TSTP Solution File: ALG382-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG382-1 : 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 : n010.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 18:37:30 EDT 2024
% Result : Unsatisfiable 1.91s 0.70s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1158
% Syntax : Number of formulae : 1859 ( 684 unt; 0 def)
% Number of atoms : 4077 ( 628 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 3819 (1601 ~;1619 |; 0 &)
% ( 599 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 669 ( 667 usr; 600 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 8 con; 0-3 aty)
% Number of variables : 2111 (2111 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6940,plain,
$false,
inference(avatar_sat_refutation,[],[f1001,f1006,f1011,f1016,f1021,f1026,f1031,f1036,f1041,f1046,f1051,f1056,f1061,f1066,f1071,f1076,f1081,f1086,f1091,f1096,f1101,f1106,f1111,f1116,f1121,f1126,f1131,f1136,f1141,f1146,f1151,f1156,f1161,f1166,f1171,f1176,f1181,f1186,f1191,f1196,f1201,f1206,f1211,f1216,f1221,f1226,f1231,f1236,f1241,f1246,f1251,f1256,f1261,f1266,f1271,f1276,f1281,f1286,f1291,f1296,f1301,f1306,f1311,f1316,f1321,f1326,f1331,f1336,f1341,f1346,f1351,f1356,f1361,f1366,f1371,f1376,f1381,f1386,f1391,f1396,f1401,f1406,f1411,f1416,f1421,f1426,f1431,f1436,f1441,f1446,f1451,f1456,f1461,f1466,f1471,f1476,f1481,f1486,f1490,f1494,f1499,f1504,f1508,f1512,f1516,f1520,f1524,f1528,f1532,f1536,f1540,f1544,f1548,f1552,f1556,f1560,f1564,f1568,f1572,f1576,f1580,f1584,f1588,f1592,f1596,f1600,f1604,f1608,f1612,f1616,f1620,f1624,f1628,f1632,f1636,f1640,f1644,f1648,f1652,f1656,f1660,f1664,f1668,f1672,f1676,f1680,f1684,f1688,f1692,f1696,f1700,f1704,f1708,f1712,f1717,f1723,f1727,f1732,f1736,f1740,f1744,f1749,f1754,f1758,f1762,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1806,f1810,f1815,f1819,f1830,f1839,f1843,f1847,f1851,f1855,f1859,f1863,f1867,f1871,f1875,f1879,f1883,f1887,f1891,f1895,f1899,f1903,f1907,f1911,f1915,f1919,f1923,f1927,f1931,f1935,f1939,f1943,f1947,f1951,f1955,f1959,f1963,f1967,f1971,f1975,f1979,f1983,f1987,f1991,f1995,f1999,f2003,f2007,f2011,f2015,f2019,f2029,f2050,f2088,f2121,f2141,f2145,f2150,f2154,f2158,f2162,f2166,f2170,f2174,f2178,f2182,f2186,f2190,f2194,f2198,f2202,f2206,f2210,f2215,f2219,f2223,f2227,f2231,f2235,f2239,f2243,f2247,f2251,f2255,f2260,f2264,f2268,f2272,f2276,f2280,f2284,f2288,f2292,f2296,f2300,f2305,f2309,f2330,f2466,f2501,f2505,f2509,f2513,f2517,f2521,f2525,f2529,f2533,f2537,f2541,f2545,f2551,f2555,f2559,f2563,f2567,f2571,f2575,f2579,f2583,f2587,f2592,f2596,f2600,f2604,f2608,f2612,f2616,f2620,f2624,f2628,f2633,f2637,f2641,f2645,f2649,f2653,f2657,f2661,f2665,f2669,f2673,f2677,f2681,f2685,f2689,f2693,f2697,f2772,f2855,f2900,f2957,f2964,f2968,f2972,f2976,f2980,f2984,f2988,f2992,f2996,f3001,f3005,f3009,f3013,f3017,f3021,f3025,f3029,f3033,f3037,f3041,f3046,f3050,f3054,f3058,f3062,f3066,f3070,f3074,f3078,f3082,f3087,f3092,f3096,f3100,f3104,f3132,f3172,f3282,f3328,f3332,f3336,f3340,f3344,f3348,f3352,f3356,f3360,f3364,f3368,f3372,f3376,f3380,f3384,f3388,f3392,f3396,f3400,f3404,f3408,f3412,f3416,f3420,f3424,f3428,f3432,f3458,f3462,f3466,f3470,f3474,f3478,f3482,f3486,f3490,f3494,f3499,f3503,f3507,f3511,f3515,f3519,f3523,f3527,f3531,f3549,f3804,f4024,f4028,f4032,f4036,f4040,f4044,f4048,f4052,f4056,f4061,f4065,f4069,f4073,f4077,f4081,f4085,f4089,f4093,f4097,f4101,f4112,f4116,f4120,f4124,f4128,f4132,f4136,f4140,f4144,f4148,f4152,f4156,f4160,f4164,f4168,f4172,f4176,f4180,f4184,f4188,f4192,f4196,f4200,f4204,f4208,f4212,f4216,f4220,f4224,f4228,f4232,f4236,f4240,f4244,f4248,f4252,f4256,f4260,f4264,f4268,f4272,f4276,f4280,f4284,f4288,f4292,f4296,f4384,f4534,f4800,f4932,f5020,f5209,f5213,f5217,f5221,f5225,f5269,f5273,f5277,f5281,f5285,f5289,f5293,f5297,f5301,f5305,f5316,f5320,f5324,f5328,f5332,f5336,f5340,f5344,f5348,f5352,f5364,f5368,f5372,f5376,f5380,f5384,f5388,f5392,f5396,f5400,f5444,f5448,f5452,f5456,f5804,f5808,f5812,f5816,f5820,f5824,f5828,f5832,f5836,f5840,f5844,f5848,f5852,f5856,f5860,f5864,f5868,f5872,f5876,f5880,f5884,f5888,f5892,f5896,f5900,f5904,f5908,f5920,f5924,f5928,f5932,f5936,f5941,f5945,f5949,f5953,f5957,f5969,f5973,f5977,f5981,f6449,f6654,f6658,f6662,f6666,f6739,f6743,f6747,f6751,f6755,f6759,f6763,f6767,f6771,f6775,f6852,f6856,f6860,f6865,f6870,f6874,f6878,f6882,f6886,f6890,f6906,f6910,f6914,f6918,f6922,f6926,f6930,f6934,f6938,f6939]) ).
fof(f6939,plain,
spl0_156,
inference(avatar_split_clause,[],[f841,f1720]) ).
fof(f1720,plain,
( spl0_156
<=> c_lessequals(c_HOL_Oplus__class_Oplus(v_da____,c_RealVector_Onorm__class_Onorm(v_aa____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f841,axiom,
c_lessequals(c_HOL_Oplus__class_Oplus(v_da____,c_RealVector_Onorm__class_Onorm(v_aa____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f6938,plain,
spl0_599,
inference(avatar_split_clause,[],[f837,f6936]) ).
fof(f6936,plain,
( spl0_599
<=> ! [X4,X0,X6,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X6,X16,X0),X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X4,X16,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f837,axiom,
! [X0,X6,X16,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X6,X16,X0),X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X4,X16,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f6934,plain,
spl0_598,
inference(avatar_split_clause,[],[f836,f6932]) ).
fof(f6932,plain,
( spl0_598
<=> ! [X4,X0,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X6,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f836,axiom,
! [X3,X0,X6,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X0),X6,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X6,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f6930,plain,
spl0_597,
inference(avatar_split_clause,[],[f835,f6928]) ).
fof(f6928,plain,
( spl0_597
<=> ! [X4,X0,X6,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X6,X16,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X6,X0),X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f835,axiom,
! [X0,X6,X16,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X6,X16,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X6,X0),X16,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(f6926,plain,
spl0_596,
inference(avatar_split_clause,[],[f834,f6924]) ).
fof(f6924,plain,
( spl0_596
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f834,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X0),X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f6922,plain,
spl0_595,
inference(avatar_split_clause,[],[f833,f6920]) ).
fof(f6920,plain,
( spl0_595
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X5,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f833,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X5,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f6918,plain,
spl0_594,
inference(avatar_split_clause,[],[f831,f6916]) ).
fof(f6916,plain,
( spl0_594
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f831,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,X0),X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f6914,plain,
spl0_593,
inference(avatar_split_clause,[],[f830,f6912]) ).
fof(f6912,plain,
( spl0_593
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f830,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f6910,plain,
spl0_592,
inference(avatar_split_clause,[],[f798,f6908]) ).
fof(f6908,plain,
( spl0_592
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X4,X3,X0),X6,X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(X3,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f798,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X4,X3,X0),X6,X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(X3,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f6906,plain,
spl0_591,
inference(avatar_split_clause,[],[f797,f6904]) ).
fof(f6904,plain,
( spl0_591
<=> ! [X37,X0,X36,X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X39,X0),X37,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X37,X0),X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f797,axiom,
! [X39,X0,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X39,X0),X37,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X37,X0),X39,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f6890,plain,
spl0_590,
inference(avatar_split_clause,[],[f795,f6888]) ).
fof(f6888,plain,
( spl0_590
<=> ! [X38,X0,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X36,c_HOL_Otimes__class_Otimes(X37,X38,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X37,X0),X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f795,axiom,
! [X38,X0,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X36,c_HOL_Otimes__class_Otimes(X37,X38,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X36,X37,X0),X38,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(f6886,plain,
spl0_589,
inference(avatar_split_clause,[],[f794,f6884]) ).
fof(f6884,plain,
( spl0_589
<=> ! [X38,X0,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X36,c_HOL_Otimes__class_Otimes(X37,X38,X0),X0) = c_HOL_Otimes__class_Otimes(X37,c_HOL_Otimes__class_Otimes(X36,X38,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f794,axiom,
! [X38,X0,X36,X37] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X36,c_HOL_Otimes__class_Otimes(X37,X38,X0),X0) = c_HOL_Otimes__class_Otimes(X37,c_HOL_Otimes__class_Otimes(X36,X38,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f6882,plain,
spl0_588,
inference(avatar_split_clause,[],[f771,f6880]) ).
fof(f6880,plain,
( spl0_588
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| 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_RealVector_Onorm__class_Onorm(X2,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f771,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| 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_RealVector_Onorm__class_Onorm(X2,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__mult_0) ).
fof(f6878,plain,
spl0_587,
inference(avatar_split_clause,[],[f741,f6876]) ).
fof(f6876,plain,
( spl0_587
<=> ! [X13,X5,X12] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X5,tc_Complex_Ocomplex),X13,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X12,X5,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X12,X13),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f741,axiom,
! [X5,X12,X13] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X5,tc_Complex_Ocomplex),X13,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X12,X5,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X12,X13),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__bound__exists_1) ).
fof(f6874,plain,
spl0_586,
inference(avatar_split_clause,[],[f711,f6872]) ).
fof(f6872,plain,
( spl0_586
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f711,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
fof(f6870,plain,
spl0_585,
inference(avatar_split_clause,[],[f709,f6868]) ).
fof(f6868,plain,
( spl0_585
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f709,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
fof(f6865,plain,
spl0_584,
inference(avatar_split_clause,[],[f539,f6862]) ).
fof(f6862,plain,
( spl0_584
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f539,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__two__squares__add__zero__iff_2) ).
fof(f6860,plain,
spl0_583,
inference(avatar_split_clause,[],[f538,f6858]) ).
fof(f6858,plain,
( spl0_583
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f538,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X2
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__squares__cancel2_0) ).
fof(f6856,plain,
spl0_582,
inference(avatar_split_clause,[],[f537,f6854]) ).
fof(f6854,plain,
( spl0_582
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f537,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__squares__cancel_0) ).
fof(f6852,plain,
spl0_581,
inference(avatar_split_clause,[],[f478,f6850]) ).
fof(f6850,plain,
( spl0_581
<=> ! [X6,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X6,X0),X6,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f478,axiom,
! [X3,X0,X6] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X6,X0),X6,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
fof(f6775,plain,
spl0_580,
inference(avatar_split_clause,[],[f466,f6773]) ).
fof(f6773,plain,
( spl0_580
<=> ! [X4,X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f466,axiom,
! [X3,X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
fof(f6771,plain,
spl0_579,
inference(avatar_split_clause,[],[f404,f6769]) ).
fof(f6769,plain,
( spl0_579
<=> ! [X4,X0,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X6,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f404,axiom,
! [X3,X0,X6,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X6,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__add_0) ).
fof(f6767,plain,
spl0_578,
inference(avatar_split_clause,[],[f393,f6765]) ).
fof(f6765,plain,
( spl0_578
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f393,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
fof(f6763,plain,
spl0_577,
inference(avatar_split_clause,[],[f392,f6761]) ).
fof(f6761,plain,
( spl0_577
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f392,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X4,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
fof(f6759,plain,
spl0_576,
inference(avatar_split_clause,[],[f386,f6757]) ).
fof(f6757,plain,
( spl0_576
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X0),c_HOL_Oabs__class_Oabs(X3,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f386,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X0),c_HOL_Oabs__class_Oabs(X3,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult_0) ).
fof(f6755,plain,
spl0_575,
inference(avatar_split_clause,[],[f364,f6753]) ).
fof(f6753,plain,
( spl0_575
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Osgn__class_Osgn(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f364,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Osgn__class_Osgn(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__mult_0) ).
fof(f6751,plain,
spl0_574,
inference(avatar_split_clause,[],[f363,f6749]) ).
fof(f6749,plain,
( spl0_574
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X4,X0),c_HOL_Osgn__class_Osgn(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f363,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X4,X0),c_HOL_Osgn__class_Osgn(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__times_0) ).
fof(f6747,plain,
spl0_573,
inference(avatar_split_clause,[],[f273,f6745]) ).
fof(f6745,plain,
( spl0_573
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X3,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f273,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X3,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
fof(f6743,plain,
spl0_572,
inference(avatar_split_clause,[],[f182,f6741]) ).
fof(f6741,plain,
( spl0_572
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(X4,X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f182,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(X4,X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
fof(f6739,plain,
spl0_571,
inference(avatar_split_clause,[],[f152,f6737]) ).
fof(f6737,plain,
( spl0_571
<=> ! [X0,X5,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X5,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f152,axiom,
! [X2,X0,X1,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X5,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X5,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
fof(f6666,plain,
spl0_570,
inference(avatar_split_clause,[],[f143,f6664]) ).
fof(f6664,plain,
( spl0_570
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f143,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__if_1) ).
fof(f6662,plain,
spl0_569,
inference(avatar_split_clause,[],[f132,f6660]) ).
fof(f6660,plain,
( spl0_569
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f132,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
fof(f6658,plain,
spl0_568,
inference(avatar_split_clause,[],[f101,f6656]) ).
fof(f6656,plain,
( spl0_568
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X4,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f101,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X4,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__abs__inverse_0) ).
fof(f6654,plain,
spl0_567,
inference(avatar_split_clause,[],[f53,f6652]) ).
fof(f6652,plain,
( spl0_567
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f53,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
fof(f6449,plain,
( spl0_566
| ~ spl0_40
| ~ spl0_320
| ~ spl0_556 ),
inference(avatar_split_clause,[],[f5937,f5934,f2683,f1193,f6447]) ).
fof(f6447,plain,
( spl0_566
<=> ! [X5,X8] : c_lessequals(c_RealVector_Onorm__class_Onorm(X8,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X5,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X8,X5,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f1193,plain,
( spl0_40
<=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f2683,plain,
( spl0_320
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X4,X3,X0) = c_HOL_Oplus__class_Oplus(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f5934,plain,
( spl0_556
<=> ! [X5,X8] : c_lessequals(c_RealVector_Onorm__class_Onorm(X8,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X8,X5,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X5,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f5937,plain,
( ! [X8,X5] : c_lessequals(c_RealVector_Onorm__class_Onorm(X8,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(X5,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X8,X5,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_40
| ~ spl0_320
| ~ spl0_556 ),
inference(forward_demodulation,[],[f5935,f2920]) ).
fof(f2920,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal)
| ~ spl0_40
| ~ spl0_320 ),
inference(resolution,[],[f2684,f1195]) ).
fof(f1195,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f1193]) ).
fof(f2684,plain,
( ! [X3,X0,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X4,X3,X0) = c_HOL_Oplus__class_Oplus(X3,X4,X0) )
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f2683]) ).
fof(f5935,plain,
( ! [X8,X5] : c_lessequals(c_RealVector_Onorm__class_Onorm(X8,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X8,X5,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X5,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_556 ),
inference(avatar_component_clause,[],[f5934]) ).
fof(f5981,plain,
spl0_565,
inference(avatar_split_clause,[],[f808,f5979]) ).
fof(f5979,plain,
( spl0_565
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X4,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X6,X4,X0),c_HOL_Oplus__class_Oplus(X6,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f808,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X4,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X6,X4,X0),c_HOL_Oplus__class_Oplus(X6,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f5977,plain,
spl0_564,
inference(avatar_split_clause,[],[f807,f5975]) ).
fof(f5975,plain,
( spl0_564
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X4,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X6,X0),c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f807,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X4,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X6,X0),c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f5973,plain,
spl0_563,
inference(avatar_split_clause,[],[f806,f5971]) ).
fof(f5971,plain,
( spl0_563
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X4,X3,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X6,X4,X0),c_HOL_Oplus__class_Oplus(X6,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f806,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X4,X3,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X6,X4,X0),c_HOL_Oplus__class_Oplus(X6,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f5969,plain,
spl0_562,
inference(avatar_split_clause,[],[f805,f5967]) ).
fof(f5967,plain,
( spl0_562
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X4,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X6,X4,X0),c_HOL_Oplus__class_Oplus(X6,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f805,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X4,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X6,X4,X0),c_HOL_Oplus__class_Oplus(X6,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f5957,plain,
spl0_561,
inference(avatar_split_clause,[],[f804,f5955]) ).
fof(f5955,plain,
( spl0_561
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X4,X3,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X6,X0),c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f804,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X4,X3,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X6,X0),c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f5953,plain,
spl0_560,
inference(avatar_split_clause,[],[f803,f5951]) ).
fof(f5951,plain,
( spl0_560
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X4,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X6,X0),c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f803,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X4,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X6,X0),c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f5949,plain,
spl0_559,
inference(avatar_split_clause,[],[f781,f5947]) ).
fof(f5947,plain,
( spl0_559
<=> ! [X0,X5,X2,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X2 = X5
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f781,axiom,
! [X2,X0,X1,X5] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X2 = X5
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f5945,plain,
spl0_558,
inference(avatar_split_clause,[],[f770,f5943]) ).
