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f550,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
fof(f1575,plain,
spl0_186,
inference(avatar_split_clause,[],[f549,f1573]) ).
fof(f549,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
fof(f1571,plain,
spl0_185,
inference(avatar_split_clause,[],[f548,f1569]) ).
fof(f548,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
fof(f1567,plain,
spl0_184,
inference(avatar_split_clause,[],[f530,f1565]) ).
fof(f530,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__one_0) ).
fof(f1563,plain,
spl0_183,
inference(avatar_split_clause,[],[f503,f1561]) ).
fof(f503,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
fof(f1559,plain,
( spl0_182
| ~ spl0_126
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1422,f1393,f1308,f1556]) ).
fof(f1422,plain,
( c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_126
| ~ spl0_145 ),
inference(resolution,[],[f1394,f1310]) ).
fof(f1554,plain,
spl0_181,
inference(avatar_split_clause,[],[f494,f1552]) ).
fof(f494,axiom,
! [X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__1_0) ).
fof(f1550,plain,
spl0_180,
inference(avatar_split_clause,[],[f452,f1548]) ).
fof(f1548,plain,
( spl0_180
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f452,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
fof(f1546,plain,
spl0_179,
inference(avatar_split_clause,[],[f426,f1544]) ).
fof(f1544,plain,
( spl0_179
<=> ! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f426,axiom,
! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
fof(f1542,plain,
spl0_178,
inference(avatar_split_clause,[],[f425,f1540]) ).
fof(f425,axiom,
! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
fof(f1538,plain,
spl0_177,
inference(avatar_split_clause,[],[f419,f1536]) ).
fof(f1536,plain,
( spl0_177
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f419,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
fof(f1534,plain,
spl0_176,
inference(avatar_split_clause,[],[f409,f1532]) ).
fof(f409,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(X3,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Opos__bounded_0) ).
fof(f1530,plain,
spl0_175,
inference(avatar_split_clause,[],[f399,f1528]) ).
fof(f399,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(X4,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Opos__bounded_0) ).
fof(f1526,plain,
spl0_174,
inference(avatar_split_clause,[],[f388,f1524]) ).
fof(f388,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__zero_0) ).
fof(f1522,plain,
spl0_173,
inference(avatar_split_clause,[],[f383,f1520]) ).
fof(f383,axiom,
! [X3] : c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(X3),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__minus_0) ).
fof(f1518,plain,
spl0_172,
inference(avatar_split_clause,[],[f369,f1516]) ).
fof(f1516,plain,
( spl0_172
<=> ! [X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f369,axiom,
! [X3] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X3
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__0__iff_0) ).
fof(f1514,plain,
spl0_171,
inference(avatar_split_clause,[],[f349,f1512]) ).
fof(f1512,plain,
( spl0_171
<=> ! [X3] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X3
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f349,axiom,
! [X3] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X3
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__1__iff_0) ).
fof(f1510,plain,
spl0_170,
inference(avatar_split_clause,[],[f331,f1508]) ).
fof(f331,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__one_0) ).
fof(f1506,plain,
spl0_169,
inference(avatar_split_clause,[],[f327,f1504]) ).
fof(f327,axiom,
! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).
fof(f1502,plain,
spl0_168,
inference(avatar_split_clause,[],[f234,f1500]) ).
fof(f234,axiom,
! [X3] : c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X3),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__minus_0) ).
fof(f1498,plain,
spl0_167,
inference(avatar_split_clause,[],[f223,f1496]) ).
fof(f1496,plain,
( spl0_167
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1(X4,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f223,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1(X4,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ononneg__bounded_0) ).
fof(f1494,plain,
spl0_166,
inference(avatar_split_clause,[],[f211,f1492]) ).
fof(f211,axiom,
! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
fof(f1490,plain,
spl0_165,
inference(avatar_split_clause,[],[f168,f1488]) ).
fof(f168,axiom,
! [X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__0_0) ).
fof(f1486,plain,
spl0_164,
inference(avatar_split_clause,[],[f162,f1484]) ).
fof(f1484,plain,
( spl0_164
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1(X3,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f162,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1(X3,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ononneg__bounded_0) ).
