TSTP Solution File: ALG396-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG396-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:30:17 EDT 2024
% Result : Unsatisfiable 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 596
% Syntax : Number of formulae : 945 ( 419 unt; 0 def)
% Number of atoms : 1766 ( 218 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1353 ( 532 ~; 515 |; 0 &)
% ( 306 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 370 ( 368 usr; 307 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 7 con; 0-3 aty)
% Number of variables : 711 ( 711 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2665,plain,
$false,
inference(avatar_sat_refutation,[],[f879,f884,f889,f894,f899,f904,f909,f914,f919,f924,f929,f934,f939,f944,f949,f954,f959,f964,f969,f974,f979,f984,f989,f994,f999,f1004,f1009,f1014,f1019,f1024,f1029,f1034,f1039,f1044,f1049,f1054,f1059,f1064,f1069,f1074,f1079,f1084,f1089,f1094,f1099,f1104,f1109,f1114,f1119,f1124,f1129,f1134,f1139,f1144,f1149,f1154,f1159,f1164,f1169,f1174,f1179,f1184,f1189,f1194,f1199,f1204,f1209,f1214,f1219,f1224,f1229,f1234,f1239,f1244,f1249,f1254,f1259,f1264,f1269,f1274,f1279,f1284,f1289,f1294,f1299,f1304,f1309,f1314,f1319,f1324,f1329,f1334,f1339,f1344,f1349,f1354,f1359,f1364,f1369,f1374,f1379,f1384,f1389,f1394,f1399,f1404,f1409,f1414,f1419,f1424,f1429,f1434,f1439,f1444,f1449,f1454,f1459,f1464,f1468,f1472,f1476,f1480,f1484,f1488,f1492,f1496,f1500,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,f1669,f1673,f1677,f1681,f1685,f1689,f1694,f1699,f1704,f1708,f1712,f1716,f1720,f1724,f1728,f1739,f1749,f1753,f1757,f1761,f1765,f1769,f1773,f1777,f1781,f1785,f1789,f1793,f1797,f1801,f1805,f1809,f1813,f1817,f1821,f1825,f1829,f1833,f1837,f1841,f1845,f1849,f1853,f1857,f1914,f1918,f1922,f1926,f1930,f1934,f1938,f1942,f1948,f1952,f1956,f1960,f1964,f1968,f1972,f1976,f1980,f1984,f1990,f1994,f1998,f2002,f2006,f2010,f2014,f2018,f2022,f2026,f2076,f2087,f2091,f2095,f2099,f2103,f2107,f2111,f2115,f2119,f2123,f2127,f2131,f2135,f2139,f2144,f2148,f2152,f2156,f2160,f2164,f2168,f2172,f2176,f2180,f2201,f2234,f2268,f2278,f2282,f2286,f2290,f2294,f2298,f2302,f2306,f2310,f2314,f2318,f2322,f2326,f2330,f2334,f2338,f2342,f2346,f2350,f2354,f2358,f2362,f2366,f2370,f2374,f2378,f2382,f2386,f2390,f2394,f2398,f2402,f2406,f2410,f2414,f2452,f2588,f2650,f2664]) ).
fof(f2664,plain,
( spl0_118
| ~ spl0_303 ),
inference(avatar_contradiction_clause,[],[f2663]) ).
fof(f2663,plain,
( $false
| spl0_118
| ~ spl0_303 ),
inference(trivial_inequality_removal,[],[f2662]) ).
fof(f2662,plain,
( c_Polynomial_Opoly(v_pa____,v_x____,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_pa____,v_x____,tc_Complex_Ocomplex)
| spl0_118
| ~ spl0_303 ),
inference(superposition,[],[f1463,f2413]) ).
fof(f2413,plain,
( ! [X4] : c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(X4,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,X4,tc_Complex_Ocomplex)
| ~ spl0_303 ),
inference(avatar_component_clause,[],[f2412]) ).
fof(f2412,plain,
( spl0_303
<=> ! [X4] : c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(X4,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,X4,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f1463,plain,
( c_Polynomial_Opoly(v_pa____,v_x____,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(v_x____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| spl0_118 ),
inference(avatar_component_clause,[],[f1461]) ).
fof(f1461,plain,
( spl0_118
<=> c_Polynomial_Opoly(v_pa____,v_x____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(v_x____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f2650,plain,
( spl0_306
| ~ spl0_78
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1890,f1815,f1261,f2648]) ).