fof(f5943,plain,
( spl0_558
<=> ! [X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X14,X14,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f770,axiom,
! [X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X14,X14,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(f5941,plain,
spl0_557,
inference(avatar_split_clause,[],[f631,f5939]) ).
fof(f5939,plain,
( spl0_557
<=> ! [X2,X0,X1] :
( ~ 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(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f631,axiom,
! [X2,X0,X1] :
( ~ 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(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
fof(f5936,plain,
spl0_556,
inference(avatar_split_clause,[],[f618,f5934]) ).
fof(f618,axiom,
! [X8,X5] : c_lessequals(c_RealVector_Onorm__class_Onorm(X8,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X8,X5,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X5,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__mod__triangle__sub_0) ).
fof(f5932,plain,
spl0_555,
inference(avatar_split_clause,[],[f583,f5930]) ).
fof(f5930,plain,
( spl0_555
<=> ! [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_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f583,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_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__1__iff_1) ).
fof(f5928,plain,
spl0_554,
inference(avatar_split_clause,[],[f578,f5926]) ).
fof(f5926,plain,
( spl0_554
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f578,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
fof(f5924,plain,
spl0_553,
inference(avatar_split_clause,[],[f566,f5922]) ).
fof(f5922,plain,
( spl0_553
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f566,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).
fof(f5920,plain,
spl0_552,
inference(avatar_split_clause,[],[f565,f5918]) ).
fof(f5918,plain,
( spl0_552
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f565,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).
fof(f5908,plain,
spl0_551,
inference(avatar_split_clause,[],[f514,f5906]) ).
fof(f5906,plain,
( spl0_551
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f514,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__inverse__iff_1) ).
fof(f5904,plain,
spl0_550,
inference(avatar_split_clause,[],[f513,f5902]) ).
fof(f5902,plain,
( spl0_550
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f513,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__1__iff_2) ).
fof(f5900,plain,
spl0_549,
inference(avatar_split_clause,[],[f505,f5898]) ).
fof(f5898,plain,
( spl0_549
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oinverse__class_Odivide(X4,X3,X0) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f505,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oinverse__class_Odivide(X4,X3,X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
fof(f5896,plain,
spl0_548,
inference(avatar_split_clause,[],[f440,f5894]) ).
fof(f5894,plain,
( spl0_548
<=> ! [X4,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X3,X4,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f440,axiom,
! [X3,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(X3,X4,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X3,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__mod__triangle__ineq2_0) ).
fof(f5892,plain,
spl0_547,
inference(avatar_split_clause,[],[f430,f5890]) ).
fof(f5890,plain,
( spl0_547
<=> ! [X6,X4,X3] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Otimes__class_Otimes(X6,X4,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X6,X3,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f430,axiom,
! [X3,X6,X4] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Otimes__class_Otimes(X6,X4,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X6,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__left__cancel_0) ).
fof(f5888,plain,
spl0_546,
inference(avatar_split_clause,[],[f429,f5886]) ).
fof(f5886,plain,
( spl0_546
<=> ! [X6,X4,X3] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Otimes__class_Otimes(X4,X6,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X3,X6,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f429,axiom,
! [X3,X6,X4] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X6
| c_HOL_Otimes__class_Otimes(X4,X6,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X3,X6,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__right__cancel_0) ).
fof(f5884,plain,
spl0_545,
inference(avatar_split_clause,[],[f406,f5882]) ).
fof(f5882,plain,
( spl0_545
<=> ! [X0,X5,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = X1
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X5,X0),X0) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f406,axiom,
! [X2,X0,X1,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X5,X0) = X1
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X5,X0),X0) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
fof(f5880,plain,
spl0_544,
inference(avatar_split_clause,[],[f399,f5878]) ).
fof(f5878,plain,
( spl0_544
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X4,X0),c_HOL_Oplus__class_Oplus(X6,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f399,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X4,X0),c_HOL_Oplus__class_Oplus(X6,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f5876,plain,
spl0_543,
inference(avatar_split_clause,[],[f398,f5874]) ).
fof(f5874,plain,
( spl0_543
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X4,X0),c_HOL_Oplus__class_Oplus(X6,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f398,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X4,X0),c_HOL_Oplus__class_Oplus(X6,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f5872,plain,
spl0_542,
inference(avatar_split_clause,[],[f397,f5870]) ).
fof(f5870,plain,
( spl0_542
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X4,X0),c_HOL_Oplus__class_Oplus(X6,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f397,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X4,X0),c_HOL_Oplus__class_Oplus(X6,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f5868,plain,
spl0_541,
inference(avatar_split_clause,[],[f396,f5866]) ).
fof(f5866,plain,
( spl0_541
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X6,X0),c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f396,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X6,X0),c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f5864,plain,
spl0_540,
inference(avatar_split_clause,[],[f395,f5862]) ).
fof(f5862,plain,
( spl0_540
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X6,X0),c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f395,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X6,X0),c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f5860,plain,
spl0_539,
inference(avatar_split_clause,[],[f394,f5858]) ).
fof(f5858,plain,
( spl0_539
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X6,X0),c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f394,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X6,X0),c_HOL_Oplus__class_Oplus(X3,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f5856,plain,
spl0_538,
inference(avatar_split_clause,[],[f369,f5854]) ).
fof(f5854,plain,
( spl0_538
<=> ! [X4,X0,X6,X3] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X6,X4,X0),c_HOL_Otimes__class_Otimes(X6,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f369,axiom,
! [X3,X0,X6,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X6,X4,X0),c_HOL_Otimes__class_Otimes(X6,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
fof(f5852,plain,
spl0_537,
inference(avatar_split_clause,[],[f368,f5850]) ).
fof(f5850,plain,
( spl0_537
<=> ! [X4,X0,X6,X3] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X6,X0),c_HOL_Otimes__class_Otimes(X3,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f368,axiom,
! [X3,X0,X6,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X6,X0),c_HOL_Otimes__class_Otimes(X3,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
fof(f5848,plain,
spl0_536,
inference(avatar_split_clause,[],[f321,f5846]) ).
fof(f5846,plain,
( spl0_536
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f321,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).
fof(f5844,plain,
spl0_535,
inference(avatar_split_clause,[],[f320,f5842]) ).
fof(f5842,plain,
( spl0_535
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f320,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).
fof(f5840,plain,
spl0_534,
inference(avatar_split_clause,[],[f304,f5838]) ).
fof(f5838,plain,
( spl0_534
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f304,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_1) ).
fof(f5836,plain,
spl0_533,
inference(avatar_split_clause,[],[f303,f5834]) ).
fof(f5834,plain,
( spl0_533
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f303,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).
fof(f5832,plain,
spl0_532,
inference(avatar_split_clause,[],[f284,f5830]) ).
fof(f5830,plain,
( spl0_532
<=> ! [X0,X1] :
( ~ 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),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f284,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_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).
fof(f5828,plain,
spl0_531,
inference(avatar_split_clause,[],[f245,f5826]) ).
fof(f5826,plain,
( spl0_531
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f245,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).
fof(f5824,plain,
spl0_530,
inference(avatar_split_clause,[],[f201,f5822]) ).
fof(f5822,plain,
( spl0_530
<=> ! [X4,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),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f201,axiom,
! [X0,X4] :
( ~ 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),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).
fof(f5820,plain,
spl0_529,
inference(avatar_split_clause,[],[f186,f5818]) ).
fof(f5818,plain,
( spl0_529
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f186,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_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__inverse__iff_0) ).
fof(f5816,plain,
spl0_528,
inference(avatar_split_clause,[],[f155,f5814]) ).
fof(f5814,plain,
( spl0_528
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = c_HOL_Oabs__class_Oabs(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f155,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = c_HOL_Oabs__class_Oabs(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).
fof(f5812,plain,
spl0_527,
inference(avatar_split_clause,[],[f72,f5810]) ).
fof(f5810,plain,
( spl0_527
<=> ! [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_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f72,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_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).
fof(f5808,plain,
spl0_526,
inference(avatar_split_clause,[],[f35,f5806]) ).
fof(f5806,plain,
( spl0_526
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f35,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_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_1) ).
fof(f5804,plain,
spl0_525,
inference(avatar_split_clause,[],[f23,f5802]) ).
fof(f5802,plain,
( spl0_525
<=> ! [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_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f23,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_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).
fof(f5456,plain,
spl0_524,
inference(avatar_split_clause,[],[f793,f5454]) ).
fof(f5454,plain,
( spl0_524
<=> ! [X34,X35,X33] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X34,tc_RealDef_Oreal),X35,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X34,X35,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f793,axiom,
! [X34,X35,X33] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X33,X34,tc_RealDef_Oreal),X35,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X33,c_HOL_Otimes__class_Otimes(X34,X35,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__assoc_0) ).
fof(f5452,plain,
spl0_523,
inference(avatar_split_clause,[],[f688,f5450]) ).
fof(f5450,plain,
( spl0_523
<=> ! [X4,X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X4,X3,X0),X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f688,axiom,
! [X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X4,X3,X0),X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__minus__commute_0) ).
fof(f5448,plain,
spl0_522,
inference(avatar_split_clause,[],[f687,f5446]) ).
fof(f5446,plain,
( spl0_522
<=> ! [X4,X0,X12] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X4,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f687,axiom,
! [X0,X4,X12] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X4,X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).
fof(f5444,plain,
spl0_521,
inference(avatar_split_clause,[],[f655,f5442]) ).
fof(f5442,plain,
( spl0_521
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f655,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f5400,plain,
spl0_520,
inference(avatar_split_clause,[],[f654,f5398]) ).
fof(f5398,plain,
( spl0_520
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f654,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f5396,plain,
spl0_519,
inference(avatar_split_clause,[],[f653,f5394]) ).
fof(f5394,plain,
( spl0_519
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X4,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f653,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X4,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f5392,plain,
spl0_518,
inference(avatar_split_clause,[],[f652,f5390]) ).
fof(f5390,plain,
( spl0_518
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X4,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f652,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X4,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f5388,plain,
spl0_517,
inference(avatar_split_clause,[],[f589,f5386]) ).
fof(f5386,plain,
( spl0_517
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f589,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__inverse_0) ).
fof(f5384,plain,
spl0_516,
inference(avatar_split_clause,[],[f588,f5382]) ).
fof(f5382,plain,
( spl0_516
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f588,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X4,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__inverse_0) ).
fof(f5380,plain,
spl0_515,
inference(avatar_split_clause,[],[f587,f5378]) ).
fof(f5378,plain,
( spl0_515
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f587,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse_0) ).
fof(f5376,plain,
spl0_514,
inference(avatar_split_clause,[],[f497,f5374]) ).
fof(f5374,plain,
( spl0_514
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X4,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f497,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X4,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(f5372,plain,
spl0_513,
inference(avatar_split_clause,[],[f496,f5370]) ).
fof(f5370,plain,
( spl0_513
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X4,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f496,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X4,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(f5368,plain,
spl0_512,
inference(avatar_split_clause,[],[f494,f5366]) ).
fof(f5366,plain,
( spl0_512
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f494,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(f5364,plain,
spl0_511,
inference(avatar_split_clause,[],[f493,f5362]) ).
fof(f5362,plain,
( spl0_511
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f493,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(f5352,plain,
spl0_510,
inference(avatar_split_clause,[],[f492,f5350]) ).
fof(f5350,plain,
( spl0_510
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f492,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
fof(f5348,plain,
spl0_509,
inference(avatar_split_clause,[],[f491,f5346]) ).
fof(f5346,plain,
( spl0_509
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f491,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
fof(f5344,plain,
spl0_508,
inference(avatar_split_clause,[],[f476,f5342]) ).
fof(f5342,plain,
( spl0_508
<=> ! [X6,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f476,axiom,
! [X0,X6] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0),X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
fof(f5340,plain,
spl0_507,
inference(avatar_split_clause,[],[f463,f5338]) ).
fof(f5338,plain,
( spl0_507
<=> ! [X6,X4,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X6,X0),X6,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f463,axiom,
! [X0,X6,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X6
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X4,X6,X0),X6,X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
fof(f5336,plain,
spl0_506,
inference(avatar_split_clause,[],[f459,f5334]) ).
fof(f5334,plain,
( spl0_506
<=> ! [X4,X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X4,X3,X0),X3,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f459,axiom,
! [X3,X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X4,X3,X0),X3,X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
fof(f5332,plain,
spl0_505,
inference(avatar_split_clause,[],[f458,f5330]) ).
fof(f5330,plain,
( spl0_505
<=> ! [X4,X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X4,X0),X3,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f458,axiom,
! [X3,X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X4,X0),X3,X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
fof(f5328,plain,
spl0_504,
inference(avatar_split_clause,[],[f384,f5326]) ).
fof(f5326,plain,
( spl0_504
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f384,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
fof(f5324,plain,
spl0_503,
inference(avatar_split_clause,[],[f383,f5322]) ).
fof(f5322,plain,
( spl0_503
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f383,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
fof(f5320,plain,
spl0_502,
inference(avatar_split_clause,[],[f377,f5318]) ).
fof(f5318,plain,
( spl0_502
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(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_502])]) ).
fof(f377,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(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/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
fof(f5316,plain,
spl0_501,
inference(avatar_split_clause,[],[f375,f5314]) ).
fof(f5314,plain,
( spl0_501
<=> ! [X0,X1,X19] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X19,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X19,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f375,axiom,
! [X0,X1,X19] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X19,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X19,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
fof(f5305,plain,
spl0_500,
inference(avatar_split_clause,[],[f374,f5303]) ).
fof(f5303,plain,
( spl0_500
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Otimes__class_Otimes(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f374,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Otimes__class_Otimes(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
fof(f5301,plain,
spl0_499,
inference(avatar_split_clause,[],[f373,f5299]) ).
fof(f5299,plain,
( spl0_499
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X4,X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f373,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X4,X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
fof(f5297,plain,
spl0_498,
inference(avatar_split_clause,[],[f367,f5295]) ).
fof(f5295,plain,
( spl0_498
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X0),c_HOL_Oabs__class_Oabs(X4,X0),X0) = c_HOL_Otimes__class_Otimes(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f367,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X4,X0),c_HOL_Oabs__class_Oabs(X4,X0),X0) = c_HOL_Otimes__class_Otimes(X4,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
fof(f5293,plain,
spl0_497,
inference(avatar_split_clause,[],[f366,f5291]) ).
fof(f5291,plain,
( spl0_497
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f366,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
fof(f5289,plain,
spl0_496,
inference(avatar_split_clause,[],[f302,f5287]) ).
fof(f5287,plain,
( spl0_496
<=> ! [X2,X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f302,axiom,
! [X2,X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__mult__self__sum__ge__zero_0) ).
fof(f5285,plain,
spl0_495,
inference(avatar_split_clause,[],[f262,f5283]) ).
fof(f5283,plain,
( spl0_495
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Osgn__class_Osgn(X4,X0) != c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f262,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Osgn__class_Osgn(X4,X0) != c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__1__neg_0) ).
fof(f5281,plain,
spl0_494,
inference(avatar_split_clause,[],[f261,f5279]) ).
fof(f5279,plain,
( spl0_494
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Osgn__class_Osgn(X4,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f261,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Osgn__class_Osgn(X4,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__neg_0) ).
fof(f5277,plain,
spl0_493,
inference(avatar_split_clause,[],[f212,f5275]) ).
fof(f5275,plain,
( spl0_493
<=> ! [X4,X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X3,X4,X0),X4,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f212,axiom,
! [X3,X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X3,X4,X0),X4,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).
fof(f5273,plain,
spl0_492,
inference(avatar_split_clause,[],[f211,f5271]) ).
fof(f5271,plain,
( spl0_492
<=> ! [X4,X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Odiv(X3,X4,X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f211,axiom,
! [X3,X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Odiv(X3,X4,X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).
fof(f5269,plain,
spl0_491,
inference(avatar_split_clause,[],[f196,f5267]) ).
fof(f5267,plain,
( spl0_491
<=> ! [X4,X0] :
( ~ 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(X4,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f196,axiom,
! [X0,X4] :
( ~ 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(X4,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__inverse_0) ).
fof(f5225,plain,
spl0_490,
inference(avatar_split_clause,[],[f183,f5223]) ).
fof(f5223,plain,
( spl0_490
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f183,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
fof(f5221,plain,
spl0_489,
inference(avatar_split_clause,[],[f54,f5219]) ).
fof(f5219,plain,
( spl0_489
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f54,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X4,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
fof(f5217,plain,
spl0_488,
inference(avatar_split_clause,[],[f52,f5215]) ).
fof(f5215,plain,
( spl0_488
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X3,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f52,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X3,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
fof(f5213,plain,
spl0_487,
inference(avatar_split_clause,[],[f48,f5211]) ).
fof(f5211,plain,
( spl0_487
<=> ! [X4,X0] :
( ~ 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(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f48,axiom,
! [X0,X4] :
( ~ 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(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
fof(f5209,plain,
spl0_486,
inference(avatar_split_clause,[],[f12,f5207]) ).
fof(f5207,plain,
( spl0_486
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X4,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f12,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X4,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
fof(f5020,plain,
( spl0_485
| ~ spl0_88
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2113,f2001,f1433,f5018]) ).
fof(f5018,plain,
( spl0_485
<=> ! [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_485])]) ).
fof(f1433,plain,
( spl0_88
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f2001,plain,
( spl0_222
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f2113,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_88
| ~ spl0_222 ),
inference(resolution,[],[f2002,f1435]) ).
fof(f1435,plain,
( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f1433]) ).
fof(f2002,plain,
( ! [X0,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X4,X0) = X4 )
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f2001]) ).
fof(f4932,plain,
( spl0_484
| ~ spl0_88
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2110,f1997,f1433,f4930]) ).
fof(f4930,plain,
( spl0_484
<=> ! [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_484])]) ).
fof(f1997,plain,
( spl0_221
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f2110,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_88
| ~ spl0_221 ),
inference(resolution,[],[f1998,f1435]) ).
fof(f1998,plain,
( ! [X0,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(X0),X0) = X4 )
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f1997]) ).
fof(f4800,plain,
( spl0_483
| ~ spl0_49
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2109,f1997,f1238,f4798]) ).
fof(f4798,plain,
( spl0_483
<=> ! [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_483])]) ).
fof(f1238,plain,
( spl0_49
<=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f2109,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_49
| ~ spl0_221 ),
inference(resolution,[],[f1998,f1240]) ).
fof(f1240,plain,
( class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f1238]) ).