fof(f1482,plain,
spl0_163,
inference(avatar_split_clause,[],[f105,f1480]) ).
fof(f105,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
fof(f1478,plain,
spl0_162,
inference(avatar_split_clause,[],[f100,f1476]) ).
fof(f1476,plain,
( spl0_162
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f100,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f1474,plain,
( spl0_161
| spl0_121
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1429,f1413,f1285,f1471]) ).
fof(f1429,plain,
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_121
| ~ spl0_150 ),
inference(resolution,[],[f1414,f1287]) ).
fof(f1469,plain,
spl0_160,
inference(avatar_split_clause,[],[f99,f1467]) ).
fof(f1467,plain,
( spl0_160
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f99,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1465,plain,
spl0_159,
inference(avatar_split_clause,[],[f98,f1463]) ).
fof(f1463,plain,
( spl0_159
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f98,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1461,plain,
spl0_158,
inference(avatar_split_clause,[],[f95,f1459]) ).
fof(f1459,plain,
( spl0_158
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f95,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1457,plain,
spl0_157,
inference(avatar_split_clause,[],[f94,f1455]) ).
fof(f94,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1453,plain,
spl0_156,
inference(avatar_split_clause,[],[f93,f1451]) ).
fof(f93,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1449,plain,
spl0_155,
inference(avatar_split_clause,[],[f70,f1447]) ).
fof(f70,axiom,
! [X10,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(X10,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Opos__bounded_0) ).
fof(f1445,plain,
spl0_154,
inference(avatar_split_clause,[],[f49,f1443]) ).
fof(f1443,plain,
( spl0_154
<=> ! [X9,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1(X9,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f49,axiom,
! [X0,X9] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1(X9,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ononneg__bounded_0) ).
fof(f1441,plain,
spl0_153,
inference(avatar_split_clause,[],[f36,f1439]) ).
fof(f1439,plain,
( spl0_153
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f36,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
fof(f1437,plain,
spl0_152,
inference(avatar_split_clause,[],[f24,f1435]) ).
fof(f24,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
fof(f1428,plain,
( spl0_151
| ~ spl0_124
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1421,f1393,f1298,f1425]) ).
fof(f1298,plain,
( spl0_124
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1421,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal)
| ~ spl0_124
| ~ spl0_145 ),
inference(resolution,[],[f1394,f1300]) ).
fof(f1300,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal)
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1298]) ).
fof(f1415,plain,
spl0_150,
inference(avatar_split_clause,[],[f521,f1413]) ).
fof(f521,axiom,
! [X8,X13] :
( c_lessequals(X8,X13,tc_RealDef_Oreal)
| c_lessequals(X13,X8,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
fof(f1411,plain,
spl0_149,
inference(avatar_split_clause,[],[f484,f1409]) ).
fof(f1409,plain,
( spl0_149
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f484,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f1407,plain,
spl0_148,
inference(avatar_split_clause,[],[f482,f1405]) ).
fof(f1405,plain,
( spl0_148
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f482,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f1403,plain,
spl0_147,
inference(avatar_split_clause,[],[f420,f1401]) ).
fof(f1401,plain,
( spl0_147
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f420,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f1399,plain,
spl0_146,
inference(avatar_split_clause,[],[f397,f1397]) ).
fof(f1397,plain,
( spl0_146
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f397,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f1395,plain,
spl0_145,
inference(avatar_split_clause,[],[f334,f1393]) ).
fof(f334,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_RealDef_Oreal)
| c_lessequals(X3,X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_0) ).
fof(f1391,plain,
spl0_144,
inference(avatar_split_clause,[],[f202,f1389]) ).
fof(f1389,plain,
( spl0_144
<=> ! [X4,X3] :
( X3 = X4
| c_NthRoot_Osqrt(X4) != c_NthRoot_Osqrt(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f202,axiom,
! [X3,X4] :
( X3 = X4
| c_NthRoot_Osqrt(X4) != c_NthRoot_Osqrt(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__iff_0) ).
fof(f1387,plain,
spl0_143,
inference(avatar_split_clause,[],[f120,f1385]) ).