fof(f2648,plain,
( spl0_306
<=> ! [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_306])]) ).
fof(f1261,plain,
( spl0_78
<=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1815,plain,
( spl0_202
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1890,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_78
| ~ spl0_202 ),
inference(resolution,[],[f1816,f1263]) ).
fof(f1263,plain,
( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1261]) ).
fof(f1816,plain,
( ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = X2 )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f1815]) ).
fof(f2588,plain,
( spl0_305
| ~ spl0_27
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1871,f1795,f1006,f2586]) ).
fof(f2586,plain,
( spl0_305
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f1006,plain,
( spl0_27
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1795,plain,
( spl0_197
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1871,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0
| ~ spl0_27
| ~ spl0_197 ),
inference(resolution,[],[f1796,f1008]) ).
fof(f1008,plain,
( class_OrderedGroup_Omonoid__add(tc_nat)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f1006]) ).
fof(f1796,plain,
( ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f1795]) ).
fof(f2452,plain,
( spl0_304
| ~ spl0_76
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1869,f1795,f1251,f2450]) ).
fof(f2450,plain,
( spl0_304
<=> ! [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_304])]) ).
fof(f1251,plain,
( spl0_76
<=> class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1869,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
| ~ spl0_76
| ~ spl0_197 ),
inference(resolution,[],[f1796,f1253]) ).
fof(f1253,plain,
( class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal)
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1251]) ).
fof(f2414,plain,
spl0_303,
inference(avatar_split_clause,[],[f708,f2412]) ).
fof(f708,axiom,
! [X4] : c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(X4,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,X4,tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f2410,plain,
spl0_302,
inference(avatar_split_clause,[],[f696,f2408]) ).
fof(f2408,plain,
( spl0_302
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X2 = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f696,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X2 = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f2406,plain,
spl0_301,
inference(avatar_split_clause,[],[f695,f2404]) ).
fof(f2404,plain,
( spl0_301
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X2 = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f695,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X2 = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X2,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f2402,plain,
spl0_300,
inference(avatar_split_clause,[],[f685,f2400]) ).
fof(f2400,plain,
( spl0_300
<=> ! [X4] : c_Polynomial_Opoly(v_q____,X4,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,c_HOL_Oplus__class_Oplus(v_c____,X4,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f685,axiom,
! [X4] : c_Polynomial_Opoly(v_q____,X4,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,c_HOL_Oplus__class_Oplus(v_c____,X4,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_q_I2_J_0) ).
fof(f2398,plain,
( spl0_299
| ~ spl0_109
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1868,f1795,f1416,f2396]) ).
fof(f2396,plain,
( spl0_299
<=> ! [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_299])]) ).
fof(f1416,plain,
( spl0_109
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1868,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_109
| ~ spl0_197 ),
inference(resolution,[],[f1796,f1418]) ).
fof(f1418,plain,
( class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1416]) ).
fof(f2394,plain,
spl0_298,
inference(avatar_split_clause,[],[f679,f2392]) ).
fof(f2392,plain,
( spl0_298
<=> ! [X4,X7] : c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(X4,X7,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(c_Complex_Ocnj(X4),c_Complex_Ocnj(X7),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f679,axiom,
! [X7,X4] : c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(X4,X7,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(c_Complex_Ocnj(X4),c_Complex_Ocnj(X7),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Odiff_0) ).
fof(f2390,plain,
spl0_297,
inference(avatar_split_clause,[],[f642,f2388]) ).
fof(f2388,plain,
( spl0_297
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f642,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X3,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
fof(f2386,plain,
spl0_296,
inference(avatar_split_clause,[],[f633,f2384]) ).
fof(f2384,plain,
( spl0_296
<=> ! [X2,X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f633,axiom,
! [X2,X3,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X3,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
fof(f2382,plain,
spl0_295,
inference(avatar_split_clause,[],[f632,f2380]) ).
fof(f2380,plain,
( spl0_295
<=> ! [X2,X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f632,axiom,
! [X2,X3,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
fof(f2378,plain,
spl0_294,
inference(avatar_split_clause,[],[f622,f2376]) ).