fof(f4534,plain,
( spl0_482
| ~ spl0_69
| ~ spl0_220 ),
inference(avatar_split_clause,[],[f2108,f1993,f1338,f4531]) ).
fof(f4531,plain,
( spl0_482
<=> 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_482])]) ).
fof(f1338,plain,
( spl0_69
<=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1993,plain,
( spl0_220
<=> ! [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_220])]) ).
fof(f2108,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_69
| ~ spl0_220 ),
inference(resolution,[],[f1994,f1340]) ).
fof(f1340,plain,
( class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f1338]) ).
fof(f1994,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_220 ),
inference(avatar_component_clause,[],[f1993]) ).
fof(f4384,plain,
( spl0_481
| ~ spl0_22
| ~ spl0_220 ),
inference(avatar_split_clause,[],[f2107,f1993,f1103,f4381]) ).
fof(f4381,plain,
( spl0_481
<=> 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_481])]) ).
fof(f1103,plain,
( spl0_22
<=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f2107,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_22
| ~ spl0_220 ),
inference(resolution,[],[f1994,f1105]) ).
fof(f1105,plain,
( class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1103]) ).
fof(f4296,plain,
spl0_480,
inference(avatar_split_clause,[],[f809,f4294]) ).
fof(f4294,plain,
( spl0_480
<=> ! [X2,X5,X1] :
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X5,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f809,axiom,
! [X2,X1,X5] :
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(X5,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X5,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__left__mono_0) ).
fof(f4292,plain,
spl0_479,
inference(avatar_split_clause,[],[f801,f4290]) ).
fof(f4290,plain,
( spl0_479
<=> ! [X4,X40,X0,X12,X3] :
( ~ class_HOL_Ozero(X0)
| X12 = X40
| c_Polynomial_OpCons(X4,X12,X0) != c_Polynomial_OpCons(X3,X40,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f801,axiom,
! [X40,X3,X0,X4,X12] :
( ~ class_HOL_Ozero(X0)
| X12 = X40
| c_Polynomial_OpCons(X4,X12,X0) != c_Polynomial_OpCons(X3,X40,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).
fof(f4288,plain,
spl0_478,
inference(avatar_split_clause,[],[f800,f4286]) ).
fof(f4286,plain,
( spl0_478
<=> ! [X4,X40,X0,X12,X3] :
( ~ class_HOL_Ozero(X0)
| X3 = X4
| c_Polynomial_OpCons(X4,X12,X0) != c_Polynomial_OpCons(X3,X40,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f800,axiom,
! [X40,X3,X0,X4,X12] :
( ~ class_HOL_Ozero(X0)
| X3 = X4
| c_Polynomial_OpCons(X4,X12,X0) != c_Polynomial_OpCons(X3,X40,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).
fof(f4284,plain,
( spl0_477
| ~ spl0_91
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2102,f1985,f1448,f4282]) ).
fof(f4282,plain,
( spl0_477
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f1448,plain,
( spl0_91
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1985,plain,
( spl0_218
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2102,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex)
| ~ spl0_91
| ~ spl0_218 ),
inference(resolution,[],[f1986,f1450]) ).
fof(f1450,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f1448]) ).
fof(f1986,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f1985]) ).
fof(f4280,plain,
spl0_476,
inference(avatar_split_clause,[],[f780,f4278]) ).
fof(f4278,plain,
( spl0_476
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X3 = X6
| c_HOL_Oplus__class_Oplus(X4,X3,X0) != c_HOL_Oplus__class_Oplus(X4,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f780,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X3 = X6
| c_HOL_Oplus__class_Oplus(X4,X3,X0) != c_HOL_Oplus__class_Oplus(X4,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f4276,plain,
spl0_475,
inference(avatar_split_clause,[],[f779,f4274]) ).
fof(f4274,plain,
( spl0_475
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X3 = X6
| c_HOL_Oplus__class_Oplus(X4,X3,X0) != c_HOL_Oplus__class_Oplus(X4,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f779,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X3 = X6
| c_HOL_Oplus__class_Oplus(X4,X3,X0) != c_HOL_Oplus__class_Oplus(X4,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f4272,plain,
spl0_474,
inference(avatar_split_clause,[],[f778,f4270]) ).
fof(f4270,plain,
( spl0_474
<=> ! [X4,X0,X6,X3] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X3 = X6
| c_HOL_Oplus__class_Oplus(X6,X4,X0) != c_HOL_Oplus__class_Oplus(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f778,axiom,
! [X3,X0,X6,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X3 = X6
| c_HOL_Oplus__class_Oplus(X6,X4,X0) != c_HOL_Oplus__class_Oplus(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f4268,plain,
spl0_473,
inference(avatar_split_clause,[],[f759,f4266]) ).
fof(f4266,plain,
( spl0_473
<=> ! [X0,X5,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X5,X0)
| c_lessequals(X1,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f759,axiom,
! [X2,X0,X1,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X5,X0)
| c_lessequals(X1,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f4264,plain,
spl0_472,
inference(avatar_split_clause,[],[f758,f4262]) ).
fof(f4262,plain,
( spl0_472
<=> ! [X0,X5,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,X2,X0)
| c_lessequals(X5,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f758,axiom,
! [X2,X0,X1,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X5,X2,X0)
| c_lessequals(X5,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f4260,plain,
spl0_471,
inference(avatar_split_clause,[],[f740,f4258]) ).
fof(f4258,plain,
( spl0_471
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X4,X3,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f740,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X4,X3,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
fof(f4256,plain,
spl0_470,
inference(avatar_split_clause,[],[f739,f4254]) ).
fof(f4254,plain,
( spl0_470
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X4,X3,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f739,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X4,X3,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
fof(f4252,plain,
spl0_469,
inference(avatar_split_clause,[],[f738,f4250]) ).
fof(f4250,plain,
( spl0_469
<=> ! [X4,X0,X12] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X4,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f738,axiom,
! [X0,X4,X12] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X4,X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).
fof(f4248,plain,
spl0_468,
inference(avatar_split_clause,[],[f729,f4246]) ).
fof(f4246,plain,
( spl0_468
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X9 = X10
| c_HOL_Ominus__class_Ominus(X9,X10,X0) != c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f729,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X9 = X10
| c_HOL_Ominus__class_Ominus(X9,X10,X0) != c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
fof(f4244,plain,
spl0_467,
inference(avatar_split_clause,[],[f725,f4242]) ).
fof(f4242,plain,
( spl0_467
<=> ! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f725,axiom,
! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f4240,plain,
( spl0_466
| ~ spl0_52
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2101,f1985,f1253,f4238]) ).
fof(f4238,plain,
( spl0_466
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f1253,plain,
( spl0_52
<=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f2101,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,X0,tc_RealDef_Oreal)
| ~ spl0_52
| ~ spl0_218 ),
inference(resolution,[],[f1986,f1255]) ).
fof(f1255,plain,
( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1253]) ).
fof(f4236,plain,
spl0_465,
inference(avatar_split_clause,[],[f703,f4234]) ).
fof(f4234,plain,
( spl0_465
<=> ! [X4,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oplus__class_Oplus(X1,X4,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f703,axiom,
! [X0,X1,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oplus__class_Oplus(X1,X4,X0) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f4232,plain,
spl0_464,
inference(avatar_split_clause,[],[f612,f4230]) ).
fof(f4230,plain,
( spl0_464
<=> ! [X2,X1] : c_lessequals(X1,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f612,axiom,
! [X2,X1] : c_lessequals(X1,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__real__sqrt__sumsq_0) ).
fof(f4228,plain,
spl0_463,
inference(avatar_split_clause,[],[f611,f4226]) ).
fof(f4226,plain,
( spl0_463
<=> ! [X2,X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f611,axiom,
! [X2,X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__self__sum__ge__zero_0) ).
fof(f4224,plain,
spl0_462,
inference(avatar_split_clause,[],[f607,f4222]) ).
fof(f4222,plain,
( spl0_462
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f607,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__sgn_1) ).
fof(f4220,plain,
spl0_461,
inference(avatar_split_clause,[],[f519,f4218]) ).
fof(f4218,plain,
( spl0_461
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(X4,X0) = X3
| c_HOL_Oone__class_Oone(X0) != c_HOL_Otimes__class_Otimes(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f519,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(X4,X0) = X3
| c_HOL_Oone__class_Oone(X0) != c_HOL_Otimes__class_Otimes(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
fof(f4216,plain,
spl0_460,
inference(avatar_split_clause,[],[f517,f4214]) ).
fof(f4214,plain,
( spl0_460
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f517,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
fof(f4212,plain,
spl0_459,
inference(avatar_split_clause,[],[f516,f4210]) ).
fof(f4210,plain,
( spl0_459
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f516,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
fof(f4208,plain,
spl0_458,
inference(avatar_split_clause,[],[f499,f4206]) ).
fof(f4206,plain,
( spl0_458
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X3,X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f499,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X3,X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
fof(f4204,plain,
spl0_457,
inference(avatar_split_clause,[],[f498,f4202]) ).
fof(f4202,plain,
( spl0_457
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f498,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
fof(f4200,plain,
spl0_456,
inference(avatar_split_clause,[],[f465,f4198]) ).
fof(f4198,plain,
( spl0_456
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f465,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
fof(f4196,plain,
( spl0_455
| ~ spl0_91
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2099,f1981,f1448,f4194]) ).
fof(f4194,plain,
( spl0_455
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f1981,plain,
( spl0_217
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f2099,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_91
| ~ spl0_217 ),
inference(resolution,[],[f1982,f1450]) ).
fof(f1982,plain,
( ! [X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 )
| ~ spl0_217 ),
inference(avatar_component_clause,[],[f1981]) ).
fof(f4192,plain,
spl0_454,
inference(avatar_split_clause,[],[f464,f4190]) ).
fof(f4190,plain,
( spl0_454
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f464,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
fof(f4188,plain,
spl0_453,
inference(avatar_split_clause,[],[f417,f4186]) ).
fof(f4186,plain,
( spl0_453
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = X1
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Oinverse(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f417,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = X1
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Oinverse(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
fof(f4184,plain,
spl0_452,
inference(avatar_split_clause,[],[f362,f4182]) ).
fof(f4182,plain,
( spl0_452
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f362,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
fof(f4180,plain,
spl0_451,
inference(avatar_split_clause,[],[f360,f4178]) ).
fof(f4178,plain,
( spl0_451
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f360,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
fof(f4176,plain,
spl0_450,
inference(avatar_split_clause,[],[f349,f4174]) ).
fof(f4174,plain,
( spl0_450
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X4,X3,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f349,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X4,X3,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
fof(f4172,plain,
spl0_449,
inference(avatar_split_clause,[],[f348,f4170]) ).
fof(f4170,plain,
( spl0_449
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X4,X3,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f348,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X4,X3,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
fof(f4168,plain,
spl0_448,
inference(avatar_split_clause,[],[f319,f4166]) ).
fof(f4166,plain,
( spl0_448
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f319,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
fof(f4164,plain,
spl0_447,
inference(avatar_split_clause,[],[f318,f4162]) ).
fof(f4162,plain,
( spl0_447
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f318,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
fof(f4160,plain,
spl0_446,
inference(avatar_split_clause,[],[f314,f4158]) ).
fof(f4158,plain,
( spl0_446
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f314,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
fof(f4156,plain,
spl0_445,
inference(avatar_split_clause,[],[f313,f4154]) ).
fof(f4154,plain,
( spl0_445
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f313,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
fof(f4152,plain,
( spl0_444
| ~ spl0_52
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2098,f1981,f1253,f4150]) ).
fof(f4150,plain,
( spl0_444
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f2098,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_52
| ~ spl0_217 ),
inference(resolution,[],[f1982,f1255]) ).
fof(f4148,plain,
spl0_443,
inference(avatar_split_clause,[],[f289,f4146]) ).
fof(f4146,plain,
( spl0_443
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f289,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
fof(f4144,plain,
spl0_442,
inference(avatar_split_clause,[],[f288,f4142]) ).
fof(f4142,plain,
( spl0_442
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f288,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
fof(f4140,plain,
spl0_441,
inference(avatar_split_clause,[],[f271,f4138]) ).
fof(f4138,plain,
( spl0_441
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X4,X0) = X4
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f271,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X4,X0) = X4
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
fof(f4136,plain,
spl0_440,
inference(avatar_split_clause,[],[f247,f4134]) ).
fof(f4134,plain,
( spl0_440
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f247,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_negative__imp__inverse__negative_0) ).
fof(f4132,plain,
spl0_439,
inference(avatar_split_clause,[],[f238,f4130]) ).
fof(f4130,plain,
( spl0_439
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f238,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f4128,plain,
spl0_438,
inference(avatar_split_clause,[],[f235,f4126]) ).
fof(f4126,plain,
( spl0_438
<=> ! [X0,X5,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X5,X0)
| c_HOL_Oord__class_Oless(X1,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f235,axiom,
! [X2,X0,X1,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X5,X0)
| c_HOL_Oord__class_Oless(X1,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f4124,plain,
spl0_437,
inference(avatar_split_clause,[],[f234,f4122]) ).
fof(f4122,plain,
( spl0_437
<=> ! [X0,X5,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X5,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f234,axiom,
! [X2,X0,X1,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X5,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f4120,plain,
spl0_436,
inference(avatar_split_clause,[],[f233,f4118]) ).
fof(f4118,plain,
( spl0_436
<=> ! [X0,X5,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X5,X2,X0)
| c_HOL_Oord__class_Oless(X5,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f233,axiom,
! [X2,X0,X1,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X5,X2,X0)
| c_HOL_Oord__class_Oless(X5,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f4116,plain,
spl0_435,
inference(avatar_split_clause,[],[f232,f4114]) ).
fof(f4114,plain,
( spl0_435
<=> ! [X0,X5,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X5,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(X5,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f232,axiom,
! [X2,X0,X1,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X5,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(X5,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f4112,plain,
spl0_434,
inference(avatar_split_clause,[],[f231,f4110]) ).
fof(f4110,plain,
( spl0_434
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f231,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
fof(f4101,plain,
spl0_433,
inference(avatar_split_clause,[],[f228,f4099]) ).
fof(f4099,plain,
( spl0_433
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f228,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
fof(f4097,plain,
spl0_432,
inference(avatar_split_clause,[],[f213,f4095]) ).
fof(f4095,plain,
( spl0_432
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = c_HOL_Oabs__class_Oabs(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f213,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = c_HOL_Oabs__class_Oabs(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).
fof(f4093,plain,
spl0_431,
inference(avatar_split_clause,[],[f199,f4091]) ).
fof(f4091,plain,
( spl0_431
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f199,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).
fof(f4089,plain,
spl0_430,
inference(avatar_split_clause,[],[f179,f4087]) ).
fof(f4087,plain,
( spl0_430
<=> ! [X0,X5,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X5,X0)
| c_HOL_Oord__class_Oless(X1,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f179,axiom,
! [X2,X0,X1,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X5,X0)
| c_HOL_Oord__class_Oless(X1,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f4085,plain,
spl0_429,
inference(avatar_split_clause,[],[f178,f4083]) ).
fof(f4083,plain,
( spl0_429
<=> ! [X0,X5,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X5,X2,X0)
| c_HOL_Oord__class_Oless(X5,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f178,axiom,
! [X2,X0,X1,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X5,X2,X0)
| c_HOL_Oord__class_Oless(X5,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f4081,plain,
spl0_428,
inference(avatar_split_clause,[],[f173,f4079]) ).
fof(f4079,plain,
( spl0_428
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f173,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
fof(f4077,plain,
spl0_427,
inference(avatar_split_clause,[],[f172,f4075]) ).
fof(f4075,plain,
( spl0_427
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f172,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
fof(f4073,plain,
spl0_426,
inference(avatar_split_clause,[],[f154,f4071]) ).
fof(f4071,plain,
( spl0_426
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = c_HOL_Oabs__class_Oabs(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f154,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = c_HOL_Oabs__class_Oabs(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_0) ).
fof(f4069,plain,
spl0_425,
inference(avatar_split_clause,[],[f153,f4067]) ).
fof(f4067,plain,
( spl0_425
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = c_HOL_Oabs__class_Oabs(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f153,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = c_HOL_Oabs__class_Oabs(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).
fof(f4065,plain,
spl0_424,
inference(avatar_split_clause,[],[f151,f4063]) ).
fof(f4063,plain,
( spl0_424
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Osgn__class_Osgn(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f151,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Osgn__class_Osgn(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_0) ).
fof(f4061,plain,
( spl0_423
| ~ spl0_173
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f3737,f3496,f1792,f4058]) ).
fof(f4058,plain,
( spl0_423
<=> 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_423])]) ).
fof(f1792,plain,
( spl0_173
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f3496,plain,
( spl0_403
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f3737,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_173
| ~ spl0_403 ),
inference(resolution,[],[f3498,f1793]) ).
fof(f1793,plain,
( ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1792]) ).
fof(f3498,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_403 ),
inference(avatar_component_clause,[],[f3496]) ).
fof(f4056,plain,
spl0_422,
inference(avatar_split_clause,[],[f150,f4054]) ).
fof(f4054,plain,
( spl0_422
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Osgn__class_Osgn(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f150,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Osgn__class_Osgn(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_1) ).
fof(f4052,plain,
spl0_421,
inference(avatar_split_clause,[],[f144,f4050]) ).
fof(f4050,plain,
( spl0_421
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f144,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
fof(f4048,plain,
spl0_420,
inference(avatar_split_clause,[],[f82,f4046]) ).
fof(f4046,plain,
( spl0_420
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f82,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__less_1) ).
fof(f4044,plain,
spl0_419,
inference(avatar_split_clause,[],[f81,f4042]) ).
fof(f4042,plain,
( spl0_419
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f81,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__less_0) ).
fof(f4040,plain,
spl0_418,
inference(avatar_split_clause,[],[f42,f4038]) ).
fof(f4038,plain,
( spl0_418
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| X3 = X4
| c_HOL_Oinverse__class_Oinverse(X4,X0) != c_HOL_Oinverse__class_Oinverse(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f42,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| X3 = X4
| c_HOL_Oinverse__class_Oinverse(X4,X0) != c_HOL_Oinverse__class_Oinverse(X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
fof(f4036,plain,
spl0_417,
inference(avatar_split_clause,[],[f39,f4034]) ).
fof(f4034,plain,
( spl0_417
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f39,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
fof(f4032,plain,
spl0_416,
inference(avatar_split_clause,[],[f38,f4030]) ).