fof(f120,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
fof(f1382,plain,
spl0_142,
inference(avatar_split_clause,[],[f552,f1380]) ).
fof(f1380,plain,
( spl0_142
<=> ! [X8] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X8,tc_RealDef_Oreal) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f552,axiom,
! [X8] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X8,tc_RealDef_Oreal) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__1_0) ).
fof(f1378,plain,
( spl0_141
| ~ spl0_127
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1360,f1345,f1313,f1375]) ).
fof(f1375,plain,
( spl0_141
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1313,plain,
( spl0_127
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1360,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_127
| ~ spl0_134 ),
inference(superposition,[],[f1346,f1315]) ).
fof(f1315,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1313]) ).
fof(f1373,plain,
spl0_140,
inference(avatar_split_clause,[],[f507,f1371]) ).
fof(f507,axiom,
! [X3] : c_lessequals(c_Complex_ORe(X3),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__Re__le__cmod_0) ).
fof(f1369,plain,
spl0_139,
inference(avatar_split_clause,[],[f418,f1367]) ).
fof(f418,axiom,
! [X3] : c_Transcendental_Ocos(X3) = c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(X3,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__minus_0) ).
fof(f1365,plain,
spl0_138,
inference(avatar_split_clause,[],[f332,f1363]) ).
fof(f1363,plain,
( spl0_138
<=> ! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f332,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f1359,plain,
spl0_137,
inference(avatar_split_clause,[],[f528,f1357]) ).
fof(f1357,plain,
( spl0_137
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f528,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1355,plain,
spl0_136,
inference(avatar_split_clause,[],[f527,f1353]) ).
fof(f1353,plain,
( spl0_136
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f527,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1351,plain,
spl0_135,
inference(avatar_split_clause,[],[f502,f1349]) ).
fof(f502,axiom,
! [X3] : c_lessequals(c_Transcendental_Ocos(X3),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__le__one_0) ).
fof(f1347,plain,
spl0_134,
inference(avatar_split_clause,[],[f501,f1345]) ).
fof(f501,axiom,
! [X3] : c_lessequals(c_Transcendental_Osin(X3),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__le__one_0) ).
fof(f1343,plain,
spl0_133,
inference(avatar_split_clause,[],[f408,f1341]) ).
fof(f1341,plain,
( spl0_133
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f408,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1339,plain,
spl0_132,
inference(avatar_split_clause,[],[f406,f1337]) ).
fof(f1337,plain,
( spl0_132
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f406,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1335,plain,
spl0_131,
inference(avatar_split_clause,[],[f405,f1333]) ).
fof(f1333,plain,
( spl0_131
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f405,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1331,plain,
spl0_130,
inference(avatar_split_clause,[],[f347,f1328]) ).
fof(f1328,plain,
( spl0_130
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f347,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__one_0) ).
fof(f1326,plain,
spl0_129,
inference(avatar_split_clause,[],[f248,f1323]) ).
fof(f1323,plain,
( spl0_129
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f248,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__zero_0) ).
fof(f1321,plain,
spl0_128,
inference(avatar_split_clause,[],[f227,f1318]) ).
fof(f1318,plain,
( spl0_128
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f227,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__zero_0) ).
fof(f1316,plain,
spl0_127,
inference(avatar_split_clause,[],[f226,f1313]) ).
fof(f226,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sin__zero_0) ).
fof(f1311,plain,
spl0_126,
inference(avatar_split_clause,[],[f508,f1308]) ).
fof(f508,axiom,
c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_t_I2_J_0) ).
fof(f1306,plain,
~ spl0_125,
inference(avatar_split_clause,[],[f348,f1303]) ).
fof(f1303,plain,
( spl0_125
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f348,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
fof(f1301,plain,
spl0_124,
inference(avatar_split_clause,[],[f27,f1298]) ).
fof(f27,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_t_I1_J_0) ).
fof(f1296,plain,
spl0_123,
inference(avatar_split_clause,[],[f525,f1294]) ).
fof(f525,axiom,
! [X13] : c_lessequals(X13,X13,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
fof(f1292,plain,
spl0_122,
inference(avatar_split_clause,[],[f407,f1290]) ).