fof(f2376,plain,
( spl0_294
<=> ! [X9,X27,X28] :
( ~ c_lessequals(X27,X28,tc_RealDef_Oreal)
| ~ c_lessequals(X28,X9,tc_RealDef_Oreal)
| c_lessequals(X27,X9,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f622,axiom,
! [X28,X9,X27] :
( ~ c_lessequals(X27,X28,tc_RealDef_Oreal)
| ~ c_lessequals(X28,X9,tc_RealDef_Oreal)
| c_lessequals(X27,X9,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f2374,plain,
spl0_293,
inference(avatar_split_clause,[],[f608,f2372]) ).
fof(f2372,plain,
( spl0_293
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f608,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
fof(f2370,plain,
spl0_292,
inference(avatar_split_clause,[],[f601,f2368]) ).
fof(f2368,plain,
( spl0_292
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f601,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_1) ).
fof(f2366,plain,
spl0_291,
inference(avatar_split_clause,[],[f567,f2364]) ).
fof(f2364,plain,
( spl0_291
<=> ! [X9,X0,X21] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X21,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X21,c_HOL_Oabs__class_Oabs(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f567,axiom,
! [X21,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X21,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X21,c_HOL_Oabs__class_Oabs(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
fof(f2362,plain,
spl0_290,
inference(avatar_split_clause,[],[f566,f2360]) ).
fof(f2360,plain,
( spl0_290
<=> ! [X9,X0,X21] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X21,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X21,c_HOL_Oabs__class_Oabs(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f566,axiom,
! [X21,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X21,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X21,c_HOL_Oabs__class_Oabs(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
fof(f2358,plain,
spl0_289,
inference(avatar_split_clause,[],[f565,f2356]) ).
fof(f2356,plain,
( spl0_289
<=> ! [X9,X0,X21] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X21,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X21,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f565,axiom,
! [X21,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X21,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X21,X0),X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
fof(f2354,plain,
( spl0_288
| ~ spl0_27
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1867,f1791,f1006,f2352]) ).
fof(f2352,plain,
( spl0_288
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f1791,plain,
( spl0_196
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1867,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_27
| ~ spl0_196 ),
inference(resolution,[],[f1792,f1008]) ).
fof(f1792,plain,
( ! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 )
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f1791]) ).
fof(f2350,plain,
spl0_287,
inference(avatar_split_clause,[],[f564,f2348]) ).
fof(f2348,plain,
( spl0_287
<=> ! [X9,X0,X21] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X21,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X21,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f564,axiom,
! [X21,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X21,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X21,X0),X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
fof(f2346,plain,
spl0_286,
inference(avatar_split_clause,[],[f495,f2344]) ).
fof(f2344,plain,
( spl0_286
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f495,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
fof(f2342,plain,
spl0_285,
inference(avatar_split_clause,[],[f442,f2340]) ).
fof(f2340,plain,
( spl0_285
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f442,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
fof(f2338,plain,
spl0_284,
inference(avatar_split_clause,[],[f364,f2336]) ).
fof(f2336,plain,
( spl0_284
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X7,X4,X0)
| c_Orderings_Oord__class_Omax(X4,X7,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f364,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X7,X4,X0)
| c_Orderings_Oord__class_Omax(X4,X7,X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
fof(f2334,plain,
spl0_283,
inference(avatar_split_clause,[],[f363,f2332]) ).
fof(f2332,plain,
( spl0_283
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X7,X0)
| c_Orderings_Oord__class_Omax(X4,X7,X0) != X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f363,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X7,X0)
| c_Orderings_Oord__class_Omax(X4,X7,X0) != X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
fof(f2330,plain,
spl0_282,
inference(avatar_split_clause,[],[f339,f2328]) ).
fof(f2328,plain,
( spl0_282
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f339,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
fof(f2326,plain,
spl0_281,
inference(avatar_split_clause,[],[f295,f2324]) ).
fof(f2324,plain,
( spl0_281
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f295,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
fof(f2322,plain,
spl0_280,
inference(avatar_split_clause,[],[f262,f2320]) ).
fof(f2320,plain,
( spl0_280
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X4,X7,X0)
| c_Orderings_Oord__class_Omax(X4,X7,X0) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f262,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X4,X7,X0)
| c_Orderings_Oord__class_Omax(X4,X7,X0) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
fof(f2318,plain,
spl0_279,
inference(avatar_split_clause,[],[f259,f2316]) ).