fof(f4030,plain,
( spl0_416
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f38,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
fof(f4028,plain,
spl0_415,
inference(avatar_split_clause,[],[f25,f4026]) ).
fof(f4026,plain,
( spl0_415
<=> ! [X4,X0,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X6,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f25,axiom,
! [X3,X0,X6,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X6,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
fof(f4024,plain,
spl0_414,
inference(avatar_split_clause,[],[f19,f4022]) ).
fof(f4022,plain,
( spl0_414
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X0),X3,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f19,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X0),X3,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
fof(f3804,plain,
( spl0_413
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f3747,f3378,f3802]) ).
fof(f3802,plain,
( spl0_413
<=> ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f3378,plain,
( spl0_379
<=> ! [X18,X0,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X18,X11,X0)
| c_HOL_Oabs__class_Oabs(X11,X0) != c_HOL_Oabs__class_Oabs(X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f3747,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_379 ),
inference(equality_resolution,[],[f3379]) ).
fof(f3379,plain,
( ! [X0,X11,X18] :
( c_HOL_Oabs__class_Oabs(X11,X0) != c_HOL_Oabs__class_Oabs(X18,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X18,X11,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_379 ),
inference(avatar_component_clause,[],[f3378]) ).
fof(f3549,plain,
( ~ spl0_412
| ~ spl0_229
| ~ spl0_257
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f3452,f3170,f2245,f2085,f3546]) ).
fof(f3546,plain,
( spl0_412
<=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f2085,plain,
( spl0_229
<=> 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_229])]) ).
fof(f2245,plain,
( spl0_257
<=> ! [X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f3170,plain,
( spl0_364
<=> ! [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_364])]) ).
fof(f3452,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_229
| ~ spl0_257
| ~ spl0_364 ),
inference(forward_demodulation,[],[f3437,f3171]) ).
fof(f3171,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
| ~ spl0_364 ),
inference(avatar_component_clause,[],[f3170]) ).
fof(f3437,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_229
| ~ spl0_257 ),
inference(superposition,[],[f2246,f2087]) ).
fof(f2087,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_229 ),
inference(avatar_component_clause,[],[f2085]) ).
fof(f2246,plain,
( ! [X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f2245]) ).
fof(f3531,plain,
spl0_411,
inference(avatar_split_clause,[],[f810,f3529]) ).
fof(f3529,plain,
( spl0_411
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f810,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
fof(f3527,plain,
spl0_410,
inference(avatar_split_clause,[],[f737,f3525]) ).
fof(f3525,plain,
( spl0_410
<=> ! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f737,axiom,
! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).
fof(f3523,plain,
spl0_409,
inference(avatar_split_clause,[],[f704,f3521]) ).
fof(f3521,plain,
( spl0_409
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f704,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X4,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
fof(f3519,plain,
spl0_408,
inference(avatar_split_clause,[],[f614,f3517]) ).
fof(f3517,plain,
( spl0_408
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f614,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__poly__def_0) ).
fof(f3515,plain,
spl0_407,
inference(avatar_split_clause,[],[f605,f3513]) ).
fof(f3513,plain,
( spl0_407
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f605,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__le__zero__iff_0) ).
fof(f3511,plain,
spl0_406,
inference(avatar_split_clause,[],[f528,f3509]) ).
fof(f3509,plain,
( spl0_406
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X4,X3,X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f528,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X4,X3,X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
fof(f3507,plain,
spl0_405,
inference(avatar_split_clause,[],[f527,f3505]) ).
fof(f3505,plain,
( spl0_405
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X4,X3,X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f527,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X4,X3,X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).
fof(f3503,plain,
spl0_404,
inference(avatar_split_clause,[],[f526,f3501]) ).
fof(f3501,plain,
( spl0_404
<=> ! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f526,axiom,
! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
fof(f3499,plain,
( spl0_403
| ~ spl0_229
| ~ spl0_284
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f3451,f3346,f2535,f2085,f3496]) ).
fof(f2535,plain,
( spl0_284
<=> ! [X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f3346,plain,
( spl0_371
<=> ! [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_371])]) ).
fof(f3451,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_229
| ~ spl0_284
| ~ spl0_371 ),
inference(forward_demodulation,[],[f3435,f3347]) ).
fof(f3347,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_371 ),
inference(avatar_component_clause,[],[f3346]) ).
fof(f3435,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_229
| ~ spl0_284 ),
inference(superposition,[],[f2536,f2087]) ).
fof(f2536,plain,
( ! [X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_284 ),
inference(avatar_component_clause,[],[f2535]) ).
fof(f3494,plain,
spl0_402,
inference(avatar_split_clause,[],[f524,f3492]) ).
fof(f3492,plain,
( spl0_402
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X4,X3,X0) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f524,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X4,X3,X0) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
fof(f3490,plain,
spl0_401,
inference(avatar_split_clause,[],[f520,f3488]) ).
fof(f3488,plain,
( spl0_401
<=> ! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f520,axiom,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
fof(f3486,plain,
spl0_400,
inference(avatar_split_clause,[],[f506,f3484]) ).
fof(f3484,plain,
( spl0_400
<=> ! [X4,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f506,axiom,
! [X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X4,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).
fof(f3482,plain,
spl0_399,
inference(avatar_split_clause,[],[f504,f3480]) ).
fof(f3480,plain,
( spl0_399
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f504,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
fof(f3478,plain,
spl0_398,
inference(avatar_split_clause,[],[f405,f3476]) ).
fof(f3476,plain,
( spl0_398
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f405,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
fof(f3474,plain,
spl0_397,
inference(avatar_split_clause,[],[f402,f3472]) ).
fof(f3472,plain,
( spl0_397
<=> ! [X5,X2,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Oplus__class_Oplus(X2,X5,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f402,axiom,
! [X2,X0,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Oplus__class_Oplus(X2,X5,X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
fof(f3470,plain,
spl0_396,
inference(avatar_split_clause,[],[f401,f3468]) ).
fof(f3468,plain,
( spl0_396
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Oplus__class_Oplus(X4,X3,X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f401,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Oplus__class_Oplus(X4,X3,X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
fof(f3466,plain,
spl0_395,
inference(avatar_split_clause,[],[f382,f3464]) ).
fof(f3464,plain,
( spl0_395
<=> ! [X4,X0,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X6,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X3,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f382,axiom,
! [X3,X0,X6,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X6,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X3,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
fof(f3462,plain,
spl0_394,
inference(avatar_split_clause,[],[f381,f3460]) ).
fof(f3460,plain,
( spl0_394
<=> ! [X4,X0,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X3,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f381,axiom,
! [X3,X0,X6,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X3,X6,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
fof(f3458,plain,
spl0_393,
inference(avatar_split_clause,[],[f380,f3456]) ).
fof(f3456,plain,
( spl0_393
<=> ! [X4,X0,X6,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X6,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X3,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f380,axiom,
! [X3,X0,X6,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X6,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X3,X0),X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
fof(f3432,plain,
spl0_392,
inference(avatar_split_clause,[],[f379,f3430]) ).
fof(f3430,plain,
( spl0_392
<=> ! [X6,X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X6,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X3,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f379,axiom,
! [X3,X0,X6,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X6,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X3,X0),X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
fof(f3428,plain,
spl0_391,
inference(avatar_split_clause,[],[f346,f3426]) ).
fof(f3426,plain,
( spl0_391
<=> ! [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_391])]) ).
fof(f346,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/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
fof(f3424,plain,
spl0_390,
inference(avatar_split_clause,[],[f343,f3422]) ).
fof(f3422,plain,
( spl0_390
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f343,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
fof(f3420,plain,
spl0_389,
inference(avatar_split_clause,[],[f329,f3418]) ).
fof(f3418,plain,
( spl0_389
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f329,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
fof(f3416,plain,
spl0_388,
inference(avatar_split_clause,[],[f328,f3414]) ).
fof(f3414,plain,
( spl0_388
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f328,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
fof(f3412,plain,
spl0_387,
inference(avatar_split_clause,[],[f327,f3410]) ).
fof(f3410,plain,
( spl0_387
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f327,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
fof(f3408,plain,
spl0_386,
inference(avatar_split_clause,[],[f326,f3406]) ).
fof(f3406,plain,
( spl0_386
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f326,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
fof(f3404,plain,
spl0_385,
inference(avatar_split_clause,[],[f325,f3402]) ).
fof(f3402,plain,
( spl0_385
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f325,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
fof(f3400,plain,
spl0_384,
inference(avatar_split_clause,[],[f324,f3398]) ).
fof(f3398,plain,
( spl0_384
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f324,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
fof(f3396,plain,
spl0_383,
inference(avatar_split_clause,[],[f323,f3394]) ).
fof(f3394,plain,
( spl0_383
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f323,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
fof(f3392,plain,
( spl0_382
| ~ spl0_72
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2079,f1961,f1353,f3390]) ).
fof(f3390,plain,
( spl0_382
<=> ! [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_382])]) ).
fof(f1353,plain,
( spl0_72
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1961,plain,
( spl0_212
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f2079,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_72
| ~ spl0_212 ),
inference(resolution,[],[f1962,f1355]) ).
fof(f1355,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f1353]) ).
fof(f1962,plain,
( ! [X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f1961]) ).
fof(f3388,plain,
spl0_381,
inference(avatar_split_clause,[],[f322,f3386]) ).
fof(f3386,plain,
( spl0_381
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f322,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
fof(f3384,plain,
spl0_380,
inference(avatar_split_clause,[],[f311,f3382]) ).
fof(f3382,plain,
( spl0_380
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f311,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
fof(f3380,plain,
spl0_379,
inference(avatar_split_clause,[],[f295,f3378]) ).
fof(f295,axiom,
! [X0,X11,X18] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X18,X11,X0)
| c_HOL_Oabs__class_Oabs(X11,X0) != c_HOL_Oabs__class_Oabs(X18,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).
fof(f3376,plain,
spl0_378,
inference(avatar_split_clause,[],[f294,f3374]) ).
fof(f3374,plain,
( spl0_378
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Osgn__class_Osgn(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f294,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Osgn__class_Osgn(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__1__pos_0) ).
fof(f3372,plain,
spl0_377,
inference(avatar_split_clause,[],[f293,f3370]) ).
fof(f3370,plain,
( spl0_377
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f293,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__pos_0) ).
fof(f3368,plain,
spl0_376,
inference(avatar_split_clause,[],[f292,f3366]) ).
fof(f3366,plain,
( spl0_376
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f292,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
fof(f3364,plain,
spl0_375,
inference(avatar_split_clause,[],[f291,f3362]) ).
fof(f3362,plain,
( spl0_375
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f291,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
fof(f3360,plain,
spl0_374,
inference(avatar_split_clause,[],[f265,f3358]) ).
fof(f3358,plain,
( spl0_374
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X4,X3,X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f265,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X4,X3,X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
fof(f3356,plain,
spl0_373,
inference(avatar_split_clause,[],[f227,f3354]) ).
fof(f3354,plain,
( spl0_373
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f227,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X4,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
fof(f3352,plain,
spl0_372,
inference(avatar_split_clause,[],[f115,f3350]) ).
fof(f3350,plain,
( spl0_372
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f115,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
fof(f3348,plain,
( spl0_371
| ~ spl0_27
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2078,f1961,f1128,f3346]) ).
fof(f1128,plain,
( spl0_27
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f2078,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_27
| ~ spl0_212 ),
inference(resolution,[],[f1962,f1130]) ).
fof(f1130,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f1128]) ).
fof(f3344,plain,
spl0_370,
inference(avatar_split_clause,[],[f93,f3342]) ).
fof(f3342,plain,
( spl0_370
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X4,X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f93,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X4,X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
fof(f3340,plain,
spl0_369,
inference(avatar_split_clause,[],[f31,f3338]) ).
fof(f3338,plain,
( spl0_369
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f31,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
fof(f3336,plain,
spl0_368,
inference(avatar_split_clause,[],[f27,f3334]) ).
fof(f3334,plain,
( spl0_368
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f27,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f3332,plain,
spl0_367,
inference(avatar_split_clause,[],[f24,f3330]) ).
fof(f3330,plain,
( spl0_367
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f24,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__minus_0) ).
fof(f3328,plain,
spl0_366,
inference(avatar_split_clause,[],[f21,f3326]) ).
fof(f3326,plain,
( spl0_366
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f21,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__norm__iff_1) ).
fof(f3282,plain,
( spl0_365
| ~ spl0_72
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2076,f1957,f1353,f3280]) ).
fof(f3280,plain,
( spl0_365
<=> ! [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_365])]) ).
fof(f1957,plain,
( spl0_211
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f2076,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_72
| ~ spl0_211 ),
inference(resolution,[],[f1958,f1355]) ).
fof(f1958,plain,
( ! [X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X4,X0) = X4 )
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f1957]) ).
fof(f3172,plain,
( spl0_364
| ~ spl0_27
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2075,f1957,f1128,f3170]) ).
fof(f2075,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
| ~ spl0_27
| ~ spl0_211 ),
inference(resolution,[],[f1958,f1130]) ).
fof(f3132,plain,
( spl0_363
| ~ spl0_76
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2074,f1937,f1373,f3129]) ).
fof(f3129,plain,
( spl0_363
<=> 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_363])]) ).
fof(f1373,plain,
( spl0_76
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1937,plain,
( spl0_206
<=> ! [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_206])]) ).
fof(f2074,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_76
| ~ spl0_206 ),
inference(resolution,[],[f1938,f1375]) ).
fof(f1375,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1373]) ).
fof(f1938,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_206 ),
inference(avatar_component_clause,[],[f1937]) ).
fof(f3104,plain,
spl0_362,
inference(avatar_split_clause,[],[f762,f3102]) ).
fof(f3102,plain,
( spl0_362
<=> ! [X11,X30,X31] :
( ~ c_lessequals(X30,X31,tc_RealDef_Oreal)
| ~ c_lessequals(X31,X11,tc_RealDef_Oreal)
| c_lessequals(X30,X11,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f762,axiom,
! [X31,X11,X30] :
( ~ c_lessequals(X30,X31,tc_RealDef_Oreal)
| ~ c_lessequals(X31,X11,tc_RealDef_Oreal)
| c_lessequals(X30,X11,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f3100,plain,
spl0_361,
inference(avatar_split_clause,[],[f727,f3098]) ).
fof(f3098,plain,
( spl0_361
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f727,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f3096,plain,
spl0_360,
inference(avatar_split_clause,[],[f726,f3094]) ).
fof(f3094,plain,
( spl0_360
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f726,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f3092,plain,
( spl0_359
| ~ spl0_31
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2073,f1937,f1148,f3089]) ).
fof(f3089,plain,
( spl0_359
<=> 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_359])]) ).
fof(f1148,plain,
( spl0_31
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f2073,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_31
| ~ spl0_206 ),
inference(resolution,[],[f1938,f1150]) ).
fof(f1150,plain,
( class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f1148]) ).
fof(f3087,plain,
spl0_358,
inference(avatar_split_clause,[],[f621,f3084]) ).
fof(f3084,plain,
( spl0_358
<=> c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f621,axiom,
c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_h_0) ).
fof(f3082,plain,
spl0_357,
inference(avatar_split_clause,[],[f590,f3080]) ).
fof(f3080,plain,
( spl0_357
<=> ! [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_357])]) ).
fof(f590,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f3078,plain,
spl0_356,
inference(avatar_split_clause,[],[f529,f3076]) ).
fof(f3076,plain,
( spl0_356
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f529,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
fof(f3074,plain,
spl0_355,
inference(avatar_split_clause,[],[f431,f3072]) ).
fof(f3072,plain,
( spl0_355
<=> ! [X2,X1] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f431,axiom,
! [X2,X1] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__mult_0) ).
fof(f3070,plain,
spl0_354,
inference(avatar_split_clause,[],[f350,f3068]) ).
fof(f3068,plain,
( spl0_354
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X4,X3,X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f350,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X4,X3,X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
fof(f3066,plain,
spl0_353,
inference(avatar_split_clause,[],[f312,f3064]) ).
fof(f3064,plain,
( spl0_353
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oabs__class_Oabs(X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f312,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oabs__class_Oabs(X4,X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
fof(f3062,plain,
spl0_352,
inference(avatar_split_clause,[],[f287,f3060]) ).
fof(f3060,plain,
( spl0_352
<=> ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f287,axiom,
! [X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_0) ).
fof(f3058,plain,
spl0_351,
inference(avatar_split_clause,[],[f278,f3056]) ).
fof(f3056,plain,
( spl0_351
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f278,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
fof(f3054,plain,
spl0_350,
inference(avatar_split_clause,[],[f272,f3052]) ).
fof(f3052,plain,
( spl0_350
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oabs__class_Oabs(X4,X0) = X4
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f272,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oabs__class_Oabs(X4,X0) = X4
| c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_1) ).
fof(f3050,plain,
spl0_349,
inference(avatar_split_clause,[],[f260,f3048]) ).
fof(f3048,plain,
( spl0_349
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oinverse__class_Oinverse(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f260,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oinverse__class_Oinverse(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
fof(f3046,plain,
( spl0_348
| ~ spl0_69
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2068,f1925,f1338,f3043]) ).
fof(f3043,plain,
( spl0_348
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f1925,plain,
( spl0_203
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2068,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_69
| ~ spl0_203 ),
inference(resolution,[],[f1926,f1340]) ).
fof(f1926,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f1925]) ).
fof(f3041,plain,
spl0_347,
inference(avatar_split_clause,[],[f249,f3039]) ).
fof(f3039,plain,
( spl0_347
<=> ! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f249,axiom,
! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__eq__diff_0) ).
fof(f3037,plain,
spl0_346,
inference(avatar_split_clause,[],[f248,f3035]) ).
fof(f3035,plain,
( spl0_346
<=> ! [X2,X1] :
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f248,axiom,
! [X2,X1] :
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__eq__diff_1) ).
fof(f3033,plain,
spl0_345,
inference(avatar_split_clause,[],[f208,f3031]) ).
fof(f3031,plain,
( spl0_345
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f208,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__zero__iff_0) ).
fof(f3029,plain,
spl0_344,
inference(avatar_split_clause,[],[f207,f3027]) ).
fof(f3027,plain,
( spl0_344
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f207,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).
fof(f3025,plain,
spl0_343,
inference(avatar_split_clause,[],[f198,f3023]) ).
fof(f3023,plain,
( spl0_343
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oabs__class_Oabs(X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f198,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oabs__class_Oabs(X4,X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
fof(f3021,plain,
spl0_342,
inference(avatar_split_clause,[],[f189,f3019]) ).