fof(f1290,plain,
( spl0_122
<=> ! [X3] : ~ c_HOL_Oord__class_Oless(X3,X3,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f407,axiom,
! [X3] : ~ c_HOL_Oord__class_Oless(X3,X3,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_1) ).
fof(f1288,plain,
( ~ spl0_121
| spl0_120 ),
inference(avatar_split_clause,[],[f1283,f1279,f1285]) ).
fof(f1279,plain,
( spl0_120
<=> c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1283,plain,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| spl0_120 ),
inference(forward_demodulation,[],[f1281,f552]) ).
fof(f1281,plain,
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_120 ),
inference(avatar_component_clause,[],[f1279]) ).
fof(f1282,plain,
~ spl0_120,
inference(avatar_split_clause,[],[f559,f1279]) ).
fof(f559,axiom,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1277,plain,
spl0_119,
inference(avatar_split_clause,[],[f678,f1274]) ).
fof(f1274,plain,
( spl0_119
<=> class_Power_Opower(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f678,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
fof(f1272,plain,
spl0_118,
inference(avatar_split_clause,[],[f677,f1269]) ).
fof(f1269,plain,
( spl0_118
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f677,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f1267,plain,
spl0_117,
inference(avatar_split_clause,[],[f676,f1264]) ).
fof(f1264,plain,
( spl0_117
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f676,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f1262,plain,
spl0_116,
inference(avatar_split_clause,[],[f675,f1259]) ).
fof(f1259,plain,
( spl0_116
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f675,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(f1257,plain,
spl0_115,
inference(avatar_split_clause,[],[f674,f1254]) ).
fof(f1254,plain,
( spl0_115
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f674,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f1252,plain,
spl0_114,
inference(avatar_split_clause,[],[f673,f1249]) ).
fof(f1249,plain,
( spl0_114
<=> class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f673,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
fof(f1247,plain,
spl0_113,
inference(avatar_split_clause,[],[f672,f1244]) ).
fof(f672,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(f1242,plain,
spl0_112,
inference(avatar_split_clause,[],[f671,f1239]) ).
fof(f671,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(f1237,plain,
spl0_111,
inference(avatar_split_clause,[],[f670,f1234]) ).
fof(f1234,plain,
( spl0_111
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f670,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(f1232,plain,
spl0_110,
inference(avatar_split_clause,[],[f669,f1229]) ).
fof(f669,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f1227,plain,
spl0_109,
inference(avatar_split_clause,[],[f668,f1224]) ).
fof(f1224,plain,
( spl0_109
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f668,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(f1222,plain,
spl0_108,
inference(avatar_split_clause,[],[f667,f1219]) ).
fof(f1219,plain,
( spl0_108
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f667,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f1217,plain,
spl0_107,
inference(avatar_split_clause,[],[f666,f1214]) ).
fof(f666,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
fof(f1212,plain,
spl0_106,
inference(avatar_split_clause,[],[f665,f1209]) ).
fof(f1209,plain,
( spl0_106
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f665,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(f1207,plain,
spl0_105,
inference(avatar_split_clause,[],[f664,f1204]) ).
fof(f1204,plain,
( spl0_105
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f664,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f1202,plain,
spl0_104,
inference(avatar_split_clause,[],[f663,f1199]) ).
fof(f1199,plain,
( spl0_104
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f663,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(f1197,plain,
spl0_103,
inference(avatar_split_clause,[],[f662,f1194]) ).
fof(f662,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(f1192,plain,
spl0_102,
inference(avatar_split_clause,[],[f661,f1189]) ).
fof(f1189,plain,
( spl0_102
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f661,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(f1187,plain,
spl0_101,
inference(avatar_split_clause,[],[f660,f1184]) ).
fof(f1184,plain,
( spl0_101
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f660,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1182,plain,
spl0_100,
inference(avatar_split_clause,[],[f659,f1179]) ).
fof(f659,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1177,plain,
spl0_99,
inference(avatar_split_clause,[],[f658,f1174]) ).
fof(f1174,plain,
( spl0_99
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f658,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f1172,plain,
spl0_98,
inference(avatar_split_clause,[],[f657,f1169]) ).