fof(f2316,plain,
( spl0_279
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X7,X4,X0)
| c_Orderings_Oord__class_Omin(X4,X7,X0) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f259,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X7,X4,X0)
| c_Orderings_Oord__class_Omin(X4,X7,X0) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
fof(f2314,plain,
spl0_278,
inference(avatar_split_clause,[],[f258,f2312]) ).
fof(f2312,plain,
( spl0_278
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X7,X0)
| c_Orderings_Oord__class_Omin(X4,X7,X0) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f258,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X7,X0)
| c_Orderings_Oord__class_Omin(X4,X7,X0) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
fof(f2310,plain,
( spl0_277
| ~ spl0_76
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1865,f1791,f1251,f2308]) ).
fof(f2308,plain,
( spl0_277
<=> ! [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_277])]) ).
fof(f1865,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_76
| ~ spl0_196 ),
inference(resolution,[],[f1792,f1253]) ).
fof(f2306,plain,
spl0_276,
inference(avatar_split_clause,[],[f257,f2304]) ).
fof(f2304,plain,
( spl0_276
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X4,X7,X0)
| c_Orderings_Oord__class_Omin(X4,X7,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f257,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X4,X7,X0)
| c_Orderings_Oord__class_Omin(X4,X7,X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
fof(f2302,plain,
spl0_275,
inference(avatar_split_clause,[],[f215,f2300]) ).
fof(f2300,plain,
( spl0_275
<=> ! [X4,X0,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X4,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f215,axiom,
! [X0,X7,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X4,X0),X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
fof(f2298,plain,
spl0_274,
inference(avatar_split_clause,[],[f214,f2296]) ).
fof(f2296,plain,
( spl0_274
<=> ! [X4,X0,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X4,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f214,axiom,
! [X0,X7,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X4,X0),X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
fof(f2294,plain,
spl0_273,
inference(avatar_split_clause,[],[f213,f2292]) ).
fof(f2292,plain,
( spl0_273
<=> ! [X4,X0,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f213,axiom,
! [X0,X7,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
fof(f2290,plain,
spl0_272,
inference(avatar_split_clause,[],[f212,f2288]) ).
fof(f2288,plain,
( spl0_272
<=> ! [X4,X0,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f212,axiom,
! [X0,X7,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X4,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
fof(f2286,plain,
spl0_271,
inference(avatar_split_clause,[],[f117,f2284]) ).
fof(f2284,plain,
( spl0_271
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X2 = X3
| c_HOL_Ouminus__class_Ouminus(X3,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f117,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X2 = X3
| c_HOL_Ouminus__class_Ouminus(X3,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f2282,plain,
spl0_270,
inference(avatar_split_clause,[],[f105,f2280]) ).
fof(f2280,plain,
( spl0_270
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f105,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
fof(f2278,plain,
spl0_269,
inference(avatar_split_clause,[],[f64,f2276]) ).
fof(f2276,plain,
( spl0_269
<=> ! [X4,X7] : c_Complex_Ocnj(c_HOL_Oplus__class_Oplus(X4,X7,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Complex_Ocnj(X4),c_Complex_Ocnj(X7),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f64,axiom,
! [X7,X4] : c_Complex_Ocnj(c_HOL_Oplus__class_Oplus(X4,X7,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Complex_Ocnj(X4),c_Complex_Ocnj(X7),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Oadd_0) ).
fof(f2268,plain,
( spl0_268
| ~ spl0_109
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1864,f1791,f1416,f2266]) ).
fof(f2266,plain,
( spl0_268
<=> ! [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_268])]) ).
fof(f1864,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_109
| ~ spl0_196 ),
inference(resolution,[],[f1792,f1418]) ).
fof(f2234,plain,
( spl0_267
| ~ spl0_28
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1862,f1787,f1011,f2232]) ).
fof(f2232,plain,
( spl0_267
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f1011,plain,
( spl0_28
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1787,plain,
( spl0_195
<=> ! [X2,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f1862,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
| ~ spl0_28
| ~ spl0_195 ),
inference(resolution,[],[f1788,f1013]) ).
fof(f1013,plain,
( class_Divides_Osemiring__div(tc_nat)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f1011]) ).
fof(f1788,plain,
( ! [X2,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X2,X0) )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f1787]) ).
fof(f2201,plain,
( spl0_266
| ~ spl0_28
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1860,f1783,f1011,f2199]) ).