fof(f3019,plain,
( spl0_342
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f189,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X4,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero_0) ).
fof(f3017,plain,
spl0_341,
inference(avatar_split_clause,[],[f181,f3015]) ).
fof(f3015,plain,
( spl0_341
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f181,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
fof(f3013,plain,
spl0_340,
inference(avatar_split_clause,[],[f162,f3011]) ).
fof(f3011,plain,
( spl0_340
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f162,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__sgn__abs_0) ).
fof(f3009,plain,
spl0_339,
inference(avatar_split_clause,[],[f139,f3007]) ).
fof(f3007,plain,
( spl0_339
<=> ! [X0,X11,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X11,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Oabs__class_Oabs(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f139,axiom,
! [X0,X11,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X11,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Oabs__class_Oabs(X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
fof(f3005,plain,
spl0_338,
inference(avatar_split_clause,[],[f138,f3003]) ).
fof(f3003,plain,
( spl0_338
<=> ! [X0,X11,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X11,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Oabs__class_Oabs(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f138,axiom,
! [X0,X11,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X11,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,c_HOL_Oabs__class_Oabs(X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
fof(f3001,plain,
( spl0_337
| ~ spl0_22
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2067,f1925,f1103,f2998]) ).
fof(f2998,plain,
( spl0_337
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f2067,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_22
| ~ spl0_203 ),
inference(resolution,[],[f1926,f1105]) ).
fof(f2996,plain,
spl0_336,
inference(avatar_split_clause,[],[f137,f2994]) ).
fof(f2994,plain,
( spl0_336
<=> ! [X0,X11,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X11,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X14,X0),X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f137,axiom,
! [X0,X11,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X14,X11,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X14,X0),X11,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
fof(f2992,plain,
spl0_335,
inference(avatar_split_clause,[],[f136,f2990]) ).
fof(f2990,plain,
( spl0_335
<=> ! [X0,X11,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X11,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X14,X0),X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f136,axiom,
! [X0,X11,X14] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X14,X11,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X14,X0),X11,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
fof(f2988,plain,
spl0_334,
inference(avatar_split_clause,[],[f130,f2986]) ).
fof(f2986,plain,
( spl0_334
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f130,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
fof(f2984,plain,
spl0_333,
inference(avatar_split_clause,[],[f80,f2982]) ).
fof(f2982,plain,
( spl0_333
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f80,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
fof(f2980,plain,
spl0_332,
inference(avatar_split_clause,[],[f79,f2978]) ).
fof(f2978,plain,
( spl0_332
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f79,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
fof(f2976,plain,
spl0_331,
inference(avatar_split_clause,[],[f78,f2974]) ).
fof(f2974,plain,
( spl0_331
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f78,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
fof(f2972,plain,
spl0_330,
inference(avatar_split_clause,[],[f77,f2970]) ).
fof(f2970,plain,
( spl0_330
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f77,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
fof(f2968,plain,
spl0_329,
inference(avatar_split_clause,[],[f73,f2966]) ).
fof(f2966,plain,
( spl0_329
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(X11,X0) = c_HOL_Otimes__class_Otimes(X11,c_HOL_Osgn__class_Osgn(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f73,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(X11,X0) = c_HOL_Otimes__class_Otimes(X11,c_HOL_Osgn__class_Osgn(X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__sgn_0) ).
fof(f2964,plain,
spl0_328,
inference(avatar_split_clause,[],[f33,f2962]) ).
fof(f2962,plain,
( spl0_328
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X3 = X4
| c_HOL_Ouminus__class_Ouminus(X4,X0) != c_HOL_Ouminus__class_Ouminus(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f33,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X3 = X4
| c_HOL_Ouminus__class_Ouminus(X4,X0) != c_HOL_Ouminus__class_Ouminus(X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f2957,plain,
( spl0_327
| ~ spl0_93
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2064,f1917,f1458,f2955]) ).
fof(f2955,plain,
( spl0_327
<=> ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f1458,plain,
( spl0_93
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1917,plain,
( spl0_201
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X4,c_HOL_Oone__class_Oone(X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f2064,plain,
( ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_93
| ~ spl0_201 ),
inference(resolution,[],[f1918,f1460]) ).
fof(f1460,plain,
( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1458]) ).
fof(f1918,plain,
( ! [X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X4,c_HOL_Oone__class_Oone(X0),X0) = X4 )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f1917]) ).
fof(f2900,plain,
( spl0_326
| ~ spl0_56
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2063,f1917,f1273,f2898]) ).
fof(f2898,plain,
( spl0_326
<=> ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f1273,plain,
( spl0_56
<=> class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f2063,plain,
( ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_56
| ~ spl0_201 ),
inference(resolution,[],[f1918,f1275]) ).
fof(f1275,plain,
( class_Ring__and__Field_Ofield(tc_RealDef_Oreal)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f1273]) ).
fof(f2855,plain,
( spl0_325
| ~ spl0_79
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2062,f1913,f1388,f2852]) ).
fof(f2852,plain,
( spl0_325
<=> 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_325])]) ).
fof(f1388,plain,
( spl0_79
<=> class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1913,plain,
( spl0_200
<=> ! [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_200])]) ).
fof(f2062,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_79
| ~ spl0_200 ),
inference(resolution,[],[f1914,f1390]) ).
fof(f1390,plain,
( class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex)
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f1388]) ).
fof(f1914,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_200 ),
inference(avatar_component_clause,[],[f1913]) ).
fof(f2772,plain,
( spl0_324
| ~ spl0_37
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f2061,f1913,f1178,f2769]) ).
fof(f2769,plain,
( spl0_324
<=> 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_324])]) ).
fof(f1178,plain,
( spl0_37
<=> class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f2061,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_37
| ~ spl0_200 ),
inference(resolution,[],[f1914,f1180]) ).
fof(f1180,plain,
( class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f1178]) ).
fof(f2697,plain,
spl0_323,
inference(avatar_split_clause,[],[f827,f2695]) ).
fof(f2695,plain,
( spl0_323
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f827,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
fof(f2693,plain,
spl0_322,
inference(avatar_split_clause,[],[f813,f2691]) ).
fof(f2691,plain,
( spl0_322
<=> ! [X5,X8] :
( X5 = X8
| ~ c_lessequals(X5,X8,tc_RealDef_Oreal)
| ~ c_lessequals(X8,X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f813,axiom,
! [X8,X5] :
( X5 = X8
| ~ c_lessequals(X5,X8,tc_RealDef_Oreal)
| ~ c_lessequals(X8,X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f2689,plain,
spl0_321,
inference(avatar_split_clause,[],[f774,f2687]) ).
fof(f2687,plain,
( spl0_321
<=> ! [X6,X4,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X4,X6,X0) = c_HOL_Oplus__class_Oplus(X6,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f774,axiom,
! [X0,X6,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X4,X6,X0) = c_HOL_Oplus__class_Oplus(X6,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f2685,plain,
spl0_320,
inference(avatar_split_clause,[],[f772,f2683]) ).
fof(f772,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X4,X3,X0) = c_HOL_Oplus__class_Oplus(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f2681,plain,
spl0_319,
inference(avatar_split_clause,[],[f736,f2679]) ).
fof(f2679,plain,
( spl0_319
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f736,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__0_0) ).
fof(f2677,plain,
( ~ spl0_59
| spl0_318
| ~ spl0_170
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2060,f1909,f1780,f2675,f1288]) ).
fof(f1288,plain,
( spl0_59
<=> class_Ring__and__Field_Odvd(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f2675,plain,
( spl0_318
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f1780,plain,
( spl0_170
<=> ! [X5] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1909,plain,
( spl0_199
<=> ! [X0,X11,X3] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f2060,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odvd(tc_RealDef_Oreal) )
| ~ spl0_170
| ~ spl0_199 ),
inference(superposition,[],[f1910,f1781]) ).
fof(f1781,plain,
( ! [X5] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) = X5
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1780]) ).
fof(f1910,plain,
( ! [X3,X0,X11] :
( c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X11,X0),X0)
| ~ class_Ring__and__Field_Odvd(X0) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f1909]) ).
fof(f2673,plain,
spl0_317,
inference(avatar_split_clause,[],[f735,f2671]) ).
fof(f2671,plain,
( spl0_317
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f735,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_1) ).
fof(f2669,plain,
spl0_316,
inference(avatar_split_clause,[],[f730,f2667]) ).
fof(f2667,plain,
( spl0_316
<=> ! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f730,axiom,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f2665,plain,
spl0_315,
inference(avatar_split_clause,[],[f702,f2663]) ).
fof(f2663,plain,
( spl0_315
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,X3,X0),X3,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f702,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,X3,X0),X3,X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f2661,plain,
spl0_314,
inference(avatar_split_clause,[],[f701,f2659]) ).
fof(f2659,plain,
( spl0_314
<=> ! [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_314])]) ).
fof(f701,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f2657,plain,
spl0_313,
inference(avatar_split_clause,[],[f696,f2655]) ).
fof(f2655,plain,
( spl0_313
<=> ! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f696,axiom,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f2653,plain,
spl0_312,
inference(avatar_split_clause,[],[f691,f2651]) ).
fof(f2651,plain,
( spl0_312
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,X0),X3,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f691,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,X0),X3,X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f2649,plain,
spl0_311,
inference(avatar_split_clause,[],[f540,f2647]) ).
fof(f2647,plain,
( spl0_311
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Polynomial_Opoly(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f540,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Polynomial_Opoly(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__1_0) ).
fof(f2645,plain,
spl0_310,
inference(avatar_split_clause,[],[f535,f2643]) ).
fof(f2643,plain,
( spl0_310
<=> ! [X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f535,axiom,
! [X1] :
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__one_0) ).
fof(f2641,plain,
spl0_309,
inference(avatar_split_clause,[],[f534,f2639]) ).
fof(f2639,plain,
( spl0_309
<=> ! [X2] :
( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f534,axiom,
! [X2] :
( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__1__iff_0) ).
fof(f2637,plain,
spl0_308,
inference(avatar_split_clause,[],[f532,f2635]) ).
fof(f2635,plain,
( spl0_308
<=> ! [X1] :
( c_lessequals(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X1),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f532,axiom,
! [X1] :
( c_lessequals(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X1),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__1__iff_0) ).
fof(f2633,plain,
( spl0_307
| ~ spl0_162
| ~ spl0_170
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2057,f1893,f1780,f1746,f2630]) ).
fof(f2630,plain,
( spl0_307
<=> 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_307])]) ).
fof(f1746,plain,
( spl0_162
<=> 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_162])]) ).
fof(f1893,plain,
( spl0_195
<=> ! [X1] : c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f2057,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_162
| ~ spl0_170
| ~ spl0_195 ),
inference(forward_demodulation,[],[f2053,f1748]) ).
fof(f1748,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1746]) ).
fof(f2053,plain,
( c_NthRoot_Osqrt(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_170
| ~ spl0_195 ),
inference(superposition,[],[f1894,f1781]) ).
fof(f1894,plain,
( ! [X1] : c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal))
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f1893]) ).
fof(f2628,plain,
spl0_306,
inference(avatar_split_clause,[],[f531,f2626]) ).
fof(f2626,plain,
( spl0_306
<=> ! [X1] :
( ~ c_lessequals(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X1),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f531,axiom,
! [X1] :
( ~ c_lessequals(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X1),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__1__iff_1) ).
fof(f2624,plain,
spl0_305,
inference(avatar_split_clause,[],[f515,f2622]) ).
fof(f2622,plain,
( spl0_305
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f515,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
fof(f2620,plain,
spl0_304,
inference(avatar_split_clause,[],[f490,f2618]) ).
fof(f2618,plain,
( spl0_304
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f490,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
fof(f2616,plain,
spl0_303,
inference(avatar_split_clause,[],[f489,f2614]) ).
fof(f2614,plain,
( spl0_303
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f489,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
fof(f2612,plain,
spl0_302,
inference(avatar_split_clause,[],[f488,f2610]) ).
fof(f2610,plain,
( spl0_302
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f488,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
fof(f2608,plain,
spl0_301,
inference(avatar_split_clause,[],[f439,f2606]) ).
fof(f2606,plain,
( spl0_301
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X4,X0) = c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f439,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X4,X0) = c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X4,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__norm__cancel_0) ).
fof(f2604,plain,
spl0_300,
inference(avatar_split_clause,[],[f438,f2602]) ).
fof(f2602,plain,
( spl0_300
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f438,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(X1,X0) = c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
fof(f2600,plain,
spl0_299,
inference(avatar_split_clause,[],[f422,f2598]) ).
fof(f2598,plain,
( spl0_299
<=> ! [X2,X1] :
( X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f422,axiom,
! [X2,X1] :
( X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_2) ).
fof(f2596,plain,
spl0_298,
inference(avatar_split_clause,[],[f412,f2594]) ).
fof(f2594,plain,
( spl0_298
<=> ! [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_298])]) ).
fof(f412,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/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
fof(f2592,plain,
spl0_297,
inference(avatar_split_clause,[],[f290,f2590]) ).
fof(f2590,plain,
( spl0_297
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f290,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__sgn_0) ).
fof(f2587,plain,
spl0_296,
inference(avatar_split_clause,[],[f193,f2585]) ).
fof(f2585,plain,
( spl0_296
<=> ! [X1] :
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f193,axiom,
! [X1] :
( ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_1) ).
fof(f2583,plain,
spl0_295,
inference(avatar_split_clause,[],[f192,f2581]) ).
fof(f2581,plain,
( spl0_295
<=> ! [X1] :
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f192,axiom,
! [X1] :
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_0) ).
fof(f2579,plain,
spl0_294,
inference(avatar_split_clause,[],[f185,f2577]) ).
fof(f2577,plain,
( spl0_294
<=> ! [X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f185,axiom,
! [X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__1__iff_1) ).
fof(f2575,plain,
spl0_293,
inference(avatar_split_clause,[],[f184,f2573]) ).
fof(f2573,plain,
( spl0_293
<=> ! [X2] :
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f184,axiom,
! [X2] :
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__1__iff_0) ).
fof(f2571,plain,
spl0_292,
inference(avatar_split_clause,[],[f177,f2569]) ).
fof(f2569,plain,
( spl0_292
<=> ! [X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f177,axiom,
! [X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_1) ).
fof(f2567,plain,
spl0_291,
inference(avatar_split_clause,[],[f176,f2565]) ).
fof(f2565,plain,
( spl0_291
<=> ! [X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f176,axiom,
! [X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_0) ).
fof(f2563,plain,
spl0_290,
inference(avatar_split_clause,[],[f175,f2561]) ).
fof(f2561,plain,
( spl0_290
<=> ! [X4,X0] :
( ~ 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(X4,X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f175,axiom,
! [X0,X4] :
( ~ 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(X4,X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
fof(f2559,plain,
spl0_289,
inference(avatar_split_clause,[],[f165,f2557]) ).
fof(f2557,plain,
( spl0_289
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Oinverse(X4,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f165,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Oinverse(X4,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
fof(f2555,plain,
spl0_288,
inference(avatar_split_clause,[],[f163,f2553]) ).
fof(f2553,plain,
( spl0_288
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f163,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
fof(f2551,plain,
spl0_287,
inference(avatar_split_clause,[],[f135,f2549]) ).
fof(f2549,plain,
( spl0_287
<=> ! [X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f135,axiom,
! [X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__1__iff_0) ).
fof(f2545,plain,
spl0_286,
inference(avatar_split_clause,[],[f134,f2543]) ).
fof(f2543,plain,
( spl0_286
<=> ! [X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f134,axiom,
! [X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__1__iff_1) ).
fof(f2541,plain,
spl0_285,
inference(avatar_split_clause,[],[f114,f2539]) ).
fof(f2539,plain,
( spl0_285
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X4,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f114,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X4,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
fof(f2537,plain,
spl0_284,
inference(avatar_split_clause,[],[f112,f2535]) ).
fof(f112,axiom,
! [X1] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__one__gt__zero_0) ).
fof(f2533,plain,
spl0_283,
inference(avatar_split_clause,[],[f99,f2531]) ).
fof(f2531,plain,
( spl0_283
<=> ! [X2] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f99,axiom,
! [X2] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__0__iff_0) ).
fof(f2529,plain,
spl0_282,
inference(avatar_split_clause,[],[f98,f2527]) ).
fof(f2527,plain,
( spl0_282
<=> ! [X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f98,axiom,
! [X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__0__iff_1) ).
fof(f2525,plain,
spl0_281,
inference(avatar_split_clause,[],[f92,f2523]) ).
fof(f2523,plain,
( spl0_281
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f92,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
fof(f2521,plain,
spl0_280,
inference(avatar_split_clause,[],[f90,f2519]) ).
fof(f2519,plain,
( spl0_280
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X4,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f90,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X4,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
fof(f2517,plain,
spl0_279,
inference(avatar_split_clause,[],[f58,f2515]) ).
fof(f2515,plain,
( spl0_279
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(X4,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f58,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(X4,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).
fof(f2513,plain,
spl0_278,
inference(avatar_split_clause,[],[f56,f2511]) ).
fof(f2511,plain,
( spl0_278
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ouminus__class_Ouminus(X4,X0) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f56,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ouminus__class_Ouminus(X4,X0) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f2509,plain,
spl0_277,
inference(avatar_split_clause,[],[f17,f2507]) ).
fof(f2507,plain,
( spl0_277
<=> ! [X2] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f17,axiom,
! [X2] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__0__iff_0) ).
fof(f2505,plain,
( spl0_276
| ~ spl0_100
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2440,f2241,f1492,f2503]) ).
fof(f2503,plain,
( spl0_276
<=> ! [X0] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f1492,plain,
( spl0_100
<=> ! [X8] : c_lessequals(X8,X8,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f2241,plain,
( spl0_256
<=> ! [X13,X1] :
( c_lessequals(X1,X13,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X13,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f2440,plain,
( ! [X0] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_100
| ~ spl0_256 ),
inference(resolution,[],[f2242,f1493]) ).
fof(f1493,plain,
( ! [X8] : c_lessequals(X8,X8,tc_RealDef_Oreal)
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1492]) ).
fof(f2242,plain,
( ! [X1,X13] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X13,tc_RealDef_Oreal)
| c_lessequals(X1,X13,tc_RealDef_Oreal) )
| ~ spl0_256 ),
inference(avatar_component_clause,[],[f2241]) ).
fof(f2501,plain,
spl0_275,
inference(avatar_split_clause,[],[f16,f2499]) ).
fof(f2499,plain,
( spl0_275
<=> ! [X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f16,axiom,
! [X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__zero_0) ).