fof(f1169,plain,
( spl0_98
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f657,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1167,plain,
spl0_97,
inference(avatar_split_clause,[],[f656,f1164]) ).
fof(f1164,plain,
( spl0_97
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f656,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(f1162,plain,
spl0_96,
inference(avatar_split_clause,[],[f655,f1159]) ).
fof(f655,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(f1157,plain,
spl0_95,
inference(avatar_split_clause,[],[f654,f1154]) ).
fof(f1154,plain,
( spl0_95
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f654,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(f1152,plain,
spl0_94,
inference(avatar_split_clause,[],[f653,f1149]) ).
fof(f653,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(f1147,plain,
spl0_93,
inference(avatar_split_clause,[],[f652,f1144]) ).
fof(f1144,plain,
( spl0_93
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f652,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1142,plain,
spl0_92,
inference(avatar_split_clause,[],[f651,f1139]) ).
fof(f1139,plain,
( spl0_92
<=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f651,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(f1137,plain,
spl0_91,
inference(avatar_split_clause,[],[f650,f1134]) ).
fof(f1134,plain,
( spl0_91
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f650,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(f1132,plain,
spl0_90,
inference(avatar_split_clause,[],[f649,f1129]) ).
fof(f649,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(f1127,plain,
spl0_89,
inference(avatar_split_clause,[],[f648,f1124]) ).
fof(f1124,plain,
( spl0_89
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f648,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(f1122,plain,
spl0_88,
inference(avatar_split_clause,[],[f647,f1119]) ).
fof(f1119,plain,
( spl0_88
<=> class_Power_Opower(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f647,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Power_Opower) ).
fof(f1117,plain,
spl0_87,
inference(avatar_split_clause,[],[f646,f1114]) ).
fof(f1114,plain,
( spl0_87
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f646,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f1112,plain,
spl0_86,
inference(avatar_split_clause,[],[f645,f1109]) ).
fof(f645,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
fof(f1107,plain,
spl0_85,
inference(avatar_split_clause,[],[f644,f1104]) ).
fof(f644,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f1102,plain,
spl0_84,
inference(avatar_split_clause,[],[f643,f1099]) ).
fof(f643,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f1097,plain,
spl0_83,
inference(avatar_split_clause,[],[f642,f1094]) ).
fof(f1094,plain,
( spl0_83
<=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f642,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
fof(f1092,plain,
spl0_82,
inference(avatar_split_clause,[],[f641,f1089]) ).
fof(f1089,plain,
( spl0_82
<=> class_Ring__and__Field_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f641,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
fof(f1087,plain,
spl0_81,
inference(avatar_split_clause,[],[f640,f1084]) ).
fof(f1084,plain,
( spl0_81
<=> class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f640,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
fof(f1082,plain,
spl0_80,
inference(avatar_split_clause,[],[f639,f1079]) ).
fof(f639,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).
fof(f1077,plain,
spl0_79,
inference(avatar_split_clause,[],[f638,f1074]) ).
fof(f1074,plain,
( spl0_79
<=> class_Ring__and__Field_Oring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f638,axiom,
class_Ring__and__Field_Oring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1) ).
fof(f1072,plain,
spl0_78,
inference(avatar_split_clause,[],[f637,f1069]) ).
fof(f637,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f1067,plain,
spl0_77,
inference(avatar_split_clause,[],[f636,f1064]) ).
fof(f636,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
fof(f1062,plain,
spl0_76,
inference(avatar_split_clause,[],[f635,f1059]) ).
fof(f1059,plain,
( spl0_76
<=> class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f635,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
fof(f1057,plain,
spl0_75,
inference(avatar_split_clause,[],[f634,f1054]) ).
fof(f634,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
fof(f1052,plain,
spl0_74,
inference(avatar_split_clause,[],[f633,f1049]) ).
fof(f1049,plain,
( spl0_74
<=> class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f633,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(f1047,plain,
spl0_73,
inference(avatar_split_clause,[],[f632,f1044]) ).
fof(f1044,plain,
( spl0_73
<=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f632,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(f1042,plain,
spl0_72,
inference(avatar_split_clause,[],[f631,f1039]) ).