fof(f2199,plain,
( spl0_266
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f1783,plain,
( spl0_194
<=> ! [X2,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f1860,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_28
| ~ spl0_194 ),
inference(resolution,[],[f1784,f1013]) ).
fof(f1784,plain,
( ! [X2,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 )
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f1783]) ).
fof(f2180,plain,
spl0_265,
inference(avatar_split_clause,[],[f706,f2178]) ).
fof(f2178,plain,
( spl0_265
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X3,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f706,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X0),X3,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f2176,plain,
spl0_264,
inference(avatar_split_clause,[],[f692,f2174]) ).
fof(f2174,plain,
( spl0_264
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X0),X3,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f692,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X0),X3,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f2172,plain,
spl0_263,
inference(avatar_split_clause,[],[f691,f2170]) ).
fof(f2170,plain,
( spl0_263
<=> ! [X4,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f691,axiom,
! [X0,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f2168,plain,
spl0_262,
inference(avatar_split_clause,[],[f534,f2166]) ).
fof(f2166,plain,
( spl0_262
<=> ! [X4,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f534,axiom,
! [X0,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f2164,plain,
spl0_261,
inference(avatar_split_clause,[],[f478,f2162]) ).
fof(f2162,plain,
( spl0_261
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f478,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
fof(f2160,plain,
spl0_260,
inference(avatar_split_clause,[],[f477,f2158]) ).
fof(f2158,plain,
( spl0_260
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f477,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
fof(f2156,plain,
spl0_259,
inference(avatar_split_clause,[],[f476,f2154]) ).
fof(f2154,plain,
( spl0_259
<=> ! [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_259])]) ).
fof(f476,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/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
fof(f2152,plain,
spl0_258,
inference(avatar_split_clause,[],[f472,f2150]) ).
fof(f2150,plain,
( spl0_258
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X4,X7,X0) = c_Orderings_Oord__class_Omin(X7,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f472,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X4,X7,X0) = c_Orderings_Oord__class_Omin(X7,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
fof(f2148,plain,
spl0_257,
inference(avatar_split_clause,[],[f398,f2146]) ).
fof(f2146,plain,
( spl0_257
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,X3,X0) = c_HOL_Oplus__class_Oplus(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f398,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,X3,X0) = c_HOL_Oplus__class_Oplus(X3,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f2144,plain,
( spl0_256
| ~ spl0_39
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1858,f1775,f1066,f2141]) ).
fof(f2141,plain,
( spl0_256
<=> 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_256])]) ).
fof(f1066,plain,
( spl0_39
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1775,plain,
( spl0_192
<=> ! [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_192])]) ).
fof(f1858,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_39
| ~ spl0_192 ),
inference(resolution,[],[f1776,f1068]) ).
fof(f1068,plain,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f1066]) ).
fof(f1776,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_192 ),
inference(avatar_component_clause,[],[f1775]) ).
fof(f2139,plain,
spl0_255,
inference(avatar_split_clause,[],[f396,f2137]) ).
fof(f2137,plain,
( spl0_255
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X2,X1,X0) = c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f396,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X2,X1,X0) = c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f2135,plain,
spl0_254,
inference(avatar_split_clause,[],[f389,f2133]) ).
fof(f2133,plain,
( spl0_254
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_RealVector_Onorm__class_Onorm(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f389,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_RealVector_Onorm__class_Onorm(X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
fof(f2131,plain,
spl0_253,
inference(avatar_split_clause,[],[f385,f2129]) ).
fof(f2129,plain,
( spl0_253
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f385,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
fof(f2127,plain,
spl0_252,
inference(avatar_split_clause,[],[f356,f2125]) ).
fof(f2125,plain,
( spl0_252
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X4,c_Orderings_Oord__class_Omax(X4,X7,X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f356,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X4,c_Orderings_Oord__class_Omax(X4,X7,X0),X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
fof(f2123,plain,
spl0_251,
inference(avatar_split_clause,[],[f325,f2121]) ).
fof(f2121,plain,
( spl0_251
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X2,X3,X0) = c_HOL_Otimes__class_Otimes(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f325,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X2,X3,X0) = c_HOL_Otimes__class_Otimes(X3,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f2119,plain,
spl0_250,
inference(avatar_split_clause,[],[f324,f2117]) ).
fof(f2117,plain,
( spl0_250
<=> ! [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_250])]) ).