fof(f2466,plain,
( spl0_274
| ~ spl0_159
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f2412,f2225,f1734,f2464]) ).
fof(f2464,plain,
( spl0_274
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f1734,plain,
( spl0_159
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f2225,plain,
( spl0_252
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f2412,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_159
| ~ spl0_252 ),
inference(duplicate_literal_removal,[],[f2396]) ).
fof(f2396,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_159
| ~ spl0_252 ),
inference(resolution,[],[f2226,f1735]) ).
fof(f1735,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1734]) ).
fof(f2226,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,X1,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_252 ),
inference(avatar_component_clause,[],[f2225]) ).
fof(f2330,plain,
( spl0_273
| ~ spl0_91
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2044,f1885,f1448,f2327]) ).
fof(f2327,plain,
( spl0_273
<=> 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_273])]) ).
fof(f1885,plain,
( spl0_193
<=> ! [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_193])]) ).
fof(f2044,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_91
| ~ spl0_193 ),
inference(resolution,[],[f1886,f1450]) ).
fof(f1886,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_193 ),
inference(avatar_component_clause,[],[f1885]) ).
fof(f2309,plain,
spl0_272,
inference(avatar_split_clause,[],[f756,f2307]) ).
fof(f2307,plain,
( spl0_272
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f756,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f2305,plain,
( spl0_271
| ~ spl0_52
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f2043,f1885,f1253,f2302]) ).
fof(f2302,plain,
( spl0_271
<=> 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_271])]) ).
fof(f2043,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_52
| ~ spl0_193 ),
inference(resolution,[],[f1886,f1255]) ).
fof(f2300,plain,
spl0_270,
inference(avatar_split_clause,[],[f722,f2298]) ).
fof(f2298,plain,
( spl0_270
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f722,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f2296,plain,
spl0_269,
inference(avatar_split_clause,[],[f721,f2294]) ).
fof(f2294,plain,
( spl0_269
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f721,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f2292,plain,
spl0_268,
inference(avatar_split_clause,[],[f720,f2290]) ).
fof(f2290,plain,
( spl0_268
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f720,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f2288,plain,
spl0_267,
inference(avatar_split_clause,[],[f719,f2286]) ).
fof(f2286,plain,
( spl0_267
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f719,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f2284,plain,
spl0_266,
inference(avatar_split_clause,[],[f717,f2282]) ).
fof(f2282,plain,
( spl0_266
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(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_266])]) ).
fof(f717,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
fof(f2280,plain,
spl0_265,
inference(avatar_split_clause,[],[f714,f2278]) ).
fof(f2278,plain,
( spl0_265
<=> ! [X2,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f714,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
fof(f2276,plain,
spl0_264,
inference(avatar_split_clause,[],[f713,f2274]) ).
fof(f2274,plain,
( spl0_264
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f713,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f2272,plain,
spl0_263,
inference(avatar_split_clause,[],[f712,f2270]) ).
fof(f2270,plain,
( spl0_263
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f712,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f2268,plain,
spl0_262,
inference(avatar_split_clause,[],[f669,f2266]) ).
fof(f2266,plain,
( spl0_262
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f669,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
fof(f2264,plain,
spl0_261,
inference(avatar_split_clause,[],[f604,f2262]) ).
fof(f2262,plain,
( spl0_261
<=> ! [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_261])]) ).
fof(f604,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/sandbox/benchmark/theBenchmark.p',cls_norm__le__zero__iff_1) ).
fof(f2260,plain,
( spl0_260
| ~ spl0_76
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2038,f1873,f1373,f2257]) ).
fof(f2257,plain,
( spl0_260
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f1873,plain,
( spl0_190
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f2038,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_76
| ~ spl0_190 ),
inference(resolution,[],[f1874,f1375]) ).
fof(f1874,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f1873]) ).
fof(f2255,plain,
spl0_259,
inference(avatar_split_clause,[],[f521,f2253]) ).
fof(f2253,plain,
( spl0_259
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f521,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X4,c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f2251,plain,
spl0_258,
inference(avatar_split_clause,[],[f474,f2249]) ).
fof(f2249,plain,
( spl0_258
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f474,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f2247,plain,
spl0_257,
inference(avatar_split_clause,[],[f437,f2245]) ).
fof(f437,axiom,
! [X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__one__not__less__self_0) ).
fof(f2243,plain,
spl0_256,
inference(avatar_split_clause,[],[f423,f2241]) ).
fof(f423,axiom,
! [X1,X13] :
( c_lessequals(X1,X13,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X13,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_1) ).
fof(f2239,plain,
spl0_255,
inference(avatar_split_clause,[],[f421,f2237]) ).
fof(f2237,plain,
( spl0_255
<=> ! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f421,axiom,
! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_1) ).
fof(f2235,plain,
spl0_254,
inference(avatar_split_clause,[],[f420,f2233]) ).
fof(f2233,plain,
( spl0_254
<=> ! [X2,X1] :
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f420,axiom,
! [X2,X1] :
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_0) ).
fof(f2231,plain,
spl0_253,
inference(avatar_split_clause,[],[f358,f2229]) ).
fof(f2229,plain,
( spl0_253
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f358,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f2227,plain,
spl0_252,
inference(avatar_split_clause,[],[f357,f2225]) ).
fof(f357,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
fof(f2223,plain,
spl0_251,
inference(avatar_split_clause,[],[f351,f2221]) ).
fof(f2221,plain,
( spl0_251
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f351,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f2219,plain,
spl0_250,
inference(avatar_split_clause,[],[f317,f2217]) ).
fof(f2217,plain,
( spl0_250
<=> ! [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_250])]) ).
fof(f317,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/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
fof(f2215,plain,
( spl0_249
| ~ spl0_31
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f2037,f1873,f1148,f2212]) ).
fof(f2212,plain,
( spl0_249
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f2037,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_31
| ~ spl0_190 ),
inference(resolution,[],[f1874,f1150]) ).
fof(f2210,plain,
spl0_248,
inference(avatar_split_clause,[],[f299,f2208]) ).
fof(f2208,plain,
( spl0_248
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f299,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f2206,plain,
spl0_247,
inference(avatar_split_clause,[],[f298,f2204]) ).
fof(f2204,plain,
( spl0_247
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f298,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f2202,plain,
spl0_246,
inference(avatar_split_clause,[],[f296,f2200]) ).
fof(f2200,plain,
( spl0_246
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f296,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f2198,plain,
spl0_245,
inference(avatar_split_clause,[],[f279,f2196]) ).
fof(f2196,plain,
( spl0_245
<=> ! [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_245])]) ).
fof(f279,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
fof(f2194,plain,
spl0_244,
inference(avatar_split_clause,[],[f270,f2192]) ).
fof(f2192,plain,
( spl0_244
<=> ! [X13] :
( c_HOL_Oabs__class_Oabs(X13,tc_RealDef_Oreal) = X13
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f270,axiom,
! [X13] :
( c_HOL_Oabs__class_Oabs(X13,tc_RealDef_Oreal) = X13
| c_HOL_Oord__class_Oless(X13,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_1) ).
fof(f2190,plain,
spl0_243,
inference(avatar_split_clause,[],[f237,f2188]) ).
fof(f2188,plain,
( spl0_243
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f237,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f2186,plain,
spl0_242,
inference(avatar_split_clause,[],[f236,f2184]) ).
fof(f2184,plain,
( spl0_242
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f236,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f2182,plain,
spl0_241,
inference(avatar_split_clause,[],[f210,f2180]) ).
fof(f2180,plain,
( spl0_241
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f210,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_1) ).
fof(f2178,plain,
spl0_240,
inference(avatar_split_clause,[],[f209,f2176]) ).
fof(f2176,plain,
( spl0_240
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f209,axiom,
! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_0) ).
fof(f2174,plain,
spl0_239,
inference(avatar_split_clause,[],[f190,f2172]) ).
fof(f2172,plain,
( spl0_239
<=> ! [X2,X0] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f190,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
fof(f2170,plain,
( spl0_238
| ~ spl0_91
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2034,f1861,f1448,f2168]) ).
fof(f2168,plain,
( spl0_238
<=> ! [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_238])]) ).
fof(f1861,plain,
( spl0_187
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f2034,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_91
| ~ spl0_187 ),
inference(resolution,[],[f1862,f1450]) ).
fof(f1862,plain,
( ! [X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = X4 )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f1861]) ).
fof(f2166,plain,
spl0_237,
inference(avatar_split_clause,[],[f187,f2164]) ).
fof(f2164,plain,
( spl0_237
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f187,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
fof(f2162,plain,
spl0_236,
inference(avatar_split_clause,[],[f149,f2160]) ).
fof(f2160,plain,
( spl0_236
<=> ! [X4,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f149,axiom,
! [X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
fof(f2158,plain,
spl0_235,
inference(avatar_split_clause,[],[f148,f2156]) ).
fof(f2156,plain,
( spl0_235
<=> ! [X4,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X4,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f148,axiom,
! [X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X4,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).
fof(f2154,plain,
spl0_234,
inference(avatar_split_clause,[],[f129,f2152]) ).
fof(f2152,plain,
( spl0_234
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Oabs__class_Oabs(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f129,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Oabs__class_Oabs(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
fof(f2150,plain,
~ spl0_233,
inference(avatar_split_clause,[],[f116,f2147]) ).
fof(f2147,plain,
( spl0_233
<=> 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_233])]) ).
fof(f116,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_1) ).
fof(f2145,plain,
spl0_232,
inference(avatar_split_clause,[],[f36,f2143]) ).
fof(f2143,plain,
( spl0_232
<=> ! [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_232])]) ).
fof(f36,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__norm__iff_0) ).
fof(f2141,plain,
spl0_231,
inference(avatar_split_clause,[],[f34,f2139]) ).
fof(f2139,plain,
( spl0_231
<=> ! [X1] :
( c_NthRoot_Osqrt(X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f34,axiom,
! [X1] :
( c_NthRoot_Osqrt(X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__not__eq__zero_0) ).
fof(f2121,plain,
( spl0_230
| ~ spl0_52
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f2033,f1861,f1253,f2119]) ).
fof(f2119,plain,
( spl0_230
<=> ! [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_230])]) ).
fof(f2033,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_52
| ~ spl0_187 ),
inference(resolution,[],[f1862,f1255]) ).
fof(f2088,plain,
( spl0_229
| ~ spl0_9
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f2030,f1853,f1038,f2085]) ).
fof(f1038,plain,
( spl0_9
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1853,plain,
( spl0_185
<=> ! [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_185])]) ).
fof(f2030,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_9
| ~ spl0_185 ),
inference(resolution,[],[f1854,f1040]) ).
fof(f1040,plain,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f1854,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_185 ),
inference(avatar_component_clause,[],[f1853]) ).
fof(f2050,plain,
( spl0_228
| ~ spl0_71
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f2021,f1837,f1348,f2047]) ).
fof(f2047,plain,
( spl0_228
<=> 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_228])]) ).
fof(f1348,plain,
( spl0_71
<=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1837,plain,
( spl0_181
<=> ! [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_181])]) ).
fof(f2021,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_71
| ~ spl0_181 ),
inference(resolution,[],[f1838,f1350]) ).
fof(f1350,plain,
( class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f1348]) ).
fof(f1838,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_181 ),
inference(avatar_component_clause,[],[f1837]) ).
fof(f2029,plain,
( spl0_227
| ~ spl0_25
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f2020,f1837,f1118,f2026]) ).
fof(f2026,plain,
( spl0_227
<=> 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_227])]) ).
fof(f1118,plain,
( spl0_25
<=> class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f2020,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_25
| ~ spl0_181 ),
inference(resolution,[],[f1838,f1120]) ).
fof(f1120,plain,
( class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f1118]) ).
fof(f2019,plain,
spl0_226,
inference(avatar_split_clause,[],[f828,f2017]) ).
fof(f2017,plain,
( spl0_226
<=> ! [X5,X8] : c_HOL_Otimes__class_Otimes(X5,X8,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X8,X5,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f828,axiom,
! [X8,X5] : c_HOL_Otimes__class_Otimes(X5,X8,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X8,X5,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
fof(f2015,plain,
spl0_225,
inference(avatar_split_clause,[],[f823,f2013]) ).
fof(f2013,plain,
( spl0_225
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f823,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(f2011,plain,
spl0_224,
inference(avatar_split_clause,[],[f821,f2009]) ).
fof(f2009,plain,
( spl0_224
<=> ! [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_224])]) ).
fof(f821,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
fof(f2007,plain,
spl0_223,
inference(avatar_split_clause,[],[f820,f2005]) ).
fof(f2005,plain,
( spl0_223
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f820,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X4,X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
fof(f2003,plain,
spl0_222,
inference(avatar_split_clause,[],[f819,f2001]) ).
fof(f819,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X4,X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
fof(f1999,plain,
spl0_221,
inference(avatar_split_clause,[],[f818,f1997]) ).
fof(f818,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X4,c_HOL_Oone__class_Oone(X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
fof(f1995,plain,
spl0_220,
inference(avatar_split_clause,[],[f777,f1993]) ).
fof(f777,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/sandbox/benchmark/theBenchmark.p',cls_norm__one_0) ).
fof(f1991,plain,
spl0_219,
inference(avatar_split_clause,[],[f734,f1989]) ).
fof(f1989,plain,
( spl0_219
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f734,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f1987,plain,
spl0_218,
inference(avatar_split_clause,[],[f733,f1985]) ).
fof(f733,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
fof(f1983,plain,
spl0_217,
inference(avatar_split_clause,[],[f732,f1981]) ).
fof(f732,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f1979,plain,
spl0_216,
inference(avatar_split_clause,[],[f699,f1977]) ).
fof(f1977,plain,
( spl0_216
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f699,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1975,plain,
spl0_215,
inference(avatar_split_clause,[],[f698,f1973]) ).
fof(f1973,plain,
( spl0_215
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f698,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X4,X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1971,plain,
spl0_214,
inference(avatar_split_clause,[],[f697,f1969]) ).
fof(f1969,plain,
( spl0_214
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f697,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1967,plain,
spl0_213,
inference(avatar_split_clause,[],[f694,f1965]) ).
fof(f1965,plain,
( spl0_213
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f694,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X4,X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1963,plain,
spl0_212,
inference(avatar_split_clause,[],[f693,f1961]) ).
fof(f693,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1959,plain,
spl0_211,
inference(avatar_split_clause,[],[f692,f1957]) ).
fof(f692,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X4,X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f1955,plain,
spl0_210,
inference(avatar_split_clause,[],[f617,f1953]) ).
fof(f1953,plain,
( spl0_210
<=> ! [X25,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(X25,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f617,axiom,
! [X0,X25] :
( ~ 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(X25,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ononneg__bounded_0) ).
fof(f1951,plain,
spl0_209,
inference(avatar_split_clause,[],[f616,f1949]) ).
fof(f1949,plain,
( spl0_209
<=> ! [X0,X1] :
( ~ 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(X1,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f616,axiom,
! [X0,X1] :
( ~ 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(X1,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ononneg__bounded_0) ).
fof(f1947,plain,
spl0_208,
inference(avatar_split_clause,[],[f615,f1945]) ).
fof(f1945,plain,
( spl0_208
<=> ! [X2,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(X2,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f615,axiom,
! [X2,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(X2,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ononneg__bounded_0) ).
fof(f1943,plain,
spl0_207,
inference(avatar_split_clause,[],[f536,f1941]) ).
fof(f1941,plain,
( spl0_207
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f536,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
fof(f1939,plain,
spl0_206,
inference(avatar_split_clause,[],[f530,f1937]) ).
fof(f530,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/sandbox/benchmark/theBenchmark.p',cls_norm__zero_0) ).
fof(f1935,plain,
spl0_205,
inference(avatar_split_clause,[],[f434,f1933]) ).
fof(f1933,plain,
( spl0_205
<=> ! [X1] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X1
| c_NthRoot_Osqrt(X1) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f434,axiom,
! [X1] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X1
| c_NthRoot_Osqrt(X1) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__eq__1__iff_0) ).
fof(f1931,plain,
spl0_204,
inference(avatar_split_clause,[],[f418,f1929]) ).
fof(f1929,plain,
( spl0_204
<=> ! [X4,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Oone__class_Oone(X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f418,axiom,
! [X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Odiv(X4,c_HOL_Oone__class_Oone(X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).
fof(f1927,plain,
spl0_203,
inference(avatar_split_clause,[],[f416,f1925]) ).
fof(f416,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__one_0) ).
fof(f1923,plain,
spl0_202,
inference(avatar_split_clause,[],[f414,f1921]) ).
fof(f1921,plain,
( spl0_202
<=> ! [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_202])]) ).
fof(f414,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/sandbox/benchmark/theBenchmark.p',cls_abs__one_0) ).
fof(f1919,plain,
spl0_201,
inference(avatar_split_clause,[],[f413,f1917]) ).
fof(f413,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X4,c_HOL_Oone__class_Oone(X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).
fof(f1915,plain,
spl0_200,
inference(avatar_split_clause,[],[f411,f1913]) ).
fof(f411,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/sandbox/benchmark/theBenchmark.p',cls_inverse__1_0) ).
fof(f1911,plain,
spl0_199,
inference(avatar_split_clause,[],[f390,f1909]) ).
fof(f390,axiom,
! [X3,X0,X11] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).
fof(f1907,plain,
spl0_198,
inference(avatar_split_clause,[],[f389,f1905]) ).
fof(f1905,plain,
( spl0_198
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f389,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
fof(f1903,plain,
spl0_197,
inference(avatar_split_clause,[],[f388,f1901]) ).
fof(f1901,plain,
( spl0_197
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f388,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
fof(f1899,plain,
spl0_196,
inference(avatar_split_clause,[],[f336,f1897]) ).
fof(f1897,plain,
( spl0_196
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f336,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
fof(f1895,plain,
spl0_195,
inference(avatar_split_clause,[],[f269,f1893]) ).
fof(f269,axiom,
! [X1] : c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__abs2_0) ).
fof(f1891,plain,
spl0_194,
inference(avatar_split_clause,[],[f264,f1889]) ).
fof(f1889,plain,
( spl0_194
<=> ! [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_194])]) ).
fof(f264,axiom,
! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
fof(f1887,plain,
spl0_193,
inference(avatar_split_clause,[],[f258,f1885]) ).
fof(f258,axiom,
! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
fof(f1883,plain,
spl0_192,
inference(avatar_split_clause,[],[f257,f1881]) ).
fof(f1881,plain,
( spl0_192
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f257,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).