fof(f1039,plain,
( spl0_72
<=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f631,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
fof(f1037,plain,
spl0_71,
inference(avatar_split_clause,[],[f630,f1034]) ).
fof(f630,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).
fof(f1032,plain,
spl0_70,
inference(avatar_split_clause,[],[f629,f1029]) ).
fof(f1029,plain,
( spl0_70
<=> class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f629,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(f1027,plain,
spl0_69,
inference(avatar_split_clause,[],[f628,f1024]) ).
fof(f628,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(f1022,plain,
spl0_68,
inference(avatar_split_clause,[],[f627,f1019]) ).
fof(f1019,plain,
( spl0_68
<=> class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f627,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(f1017,plain,
spl0_67,
inference(avatar_split_clause,[],[f626,f1014]) ).
fof(f1014,plain,
( spl0_67
<=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f626,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
fof(f1012,plain,
spl0_66,
inference(avatar_split_clause,[],[f625,f1009]) ).
fof(f1009,plain,
( spl0_66
<=> class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f625,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(f1007,plain,
spl0_65,
inference(avatar_split_clause,[],[f624,f1004]) ).
fof(f624,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(f1002,plain,
spl0_64,
inference(avatar_split_clause,[],[f623,f999]) ).
fof(f999,plain,
( spl0_64
<=> class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f623,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(f997,plain,
spl0_63,
inference(avatar_split_clause,[],[f622,f994]) ).
fof(f994,plain,
( spl0_63
<=> class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f622,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(f992,plain,
spl0_62,
inference(avatar_split_clause,[],[f621,f989]) ).
fof(f989,plain,
( spl0_62
<=> class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f621,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(f987,plain,
spl0_61,
inference(avatar_split_clause,[],[f620,f984]) ).
fof(f984,plain,
( spl0_61
<=> class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f620,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
fof(f982,plain,
spl0_60,
inference(avatar_split_clause,[],[f619,f979]) ).
fof(f979,plain,
( spl0_60
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f619,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).
fof(f977,plain,
spl0_59,
inference(avatar_split_clause,[],[f618,f974]) ).
fof(f618,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f972,plain,
spl0_58,
inference(avatar_split_clause,[],[f617,f969]) ).
fof(f969,plain,
( spl0_58
<=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f617,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
fof(f967,plain,
spl0_57,
inference(avatar_split_clause,[],[f616,f964]) ).
fof(f964,plain,
( spl0_57
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f616,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f962,plain,
spl0_56,
inference(avatar_split_clause,[],[f615,f959]) ).
fof(f615,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(f957,plain,
spl0_55,
inference(avatar_split_clause,[],[f614,f954]) ).
fof(f614,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(f952,plain,
spl0_54,
inference(avatar_split_clause,[],[f613,f949]) ).
fof(f613,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(f947,plain,
spl0_53,
inference(avatar_split_clause,[],[f612,f944]) ).
fof(f944,plain,
( spl0_53
<=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f612,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(f942,plain,
spl0_52,
inference(avatar_split_clause,[],[f611,f939]) ).
fof(f939,plain,
( spl0_52
<=> class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f611,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).
fof(f937,plain,
spl0_51,
inference(avatar_split_clause,[],[f610,f934]) ).
fof(f610,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(f932,plain,
spl0_50,
inference(avatar_split_clause,[],[f609,f929]) ).
fof(f929,plain,
( spl0_50
<=> class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f609,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(f927,plain,
spl0_49,
inference(avatar_split_clause,[],[f608,f924]) ).
fof(f924,plain,
( spl0_49
<=> class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f608,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(f922,plain,
spl0_48,
inference(avatar_split_clause,[],[f607,f919]) ).
fof(f919,plain,
( spl0_48
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f607,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
fof(f917,plain,
spl0_47,
inference(avatar_split_clause,[],[f606,f914]) ).
fof(f914,plain,
( spl0_47
<=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f606,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(f912,plain,
spl0_46,
inference(avatar_split_clause,[],[f605,f909]) ).
fof(f909,plain,
( spl0_46
<=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f605,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(f907,plain,
spl0_45,
inference(avatar_split_clause,[],[f604,f904]) ).