fof(f324,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f2115,plain,
spl0_249,
inference(avatar_split_clause,[],[f285,f2113]) ).
fof(f2113,plain,
( spl0_249
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f285,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
fof(f2111,plain,
spl0_248,
inference(avatar_split_clause,[],[f242,f2109]) ).
fof(f2109,plain,
( spl0_248
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f242,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
fof(f2107,plain,
spl0_247,
inference(avatar_split_clause,[],[f224,f2105]) ).
fof(f2105,plain,
( spl0_247
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f224,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
fof(f2103,plain,
spl0_246,
inference(avatar_split_clause,[],[f203,f2101]) ).
fof(f2101,plain,
( spl0_246
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f203,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
fof(f2099,plain,
spl0_245,
inference(avatar_split_clause,[],[f202,f2097]) ).
fof(f2097,plain,
( spl0_245
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X4,X7,X0) = c_Orderings_Oord__class_Omax(X7,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f202,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X4,X7,X0) = c_Orderings_Oord__class_Omax(X7,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
fof(f2095,plain,
spl0_244,
inference(avatar_split_clause,[],[f195,f2093]) ).
fof(f2093,plain,
( spl0_244
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X4,c_Orderings_Oord__class_Omin(X4,X7,X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f195,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X4,c_Orderings_Oord__class_Omin(X4,X7,X0),X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
fof(f2091,plain,
spl0_243,
inference(avatar_split_clause,[],[f169,f2089]) ).
fof(f2089,plain,
( spl0_243
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f169,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f2087,plain,
spl0_242,
inference(avatar_split_clause,[],[f115,f2085]) ).
fof(f2085,plain,
( spl0_242
<=> ! [X20,X8] :
( X8 = X20
| ~ c_lessequals(X8,X20,tc_RealDef_Oreal)
| ~ c_lessequals(X20,X8,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f115,axiom,
! [X8,X20] :
( X8 = X20
| ~ c_lessequals(X8,X20,tc_RealDef_Oreal)
| ~ c_lessequals(X20,X8,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f2076,plain,
( spl0_241
| ~ spl0_170
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2035,f1932,f1671,f2074]) ).
fof(f2074,plain,
( spl0_241
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f1671,plain,
( spl0_170
<=> ! [X4,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1932,plain,
( spl0_218
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X7,X4,X0)
| c_HOL_Oord__class_Oless(X4,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2035,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_170
| ~ spl0_218 ),
inference(duplicate_literal_removal,[],[f2031]) ).
fof(f2031,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_170
| ~ spl0_218 ),
inference(resolution,[],[f1933,f1672]) ).
fof(f1672,plain,
( ! [X0,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X4,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1671]) ).
fof(f1933,plain,
( ! [X0,X7,X4] :
( c_HOL_Oord__class_Oless(X4,X7,X0)
| c_lessequals(X7,X4,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f1932]) ).
fof(f2026,plain,
( ~ spl0_31
| spl0_240
| ~ spl0_184
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1876,f1751,f1737,f2024,f1026]) ).
fof(f1026,plain,
( spl0_31
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f2024,plain,
( spl0_240
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f1737,plain,
( spl0_184
<=> ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1751,plain,
( spl0_186
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X7,c_Orderings_Oord__class_Omax(X4,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f1876,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_184
| ~ spl0_186 ),
inference(superposition,[],[f1752,f1738]) ).
fof(f1738,plain,
( ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1737]) ).
fof(f1752,plain,
( ! [X0,X7,X4] :
( c_lessequals(X7,c_Orderings_Oord__class_Omax(X4,X7,X0),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f1751]) ).
fof(f2022,plain,
spl0_239,
inference(avatar_split_clause,[],[f662,f2020]) ).
fof(f2020,plain,
( spl0_239
<=> ! [X2,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f662,axiom,
! [X2,X3,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f2018,plain,
spl0_238,
inference(avatar_split_clause,[],[f661,f2016]) ).
fof(f2016,plain,
( spl0_238
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X7,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f661,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X7,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f2014,plain,
spl0_237,
inference(avatar_split_clause,[],[f659,f2012]) ).
fof(f2012,plain,
( spl0_237
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X7,X0)
| c_lessequals(X7,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f659,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X7,X0)
| c_lessequals(X7,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f2010,plain,
spl0_236,
inference(avatar_split_clause,[],[f657,f2008]) ).