fof(f1879,plain,
spl0_191,
inference(avatar_split_clause,[],[f256,f1877]) ).
fof(f1877,plain,
( spl0_191
<=> ! [X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f256,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn0_0) ).
fof(f1875,plain,
spl0_190,
inference(avatar_split_clause,[],[f255,f1873]) ).
fof(f255,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__zero_0) ).
fof(f1871,plain,
spl0_189,
inference(avatar_split_clause,[],[f252,f1869]) ).
fof(f1869,plain,
( spl0_189
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f252,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
fof(f1867,plain,
spl0_188,
inference(avatar_split_clause,[],[f244,f1865]) ).
fof(f1865,plain,
( spl0_188
<=> ! [X0,X1] :
( ~ 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(X1,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f244,axiom,
! [X0,X1] :
( ~ 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(X1,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Opos__bounded_0) ).
fof(f1863,plain,
spl0_187,
inference(avatar_split_clause,[],[f226,f1861]) ).
fof(f226,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
fof(f1859,plain,
spl0_186,
inference(avatar_split_clause,[],[f202,f1857]) ).
fof(f1857,plain,
( spl0_186
<=> ! [X0,X17] :
( ~ 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(X17,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f202,axiom,
! [X0,X17] :
( ~ 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(X17,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Opos__bounded_0) ).
fof(f1855,plain,
spl0_185,
inference(avatar_split_clause,[],[f180,f1853]) ).
fof(f180,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/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
fof(f1851,plain,
spl0_184,
inference(avatar_split_clause,[],[f169,f1849]) ).
fof(f1849,plain,
( spl0_184
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f169,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
fof(f1847,plain,
spl0_183,
inference(avatar_split_clause,[],[f131,f1845]) ).
fof(f1845,plain,
( spl0_183
<=> ! [X2,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(X2,X0),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f131,axiom,
! [X2,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(X2,X0),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Opos__bounded_0) ).
fof(f1843,plain,
spl0_182,
inference(avatar_split_clause,[],[f113,f1841]) ).
fof(f1841,plain,
( spl0_182
<=> ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_NthRoot_Osqrt(X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f113,axiom,
! [X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_NthRoot_Osqrt(X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__eq__0__iff_0) ).
fof(f1839,plain,
spl0_181,
inference(avatar_split_clause,[],[f45,f1837]) ).
fof(f45,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/sandbox/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
fof(f1830,plain,
( spl0_180
| ~ spl0_166
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1825,f1792,f1764,f1828]) ).
fof(f1828,plain,
( spl0_180
<=> ! [X0,X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1764,plain,
( spl0_166
<=> ! [X13,X12] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X12,X13),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1825,plain,
( ! [X0,X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),tc_RealDef_Oreal)
| ~ spl0_166
| ~ spl0_173 ),
inference(resolution,[],[f1793,f1765]) ).
fof(f1765,plain,
( ! [X12,X13] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X12,X13),tc_RealDef_Oreal)
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1764]) ).
fof(f1819,plain,
spl0_179,
inference(avatar_split_clause,[],[f755,f1817]) ).
fof(f1817,plain,
( spl0_179
<=> ! [X5,X8] :
( c_lessequals(X5,X8,tc_RealDef_Oreal)
| c_lessequals(X8,X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f755,axiom,
! [X8,X5] :
( c_lessequals(X5,X8,tc_RealDef_Oreal)
| c_lessequals(X8,X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
fof(f1815,plain,
~ spl0_178,
inference(avatar_split_clause,[],[f753,f1812]) ).
fof(f1812,plain,
( spl0_178
<=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f753,axiom,
c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons_Oprems_0) ).
fof(f1810,plain,
spl0_177,
inference(avatar_split_clause,[],[f629,f1808]) ).
fof(f1808,plain,
( spl0_177
<=> ! [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_177])]) ).
fof(f629,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
fof(f1806,plain,
spl0_176,
inference(avatar_split_clause,[],[f628,f1804]) ).
fof(f1804,plain,
( spl0_176
<=> ! [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_176])]) ).
fof(f628,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
fof(f1802,plain,
spl0_175,
inference(avatar_split_clause,[],[f508,f1800]) ).
fof(f1800,plain,
( spl0_175
<=> ! [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_175])]) ).
fof(f508,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f1798,plain,
spl0_174,
inference(avatar_split_clause,[],[f507,f1796]) ).
fof(f1796,plain,
( spl0_174
<=> ! [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_174])]) ).
fof(f507,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f1794,plain,
spl0_173,
inference(avatar_split_clause,[],[f419,f1792]) ).
fof(f419,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_0) ).
fof(f1790,plain,
spl0_172,
inference(avatar_split_clause,[],[f239,f1788]) ).
fof(f1788,plain,
( spl0_172
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X4,c_HOL_Oabs__class_Oabs(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f239,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X4,c_HOL_Oabs__class_Oabs(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
fof(f1786,plain,
spl0_171,
inference(avatar_split_clause,[],[f15,f1784]) ).
fof(f1784,plain,
( spl0_171
<=> ! [X2,X1] :
( X1 = X2
| c_NthRoot_Osqrt(X1) != c_NthRoot_Osqrt(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f15,axiom,
! [X2,X1] :
( X1 = X2
| c_NthRoot_Osqrt(X1) != c_NthRoot_Osqrt(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__eq__iff_0) ).
fof(f1782,plain,
spl0_170,
inference(avatar_split_clause,[],[f822,f1780]) ).
fof(f822,axiom,
! [X5] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__1_0) ).
fof(f1778,plain,
spl0_169,
inference(avatar_split_clause,[],[f689,f1776]) ).
fof(f1776,plain,
( spl0_169
<=> ! [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_169])]) ).
fof(f689,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f1774,plain,
spl0_168,
inference(avatar_split_clause,[],[f415,f1772]) ).
fof(f1772,plain,
( spl0_168
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f415,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).
fof(f1770,plain,
spl0_167,
inference(avatar_split_clause,[],[f133,f1768]) ).
fof(f1768,plain,
( spl0_167
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f133,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
fof(f1766,plain,
spl0_166,
inference(avatar_split_clause,[],[f91,f1764]) ).
fof(f91,axiom,
! [X12,X13] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X12,X13),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__bound__exists_0) ).
fof(f1762,plain,
spl0_165,
inference(avatar_split_clause,[],[f764,f1760]) ).
fof(f1760,plain,
( spl0_165
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f764,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1758,plain,
spl0_164,
inference(avatar_split_clause,[],[f763,f1756]) ).
fof(f1756,plain,
( spl0_164
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f763,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1754,plain,
spl0_163,
inference(avatar_split_clause,[],[f752,f1751]) ).
fof(f1751,plain,
( spl0_163
<=> c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f752,axiom,
c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r0_0) ).
fof(f1749,plain,
spl0_162,
inference(avatar_split_clause,[],[f432,f1746]) ).
fof(f432,axiom,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__one_0) ).
fof(f1744,plain,
spl0_161,
inference(avatar_split_clause,[],[f243,f1742]) ).
fof(f1742,plain,
( spl0_161
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f243,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1740,plain,
spl0_160,
inference(avatar_split_clause,[],[f241,f1738]) ).
fof(f1738,plain,
( spl0_160
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f241,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1736,plain,
spl0_159,
inference(avatar_split_clause,[],[f140,f1734]) ).
fof(f140,axiom,
! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1732,plain,
spl0_158,
inference(avatar_split_clause,[],[f71,f1729]) ).
fof(f1729,plain,
( spl0_158
<=> 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_158])]) ).
fof(f71,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__zero_0) ).
fof(f1727,plain,
spl0_157,
inference(avatar_split_clause,[],[f26,f1725]) ).
fof(f1725,plain,
( spl0_157
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f26,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
fof(f1723,plain,
( ~ spl0_156
| spl0_155 ),
inference(avatar_split_clause,[],[f1718,f1714,f1720]) ).
fof(f1714,plain,
( spl0_155
<=> c_lessequals(c_HOL_Oplus__class_Oplus(v_da____,c_RealVector_Onorm__class_Onorm(v_aa____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1718,plain,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(v_da____,c_RealVector_Onorm__class_Onorm(v_aa____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| spl0_155 ),
inference(forward_demodulation,[],[f1716,f822]) ).
fof(f1716,plain,
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(v_da____,c_RealVector_Onorm__class_Onorm(v_aa____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_155 ),
inference(avatar_component_clause,[],[f1714]) ).
fof(f1717,plain,
~ spl0_155,
inference(avatar_split_clause,[],[f842,f1714]) ).
fof(f842,axiom,
~ c_lessequals(c_HOL_Oplus__class_Oplus(v_da____,c_RealVector_Onorm__class_Onorm(v_aa____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1712,plain,
spl0_154,
inference(avatar_split_clause,[],[f992,f1710]) ).
fof(f1710,plain,
( spl0_154
<=> ! [X41] :
( ~ class_HOL_Ozero(X41)
| class_HOL_Ozero(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f992,axiom,
! [X41] :
( ~ class_HOL_Ozero(X41)
| class_HOL_Ozero(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).
fof(f1708,plain,
spl0_153,
inference(avatar_split_clause,[],[f991,f1706]) ).
fof(f1706,plain,
( spl0_153
<=> ! [X41] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f991,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(f1704,plain,
spl0_152,
inference(avatar_split_clause,[],[f990,f1702]) ).
fof(f1702,plain,
( spl0_152
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f990,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Oorder) ).
fof(f1700,plain,
spl0_151,
inference(avatar_split_clause,[],[f989,f1698]) ).
fof(f1698,plain,
( spl0_151
<=> ! [X41] :
( ~ class_Ring__and__Field_Ofield(X41)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f989,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ofield(X41)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Oring__div) ).
fof(f1696,plain,
spl0_150,
inference(avatar_split_clause,[],[f988,f1694]) ).
fof(f1694,plain,
( spl0_150
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f988,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(f1692,plain,
spl0_149,
inference(avatar_split_clause,[],[f987,f1690]) ).
fof(f1690,plain,
( spl0_149
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f987,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(f1688,plain,
spl0_148,
inference(avatar_split_clause,[],[f986,f1686]) ).
fof(f1686,plain,
( spl0_148
<=> ! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
| class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f986,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
| class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).
fof(f1684,plain,
spl0_147,
inference(avatar_split_clause,[],[f985,f1682]) ).
fof(f1682,plain,
( spl0_147
<=> ! [X41] :
( ~ class_Ring__and__Field_Oidom(X41)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f985,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oidom(X41)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
fof(f1680,plain,
spl0_146,
inference(avatar_split_clause,[],[f984,f1678]) ).
fof(f1678,plain,
( spl0_146
<=> ! [X41] :
( ~ class_Ring__and__Field_Ocomm__ring(X41)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f984,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ocomm__ring(X41)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
fof(f1676,plain,
spl0_145,
inference(avatar_split_clause,[],[f983,f1674]) ).
fof(f1674,plain,
( spl0_145
<=> ! [X41] :
( ~ class_Ring__and__Field_Ofield(X41)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f983,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ofield(X41)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(f1672,plain,
spl0_144,
inference(avatar_split_clause,[],[f982,f1670]) ).
fof(f1670,plain,
( spl0_144
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f982,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if) ).
fof(f1668,plain,
spl0_143,
inference(avatar_split_clause,[],[f981,f1666]) ).
fof(f1666,plain,
( spl0_143
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Osgn__if(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f981,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Osgn__if(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osgn__if) ).
fof(f1664,plain,
spl0_142,
inference(avatar_split_clause,[],[f980,f1662]) ).
fof(f1662,plain,
( spl0_142
<=> ! [X41] :
( ~ class_OrderedGroup_Oab__group__add(X41)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f980,axiom,
! [X41] :
( ~ class_OrderedGroup_Oab__group__add(X41)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
fof(f1660,plain,
spl0_141,
inference(avatar_split_clause,[],[f979,f1658]) ).
fof(f1658,plain,
( spl0_141
<=> ! [X41] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X41)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f979,axiom,
! [X41] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X41)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
fof(f1656,plain,
spl0_140,
inference(avatar_split_clause,[],[f978,f1654]) ).
fof(f1654,plain,
( spl0_140
<=> ! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f978,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
fof(f1652,plain,
spl0_139,
inference(avatar_split_clause,[],[f977,f1650]) ).
fof(f1650,plain,
( spl0_139
<=> ! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f977,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
fof(f1648,plain,
spl0_138,
inference(avatar_split_clause,[],[f976,f1646]) ).
fof(f1646,plain,
( spl0_138
<=> ! [X41] :
( ~ class_Ring__and__Field_Ocomm__ring(X41)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f976,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ocomm__ring(X41)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
fof(f1644,plain,
spl0_137,
inference(avatar_split_clause,[],[f975,f1642]) ).
fof(f1642,plain,
( spl0_137
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f975,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).
fof(f1640,plain,
spl0_136,
inference(avatar_split_clause,[],[f974,f1638]) ).
fof(f1638,plain,
( spl0_136
<=> ! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f974,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
fof(f1636,plain,
spl0_135,
inference(avatar_split_clause,[],[f973,f1634]) ).
fof(f1634,plain,
( spl0_135
<=> ! [X41] :
( ~ class_OrderedGroup_Oab__group__add(X41)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f973,axiom,
! [X41] :
( ~ class_OrderedGroup_Oab__group__add(X41)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
fof(f1632,plain,
spl0_134,
inference(avatar_split_clause,[],[f972,f1630]) ).
fof(f1630,plain,
( spl0_134
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f972,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).
fof(f1628,plain,
spl0_133,
inference(avatar_split_clause,[],[f971,f1626]) ).
fof(f1626,plain,
( spl0_133
<=> ! [X41] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f971,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X41)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
fof(f1624,plain,
spl0_132,
inference(avatar_split_clause,[],[f970,f1622]) ).
fof(f1622,plain,
( spl0_132
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f970,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
fof(f1620,plain,
spl0_131,
inference(avatar_split_clause,[],[f969,f1618]) ).
fof(f1618,plain,
( spl0_131
<=> ! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f969,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
fof(f1616,plain,
spl0_130,
inference(avatar_split_clause,[],[f968,f1614]) ).
fof(f1614,plain,
( spl0_130
<=> ! [X41] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X41)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f968,axiom,
! [X41] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X41)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
fof(f1612,plain,
spl0_129,
inference(avatar_split_clause,[],[f967,f1610]) ).
fof(f1610,plain,
( spl0_129
<=> ! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f967,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
fof(f1608,plain,
spl0_128,
inference(avatar_split_clause,[],[f966,f1606]) ).
fof(f1606,plain,
( spl0_128
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f966,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).
fof(f1604,plain,
spl0_127,
inference(avatar_split_clause,[],[f965,f1602]) ).
fof(f1602,plain,
( spl0_127
<=> ! [X41] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X41)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f965,axiom,
! [X41] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X41)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
fof(f1600,plain,
spl0_126,
inference(avatar_split_clause,[],[f964,f1598]) ).
fof(f1598,plain,
( spl0_126
<=> ! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f964,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1596,plain,
spl0_125,
inference(avatar_split_clause,[],[f963,f1594]) ).
fof(f1594,plain,
( spl0_125
<=> ! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f963,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
fof(f1592,plain,
spl0_124,
inference(avatar_split_clause,[],[f962,f1590]) ).
fof(f1590,plain,
( spl0_124
<=> ! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f962,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X41)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1588,plain,
spl0_123,
inference(avatar_split_clause,[],[f961,f1586]) ).
fof(f1586,plain,
( spl0_123
<=> ! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f961,axiom,
! [X41] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X41)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1584,plain,
spl0_122,
inference(avatar_split_clause,[],[f960,f1582]) ).
fof(f1582,plain,
( spl0_122
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f960,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).
fof(f1580,plain,
spl0_121,
inference(avatar_split_clause,[],[f959,f1578]) ).
fof(f1578,plain,
( spl0_121
<=> ! [X41] :
( ~ class_Ring__and__Field_Oidom(X41)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f959,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oidom(X41)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
fof(f1576,plain,
spl0_120,
inference(avatar_split_clause,[],[f958,f1574]) ).
fof(f1574,plain,
( spl0_120
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f958,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).
fof(f1572,plain,
spl0_119,
inference(avatar_split_clause,[],[f957,f1570]) ).
fof(f1570,plain,
( spl0_119
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f957,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs) ).
fof(f1568,plain,
spl0_118,
inference(avatar_split_clause,[],[f956,f1566]) ).
fof(f1566,plain,
( spl0_118
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f956,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).
fof(f1564,plain,
spl0_117,
inference(avatar_split_clause,[],[f955,f1562]) ).
fof(f1562,plain,
( spl0_117
<=> ! [X41] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X41)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f955,axiom,
! [X41] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X41)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1560,plain,
spl0_116,
inference(avatar_split_clause,[],[f954,f1558]) ).
fof(f1558,plain,
( spl0_116
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f954,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
fof(f1556,plain,
spl0_115,
inference(avatar_split_clause,[],[f953,f1554]) ).
fof(f1554,plain,
( spl0_115
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f953,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
fof(f1552,plain,
spl0_114,
inference(avatar_split_clause,[],[f952,f1550]) ).
fof(f1550,plain,
( spl0_114
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f952,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
fof(f1548,plain,
spl0_113,
inference(avatar_split_clause,[],[f951,f1546]) ).
fof(f1546,plain,
( spl0_113
<=> ! [X41] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X41)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f951,axiom,
! [X41] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X41)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1544,plain,
spl0_112,
inference(avatar_split_clause,[],[f950,f1542]) ).
fof(f1542,plain,
( spl0_112
<=> ! [X41] :
( ~ class_Ring__and__Field_Oidom(X41)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f950,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oidom(X41)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1540,plain,
spl0_111,
inference(avatar_split_clause,[],[f949,f1538]) ).
fof(f1538,plain,
( spl0_111
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f949,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1536,plain,
spl0_110,
inference(avatar_split_clause,[],[f948,f1534]) ).
fof(f1534,plain,
( spl0_110
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f948,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f1532,plain,
spl0_109,
inference(avatar_split_clause,[],[f947,f1530]) ).
fof(f1530,plain,
( spl0_109
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f947,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1528,plain,
spl0_108,
inference(avatar_split_clause,[],[f946,f1526]) ).
fof(f1526,plain,
( spl0_108
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f946,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1524,plain,
spl0_107,
inference(avatar_split_clause,[],[f945,f1522]) ).
fof(f1522,plain,
( spl0_107
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f945,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1520,plain,
spl0_106,
inference(avatar_split_clause,[],[f944,f1518]) ).