fof(f904,plain,
( spl0_45
<=> class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f604,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(f902,plain,
spl0_44,
inference(avatar_split_clause,[],[f603,f899]) ).
fof(f899,plain,
( spl0_44
<=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f603,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(f897,plain,
spl0_43,
inference(avatar_split_clause,[],[f602,f894]) ).
fof(f894,plain,
( spl0_43
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f602,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(f892,plain,
spl0_42,
inference(avatar_split_clause,[],[f601,f889]) ).
fof(f889,plain,
( spl0_42
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f601,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(f887,plain,
spl0_41,
inference(avatar_split_clause,[],[f600,f884]) ).
fof(f600,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(f882,plain,
spl0_40,
inference(avatar_split_clause,[],[f599,f879]) ).
fof(f879,plain,
( spl0_40
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f599,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(f877,plain,
spl0_39,
inference(avatar_split_clause,[],[f598,f874]) ).
fof(f874,plain,
( spl0_39
<=> class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f598,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(f872,plain,
spl0_38,
inference(avatar_split_clause,[],[f597,f869]) ).
fof(f597,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(f867,plain,
spl0_37,
inference(avatar_split_clause,[],[f596,f864]) ).
fof(f864,plain,
( spl0_37
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f596,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(f862,plain,
spl0_36,
inference(avatar_split_clause,[],[f595,f859]) ).
fof(f595,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).
fof(f857,plain,
spl0_35,
inference(avatar_split_clause,[],[f594,f854]) ).
fof(f854,plain,
( spl0_35
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f594,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(f852,plain,
spl0_34,
inference(avatar_split_clause,[],[f593,f849]) ).
fof(f849,plain,
( spl0_34
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f593,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(f847,plain,
spl0_33,
inference(avatar_split_clause,[],[f592,f844]) ).
fof(f844,plain,
( spl0_33
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f592,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f842,plain,
spl0_32,
inference(avatar_split_clause,[],[f591,f839]) ).
fof(f839,plain,
( spl0_32
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f591,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(f837,plain,
spl0_31,
inference(avatar_split_clause,[],[f590,f834]) ).
fof(f834,plain,
( spl0_31
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f590,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f832,plain,
spl0_30,
inference(avatar_split_clause,[],[f589,f829]) ).
fof(f829,plain,
( spl0_30
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f589,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f827,plain,
spl0_29,
inference(avatar_split_clause,[],[f588,f824]) ).
fof(f824,plain,
( spl0_29
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f588,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f822,plain,
spl0_28,
inference(avatar_split_clause,[],[f587,f819]) ).
fof(f819,plain,
( spl0_28
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f587,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f817,plain,
spl0_27,
inference(avatar_split_clause,[],[f586,f814]) ).
fof(f814,plain,
( spl0_27
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f586,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f812,plain,
spl0_26,
inference(avatar_split_clause,[],[f585,f809]) ).
fof(f585,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f807,plain,
spl0_25,
inference(avatar_split_clause,[],[f584,f804]) ).
fof(f804,plain,
( spl0_25
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f584,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f802,plain,
spl0_24,
inference(avatar_split_clause,[],[f583,f799]) ).
fof(f583,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f797,plain,
spl0_23,
inference(avatar_split_clause,[],[f582,f794]) ).
fof(f794,plain,
( spl0_23
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f582,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f792,plain,
spl0_22,
inference(avatar_split_clause,[],[f581,f789]) ).
fof(f581,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f787,plain,
spl0_21,
inference(avatar_split_clause,[],[f580,f784]) ).
fof(f784,plain,
( spl0_21
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f580,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f782,plain,
spl0_20,
inference(avatar_split_clause,[],[f579,f779]) ).
fof(f779,plain,
( spl0_20
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f579,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(f777,plain,
spl0_19,
inference(avatar_split_clause,[],[f578,f774]) ).
fof(f774,plain,
( spl0_19
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f578,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f772,plain,
spl0_18,
inference(avatar_split_clause,[],[f577,f769]) ).
fof(f769,plain,
( spl0_18
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f577,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f767,plain,
spl0_17,
inference(avatar_split_clause,[],[f576,f764]) ).