fof(f2008,plain,
( spl0_236
<=> ! [X2,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f657,axiom,
! [X2,X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f2006,plain,
spl0_235,
inference(avatar_split_clause,[],[f609,f2004]) ).
fof(f2004,plain,
( spl0_235
<=> ! [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_235])]) ).
fof(f609,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
fof(f2002,plain,
spl0_234,
inference(avatar_split_clause,[],[f577,f2000]) ).
fof(f2000,plain,
( spl0_234
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X7,X0)
| c_lessequals(X4,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f577,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X7,X0)
| c_lessequals(X4,X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1998,plain,
spl0_233,
inference(avatar_split_clause,[],[f576,f1996]) ).
fof(f1996,plain,
( spl0_233
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X7,X0)
| c_lessequals(X4,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f576,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X7,X0)
| c_lessequals(X4,X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1994,plain,
spl0_232,
inference(avatar_split_clause,[],[f486,f1992]) ).
fof(f1992,plain,
( spl0_232
<=> ! [X0,X7] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f486,axiom,
! [X0,X7] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
fof(f1990,plain,
spl0_231,
inference(avatar_split_clause,[],[f483,f1988]) ).
fof(f1988,plain,
( spl0_231
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f483,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
fof(f1984,plain,
spl0_230,
inference(avatar_split_clause,[],[f474,f1982]) ).
fof(f1982,plain,
( spl0_230
<=> ! [X2,X0] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f474,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_2) ).
fof(f1980,plain,
spl0_229,
inference(avatar_split_clause,[],[f473,f1978]) ).
fof(f1978,plain,
( spl0_229
<=> ! [X2,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f473,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ozero__right_0) ).
fof(f1976,plain,
spl0_228,
inference(avatar_split_clause,[],[f462,f1974]) ).
fof(f1974,plain,
( spl0_228
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f462,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f1972,plain,
spl0_227,
inference(avatar_split_clause,[],[f461,f1970]) ).
fof(f1970,plain,
( spl0_227
<=> ! [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_227])]) ).
fof(f461,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/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f1968,plain,
spl0_226,
inference(avatar_split_clause,[],[f460,f1966]) ).
fof(f1966,plain,
( spl0_226
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f460,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f1964,plain,
spl0_225,
inference(avatar_split_clause,[],[f459,f1962]) ).
fof(f1962,plain,
( spl0_225
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f459,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f1960,plain,
spl0_224,
inference(avatar_split_clause,[],[f456,f1958]) ).
fof(f1958,plain,
( spl0_224
<=> ! [X2,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f456,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
fof(f1956,plain,
spl0_223,
inference(avatar_split_clause,[],[f455,f1954]) ).
fof(f1954,plain,
( spl0_223
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f455,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
fof(f1952,plain,
spl0_222,
inference(avatar_split_clause,[],[f453,f1950]) ).
fof(f1950,plain,
( spl0_222
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f453,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f1948,plain,
spl0_221,
inference(avatar_split_clause,[],[f452,f1946]) ).
fof(f1946,plain,
( spl0_221
<=> ! [X2,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),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f452,axiom,
! [X2,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),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f1942,plain,
spl0_220,
inference(avatar_split_clause,[],[f422,f1940]) ).
fof(f1940,plain,
( spl0_220
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f422,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
fof(f1938,plain,
spl0_219,
inference(avatar_split_clause,[],[f348,f1936]) ).
fof(f1936,plain,
( spl0_219
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X4,X7,X0)
| ~ c_HOL_Oord__class_Oless(X7,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f348,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X4,X7,X0)
| ~ c_HOL_Oord__class_Oless(X7,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f1934,plain,
spl0_218,
inference(avatar_split_clause,[],[f346,f1932]) ).
fof(f346,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X7,X4,X0)
| c_HOL_Oord__class_Oless(X4,X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
fof(f1930,plain,
spl0_217,
inference(avatar_split_clause,[],[f341,f1928]) ).
fof(f1928,plain,
( spl0_217
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X7,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f341,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X7,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1926,plain,
spl0_216,
inference(avatar_split_clause,[],[f314,f1924]) ).
fof(f1924,plain,
( spl0_216
<=> ! [X2,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f314,axiom,
! [X2,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).
fof(f1922,plain,
spl0_215,
inference(avatar_split_clause,[],[f237,f1920]) ).