fof(f1518,plain,
( spl0_106
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f944,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1516,plain,
spl0_105,
inference(avatar_split_clause,[],[f943,f1514]) ).
fof(f1514,plain,
( spl0_105
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f943,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1512,plain,
spl0_104,
inference(avatar_split_clause,[],[f942,f1510]) ).
fof(f1510,plain,
( spl0_104
<=> ! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f942,axiom,
! [X41] :
( ~ class_Ring__and__Field_Oordered__idom(X41)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1508,plain,
spl0_103,
inference(avatar_split_clause,[],[f843,f1506]) ).
fof(f1506,plain,
( spl0_103
<=> ! [X41] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X41)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X41)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f843,axiom,
! [X41] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X41)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f1504,plain,
~ spl0_102,
inference(avatar_split_clause,[],[f686,f1501]) ).
fof(f1501,plain,
( spl0_102
<=> v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f686,axiom,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_H_0) ).
fof(f1499,plain,
~ spl0_101,
inference(avatar_split_clause,[],[f433,f1496]) ).
fof(f1496,plain,
( spl0_101
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f433,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
fof(f1494,plain,
spl0_100,
inference(avatar_split_clause,[],[f761,f1492]) ).
fof(f761,axiom,
! [X8] : c_lessequals(X8,X8,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
fof(f1490,plain,
spl0_99,
inference(avatar_split_clause,[],[f242,f1488]) ).
fof(f1488,plain,
( spl0_99
<=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f242,axiom,
! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_1) ).
fof(f1486,plain,
spl0_98,
inference(avatar_split_clause,[],[f941,f1483]) ).
fof(f1483,plain,
( spl0_98
<=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f941,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
fof(f1481,plain,
spl0_97,
inference(avatar_split_clause,[],[f940,f1478]) ).
fof(f1478,plain,
( spl0_97
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f940,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f1476,plain,
spl0_96,
inference(avatar_split_clause,[],[f939,f1473]) ).
fof(f1473,plain,
( spl0_96
<=> class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f939,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
fof(f1471,plain,
spl0_95,
inference(avatar_split_clause,[],[f938,f1468]) ).
fof(f1468,plain,
( spl0_95
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f938,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f1466,plain,
spl0_94,
inference(avatar_split_clause,[],[f937,f1463]) ).
fof(f1463,plain,
( spl0_94
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f937,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(f1461,plain,
spl0_93,
inference(avatar_split_clause,[],[f936,f1458]) ).
fof(f936,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f1456,plain,
spl0_92,
inference(avatar_split_clause,[],[f935,f1453]) ).
fof(f1453,plain,
( spl0_92
<=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f935,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(f1451,plain,
spl0_91,
inference(avatar_split_clause,[],[f934,f1448]) ).
fof(f934,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(f1446,plain,
spl0_90,
inference(avatar_split_clause,[],[f933,f1443]) ).
fof(f1443,plain,
( spl0_90
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f933,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(f1441,plain,
spl0_89,
inference(avatar_split_clause,[],[f932,f1438]) ).
fof(f1438,plain,
( spl0_89
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f932,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(f1436,plain,
spl0_88,
inference(avatar_split_clause,[],[f931,f1433]) ).
fof(f931,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f1431,plain,
spl0_87,
inference(avatar_split_clause,[],[f930,f1428]) ).
fof(f1428,plain,
( spl0_87
<=> class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f930,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
fof(f1426,plain,
spl0_86,
inference(avatar_split_clause,[],[f929,f1423]) ).
fof(f1423,plain,
( spl0_86
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f929,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
fof(f1421,plain,
spl0_85,
inference(avatar_split_clause,[],[f928,f1418]) ).
fof(f1418,plain,
( spl0_85
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f928,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f1416,plain,
spl0_84,
inference(avatar_split_clause,[],[f927,f1413]) ).
fof(f1413,plain,
( spl0_84
<=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f927,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
fof(f1411,plain,
spl0_83,
inference(avatar_split_clause,[],[f926,f1408]) ).
fof(f1408,plain,
( spl0_83
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f926,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
fof(f1406,plain,
spl0_82,
inference(avatar_split_clause,[],[f925,f1403]) ).
fof(f1403,plain,
( spl0_82
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f925,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f1401,plain,
spl0_81,
inference(avatar_split_clause,[],[f924,f1398]) ).
fof(f1398,plain,
( spl0_81
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f924,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f1396,plain,
spl0_80,
inference(avatar_split_clause,[],[f923,f1393]) ).
fof(f1393,plain,
( spl0_80
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f923,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
fof(f1391,plain,
spl0_79,
inference(avatar_split_clause,[],[f922,f1388]) ).
fof(f922,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
fof(f1386,plain,
spl0_78,
inference(avatar_split_clause,[],[f921,f1383]) ).
fof(f1383,plain,
( spl0_78
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f921,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(f1381,plain,
spl0_77,
inference(avatar_split_clause,[],[f920,f1378]) ).
fof(f1378,plain,
( spl0_77
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f920,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1376,plain,
spl0_76,
inference(avatar_split_clause,[],[f919,f1373]) ).
fof(f919,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1371,plain,
spl0_75,
inference(avatar_split_clause,[],[f918,f1368]) ).
fof(f1368,plain,
( spl0_75
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f918,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f1366,plain,
spl0_74,
inference(avatar_split_clause,[],[f917,f1363]) ).
fof(f1363,plain,
( spl0_74
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f917,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1361,plain,
spl0_73,
inference(avatar_split_clause,[],[f916,f1358]) ).
fof(f1358,plain,
( spl0_73
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f916,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1356,plain,
spl0_72,
inference(avatar_split_clause,[],[f915,f1353]) ).
fof(f915,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1351,plain,
spl0_71,
inference(avatar_split_clause,[],[f914,f1348]) ).
fof(f914,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
fof(f1346,plain,
spl0_70,
inference(avatar_split_clause,[],[f913,f1343]) ).
fof(f1343,plain,
( spl0_70
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f913,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
fof(f1341,plain,
spl0_69,
inference(avatar_split_clause,[],[f912,f1338]) ).
fof(f912,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(f1336,plain,
spl0_68,
inference(avatar_split_clause,[],[f911,f1333]) ).
fof(f1333,plain,
( spl0_68
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f911,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1331,plain,
spl0_67,
inference(avatar_split_clause,[],[f910,f1328]) ).
fof(f1328,plain,
( spl0_67
<=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f910,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(f1326,plain,
spl0_66,
inference(avatar_split_clause,[],[f909,f1323]) ).
fof(f1323,plain,
( spl0_66
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f909,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1321,plain,
spl0_65,
inference(avatar_split_clause,[],[f908,f1318]) ).
fof(f1318,plain,
( spl0_65
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f908,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1316,plain,
spl0_64,
inference(avatar_split_clause,[],[f907,f1313]) ).
fof(f1313,plain,
( spl0_64
<=> class_HOL_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f907,axiom,
class_HOL_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Ozero) ).
fof(f1311,plain,
spl0_63,
inference(avatar_split_clause,[],[f906,f1308]) ).
fof(f1308,plain,
( spl0_63
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f906,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f1306,plain,
spl0_62,
inference(avatar_split_clause,[],[f905,f1303]) ).
fof(f1303,plain,
( spl0_62
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f905,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
fof(f1301,plain,
spl0_61,
inference(avatar_split_clause,[],[f904,f1298]) ).
fof(f1298,plain,
( spl0_61
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f904,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f1296,plain,
spl0_60,
inference(avatar_split_clause,[],[f903,f1293]) ).
fof(f1293,plain,
( spl0_60
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f903,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f1291,plain,
spl0_59,
inference(avatar_split_clause,[],[f902,f1288]) ).
fof(f902,axiom,
class_Ring__and__Field_Odvd(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odvd) ).
fof(f1286,plain,
spl0_58,
inference(avatar_split_clause,[],[f901,f1283]) ).
fof(f1283,plain,
( spl0_58
<=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f901,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
fof(f1281,plain,
spl0_57,
inference(avatar_split_clause,[],[f900,f1278]) ).
fof(f1278,plain,
( spl0_57
<=> class_Ring__and__Field_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f900,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
fof(f1276,plain,
spl0_56,
inference(avatar_split_clause,[],[f899,f1273]) ).
fof(f899,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
fof(f1271,plain,
spl0_55,
inference(avatar_split_clause,[],[f898,f1268]) ).
fof(f1268,plain,
( spl0_55
<=> class_RealVector_Oreal__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f898,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__field) ).
fof(f1266,plain,
spl0_54,
inference(avatar_split_clause,[],[f897,f1263]) ).
fof(f1263,plain,
( spl0_54
<=> class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f897,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).
fof(f1261,plain,
spl0_53,
inference(avatar_split_clause,[],[f896,f1258]) ).
fof(f1258,plain,
( spl0_53
<=> class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f896,axiom,
class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if) ).
fof(f1256,plain,
spl0_52,
inference(avatar_split_clause,[],[f895,f1253]) ).
fof(f895,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f1251,plain,
spl0_51,
inference(avatar_split_clause,[],[f894,f1248]) ).
fof(f1248,plain,
( spl0_51
<=> class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f894,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
fof(f1246,plain,
spl0_50,
inference(avatar_split_clause,[],[f893,f1243]) ).
fof(f1243,plain,
( spl0_50
<=> class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f893,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
fof(f1241,plain,
spl0_49,
inference(avatar_split_clause,[],[f892,f1238]) ).
fof(f892,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
fof(f1236,plain,
spl0_48,
inference(avatar_split_clause,[],[f891,f1233]) ).
fof(f1233,plain,
( spl0_48
<=> class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f891,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring) ).
fof(f1231,plain,
spl0_47,
inference(avatar_split_clause,[],[f890,f1228]) ).
fof(f1228,plain,
( spl0_47
<=> class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f890,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) ).
fof(f1226,plain,
spl0_46,
inference(avatar_split_clause,[],[f889,f1223]) ).
fof(f1223,plain,
( spl0_46
<=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f889,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
fof(f1221,plain,
spl0_45,
inference(avatar_split_clause,[],[f888,f1218]) ).
fof(f1218,plain,
( spl0_45
<=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f888,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
fof(f1216,plain,
spl0_44,
inference(avatar_split_clause,[],[f887,f1213]) ).
fof(f1213,plain,
( spl0_44
<=> class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f887,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).
fof(f1211,plain,
spl0_43,
inference(avatar_split_clause,[],[f886,f1208]) ).
fof(f1208,plain,
( spl0_43
<=> class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f886,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) ).
fof(f1206,plain,
spl0_42,
inference(avatar_split_clause,[],[f885,f1203]) ).
fof(f1203,plain,
( spl0_42
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f885,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
fof(f1201,plain,
spl0_41,
inference(avatar_split_clause,[],[f884,f1198]) ).
fof(f1198,plain,
( spl0_41
<=> class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f884,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).
fof(f1196,plain,
spl0_40,
inference(avatar_split_clause,[],[f883,f1193]) ).
fof(f883,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
fof(f1191,plain,
spl0_39,
inference(avatar_split_clause,[],[f882,f1188]) ).
fof(f1188,plain,
( spl0_39
<=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f882,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(f1186,plain,
spl0_38,
inference(avatar_split_clause,[],[f881,f1183]) ).
fof(f1183,plain,
( spl0_38
<=> class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f881,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
fof(f1181,plain,
spl0_37,
inference(avatar_split_clause,[],[f880,f1178]) ).
fof(f880,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).
fof(f1176,plain,
spl0_36,
inference(avatar_split_clause,[],[f879,f1173]) ).
fof(f1173,plain,
( spl0_36
<=> class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f879,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) ).
fof(f1171,plain,
spl0_35,
inference(avatar_split_clause,[],[f878,f1168]) ).
fof(f1168,plain,
( spl0_35
<=> class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f878,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
fof(f1166,plain,
spl0_34,
inference(avatar_split_clause,[],[f877,f1163]) ).
fof(f1163,plain,
( spl0_34
<=> class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f877,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) ).
fof(f1161,plain,
spl0_33,
inference(avatar_split_clause,[],[f876,f1158]) ).
fof(f1158,plain,
( spl0_33
<=> class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f876,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
fof(f1156,plain,
spl0_32,
inference(avatar_split_clause,[],[f875,f1153]) ).
fof(f1153,plain,
( spl0_32
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f875,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1151,plain,
spl0_31,
inference(avatar_split_clause,[],[f874,f1148]) ).
fof(f874,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f1146,plain,
spl0_30,
inference(avatar_split_clause,[],[f873,f1143]) ).
fof(f1143,plain,
( spl0_30
<=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f873,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
fof(f1141,plain,
spl0_29,
inference(avatar_split_clause,[],[f872,f1138]) ).
fof(f1138,plain,
( spl0_29
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f872,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f1136,plain,
spl0_28,
inference(avatar_split_clause,[],[f871,f1133]) ).
fof(f1133,plain,
( spl0_28
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f871,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1131,plain,
spl0_27,
inference(avatar_split_clause,[],[f870,f1128]) ).
fof(f870,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1126,plain,
spl0_26,
inference(avatar_split_clause,[],[f869,f1123]) ).
fof(f1123,plain,
( spl0_26
<=> class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f869,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
fof(f1121,plain,
spl0_25,
inference(avatar_split_clause,[],[f868,f1118]) ).
fof(f868,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
fof(f1116,plain,
spl0_24,
inference(avatar_split_clause,[],[f867,f1113]) ).
fof(f1113,plain,
( spl0_24
<=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f867,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).
fof(f1111,plain,
spl0_23,
inference(avatar_split_clause,[],[f866,f1108]) ).
fof(f1108,plain,
( spl0_23
<=> class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f866,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).
fof(f1106,plain,
spl0_22,
inference(avatar_split_clause,[],[f865,f1103]) ).
fof(f865,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(f1101,plain,
spl0_21,
inference(avatar_split_clause,[],[f864,f1098]) ).
fof(f1098,plain,
( spl0_21
<=> class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f864,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) ).
fof(f1096,plain,
spl0_20,
inference(avatar_split_clause,[],[f863,f1093]) ).
fof(f1093,plain,
( spl0_20
<=> class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f863,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) ).
fof(f1091,plain,
spl0_19,
inference(avatar_split_clause,[],[f862,f1088]) ).
fof(f1088,plain,
( spl0_19
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f862,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1086,plain,
spl0_18,
inference(avatar_split_clause,[],[f861,f1083]) ).
fof(f1083,plain,
( spl0_18
<=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f861,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
fof(f1081,plain,
spl0_17,
inference(avatar_split_clause,[],[f860,f1078]) ).
fof(f1078,plain,
( spl0_17
<=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f860,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
fof(f1076,plain,
spl0_16,
inference(avatar_split_clause,[],[f859,f1073]) ).
fof(f1073,plain,
( spl0_16
<=> class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f859,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
fof(f1071,plain,
spl0_15,
inference(avatar_split_clause,[],[f858,f1068]) ).
fof(f1068,plain,
( spl0_15
<=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f858,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(f1066,plain,
spl0_14,
inference(avatar_split_clause,[],[f857,f1063]) ).
fof(f1063,plain,
( spl0_14
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f857,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
fof(f1061,plain,
spl0_13,
inference(avatar_split_clause,[],[f856,f1058]) ).
fof(f1058,plain,
( spl0_13
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f856,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1056,plain,
spl0_12,
inference(avatar_split_clause,[],[f855,f1053]) ).
fof(f1053,plain,
( spl0_12
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f855,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1051,plain,
spl0_11,
inference(avatar_split_clause,[],[f854,f1048]) ).
fof(f1048,plain,
( spl0_11
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f854,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1046,plain,
spl0_10,
inference(avatar_split_clause,[],[f853,f1043]) ).
fof(f1043,plain,
( spl0_10
<=> class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f853,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).
fof(f1041,plain,
spl0_9,
inference(avatar_split_clause,[],[f852,f1038]) ).
fof(f852,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f1036,plain,
spl0_8,
inference(avatar_split_clause,[],[f851,f1033]) ).
fof(f1033,plain,
( spl0_8
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f851,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1031,plain,
spl0_7,
inference(avatar_split_clause,[],[f850,f1028]) ).
fof(f1028,plain,
( spl0_7
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f850,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1026,plain,
spl0_6,
inference(avatar_split_clause,[],[f849,f1023]) ).
fof(f1023,plain,
( spl0_6
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f849,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1021,plain,
spl0_5,
inference(avatar_split_clause,[],[f848,f1018]) ).
fof(f1018,plain,
( spl0_5
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f848,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1016,plain,
spl0_4,
inference(avatar_split_clause,[],[f847,f1013]) ).
fof(f1013,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f847,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1011,plain,
spl0_3,
inference(avatar_split_clause,[],[f846,f1008]) ).
fof(f1008,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f846,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1006,plain,
spl0_2,
inference(avatar_split_clause,[],[f845,f1003]) ).
fof(f1003,plain,
( spl0_2
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f845,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f1001,plain,
spl0_1,
inference(avatar_split_clause,[],[f844,f998]) ).
fof(f998,plain,
( spl0_1
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f844,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG382-1 : TPTP v8.2.0. Released v4.1.0.
% 0.03/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat May 18 23:39:38 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % (27859)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (27860)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.42 % (27863)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.42 % (27865)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)
% 0.20/0.43 % (27864)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)
% 0.20/0.43 % (27862)WARNING: value z3 for option sas not known
% 0.20/0.43 % (27866)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)
% 0.20/0.43 % (27862)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)
% 0.20/0.43 % (27861)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.53 TRYING [1]
% 0.20/0.55 TRYING [2]
% 1.19/0.57 TRYING [1]
% 1.32/0.59 TRYING [2]
% 1.91/0.67 % (27864)First to succeed.
% 1.91/0.70 % (27864)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27859"
% 1.91/0.70 % (27864)Refutation found. Thanks to Tanya!
% 1.91/0.70 % SZS status Unsatisfiable for theBenchmark
% 1.91/0.70 % SZS output start Proof for theBenchmark
% See solution above
% 1.91/0.72 % (27864)------------------------------
% 1.91/0.72 % (27864)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.91/0.72 % (27864)Termination reason: Refutation
% 1.91/0.72
% 1.91/0.72 % (27864)Memory used [KB]: 4594
% 1.91/0.72 % (27864)Time elapsed: 0.273 s
% 1.91/0.72 % (27864)Instructions burned: 415 (million)
% 1.91/0.72 % (27859)Success in time 0.361 s
%------------------------------------------------------------------------------