fof(f764,plain,
( spl0_17
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f576,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f762,plain,
spl0_16,
inference(avatar_split_clause,[],[f575,f759]) ).
fof(f759,plain,
( spl0_16
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f575,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f757,plain,
spl0_15,
inference(avatar_split_clause,[],[f574,f754]) ).
fof(f754,plain,
( spl0_15
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f574,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f752,plain,
spl0_14,
inference(avatar_split_clause,[],[f573,f749]) ).
fof(f749,plain,
( spl0_14
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f573,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(f747,plain,
spl0_13,
inference(avatar_split_clause,[],[f572,f744]) ).
fof(f744,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f572,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f742,plain,
spl0_12,
inference(avatar_split_clause,[],[f571,f739]) ).
fof(f739,plain,
( spl0_12
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f571,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(f737,plain,
spl0_11,
inference(avatar_split_clause,[],[f570,f734]) ).
fof(f734,plain,
( spl0_11
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f570,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f732,plain,
spl0_10,
inference(avatar_split_clause,[],[f569,f729]) ).
fof(f729,plain,
( spl0_10
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f569,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f727,plain,
spl0_9,
inference(avatar_split_clause,[],[f568,f724]) ).
fof(f724,plain,
( spl0_9
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f568,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f722,plain,
spl0_8,
inference(avatar_split_clause,[],[f567,f719]) ).
fof(f719,plain,
( spl0_8
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f567,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f717,plain,
spl0_7,
inference(avatar_split_clause,[],[f566,f714]) ).
fof(f714,plain,
( spl0_7
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f566,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f712,plain,
spl0_6,
inference(avatar_split_clause,[],[f565,f709]) ).
fof(f709,plain,
( spl0_6
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f565,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f707,plain,
spl0_5,
inference(avatar_split_clause,[],[f564,f704]) ).
fof(f704,plain,
( spl0_5
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f564,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f702,plain,
spl0_4,
inference(avatar_split_clause,[],[f563,f699]) ).
fof(f699,plain,
( spl0_4
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f563,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(f697,plain,
spl0_3,
inference(avatar_split_clause,[],[f562,f694]) ).
fof(f694,plain,
( spl0_3
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f562,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f692,plain,
spl0_2,
inference(avatar_split_clause,[],[f561,f689]) ).
fof(f689,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f561,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(f687,plain,
spl0_1,
inference(avatar_split_clause,[],[f560,f684]) ).
fof(f684,plain,
( spl0_1
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f560,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ALG406-1 : TPTP v8.2.0. Released v4.1.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.39 % Computer : n018.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8042.1875MB
% 0.14/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat May 18 22:39:23 EDT 2024
% 0.14/0.39 % CPUTime :
% 0.14/0.39 % (17656)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.44 % (17659)WARNING: value z3 for option sas not known
% 0.14/0.44 % (17661)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)
% 0.14/0.44 % (17657)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.44 % (17663)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)
% 0.14/0.44 % (17658)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.44 % (17660)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.44 % (17662)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)
% 0.14/0.44 % (17659)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)
% 0.24/0.50 TRYING [1]
% 0.24/0.51 TRYING [2]
% 1.65/0.65 TRYING [3]
% 2.56/0.79 TRYING [1]
% 3.06/0.85 TRYING [2]
% 5.26/1.17 % (17661)First to succeed.
% 5.52/1.20 % (17661)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-17656"
% 5.52/1.20 % (17661)Refutation found. Thanks to Tanya!
% 5.52/1.20 % SZS status Unsatisfiable for theBenchmark
% 5.52/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 5.52/1.22 % (17661)------------------------------
% 5.52/1.22 % (17661)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 5.52/1.22 % (17661)Termination reason: Refutation
% 5.52/1.22
% 5.52/1.22 % (17661)Memory used [KB]: 8435
% 5.52/1.22 % (17661)Time elapsed: 0.756 s
% 5.52/1.22 % (17661)Instructions burned: 1344 (million)
% 5.52/1.22 % (17656)Success in time 0.808 s
%------------------------------------------------------------------------------