fof(f1920,plain,
( spl0_215
<=> ! [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_215])]) ).
fof(f237,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
fof(f1918,plain,
spl0_214,
inference(avatar_split_clause,[],[f229,f1916]) ).
fof(f1916,plain,
( spl0_214
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f229,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f1914,plain,
spl0_213,
inference(avatar_split_clause,[],[f41,f1912]) ).
fof(f1912,plain,
( spl0_213
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f41,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
fof(f1857,plain,
( spl0_212
| ~ spl0_86
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1733,f1710,f1301,f1855]) ).
fof(f1855,plain,
( spl0_212
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1301,plain,
( spl0_86
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1710,plain,
( spl0_179
<=> ! [X4,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X4,X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1733,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_RealDef_Oreal) = X0
| ~ spl0_86
| ~ spl0_179 ),
inference(resolution,[],[f1711,f1303]) ).
fof(f1303,plain,
( class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f1301]) ).
fof(f1711,plain,
( ! [X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X4,X4,X0) = X4 )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1710]) ).
fof(f1853,plain,
spl0_211,
inference(avatar_split_clause,[],[f690,f1851]) ).
fof(f1851,plain,
( spl0_211
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f690,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
fof(f1849,plain,
spl0_210,
inference(avatar_split_clause,[],[f689,f1847]) ).
fof(f1847,plain,
( spl0_210
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f689,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f1845,plain,
spl0_209,
inference(avatar_split_clause,[],[f687,f1843]) ).
fof(f1843,plain,
( spl0_209
<=> ! [X4,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f687,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f1841,plain,
spl0_208,
inference(avatar_split_clause,[],[f652,f1839]) ).
fof(f1839,plain,
( spl0_208
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f652,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
fof(f1837,plain,
spl0_207,
inference(avatar_split_clause,[],[f596,f1835]) ).
fof(f1835,plain,
( spl0_207
<=> ! [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_207])]) ).
fof(f596,axiom,
! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
fof(f1833,plain,
spl0_206,
inference(avatar_split_clause,[],[f595,f1831]) ).
fof(f1831,plain,
( spl0_206
<=> ! [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_206])]) ).
fof(f595,axiom,
! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
fof(f1829,plain,
spl0_205,
inference(avatar_split_clause,[],[f591,f1827]) ).
fof(f1827,plain,
( spl0_205
<=> ! [X8] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X8
| c_Complex_Ocnj(X8) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f591,axiom,
! [X8] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X8
| c_Complex_Ocnj(X8) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__zero__iff_0) ).
fof(f1825,plain,
( spl0_204
| ~ spl0_31
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1732,f1710,f1026,f1823]) ).
fof(f1823,plain,
( spl0_204
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f1732,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0
| ~ spl0_31
| ~ spl0_179 ),
inference(resolution,[],[f1711,f1028]) ).
fof(f1028,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f1026]) ).
fof(f1821,plain,
spl0_203,
inference(avatar_split_clause,[],[f585,f1819]) ).
fof(f1819,plain,
( spl0_203
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f585,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
fof(f1817,plain,
spl0_202,
inference(avatar_split_clause,[],[f549,f1815]) ).
fof(f549,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
fof(f1813,plain,
spl0_201,
inference(avatar_split_clause,[],[f538,f1811]) ).
fof(f1811,plain,
( spl0_201
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f538,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f1809,plain,
spl0_200,
inference(avatar_split_clause,[],[f537,f1807]) ).
fof(f1807,plain,
( spl0_200
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f537,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1805,plain,
spl0_199,
inference(avatar_split_clause,[],[f536,f1803]) ).
fof(f1803,plain,
( spl0_199
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f536,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1801,plain,
spl0_198,
inference(avatar_split_clause,[],[f533,f1799]) ).
fof(f1799,plain,
( spl0_198
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f533,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1797,plain,
spl0_197,
inference(avatar_split_clause,[],[f532,f1795]) ).
fof(f532,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1793,plain,
spl0_196,
inference(avatar_split_clause,[],[f531,f1791]) ).
fof(f531,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1789,plain,
spl0_195,
inference(avatar_split_clause,[],[f395,f1787]) ).
fof(f395,axiom,
! [X2,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).
fof(f1785,plain,
spl0_194,
inference(avatar_split_clause,[],[f394,f1783]) ).
fof(f394,axiom,
! [X2,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
fof(f1781,plain,
( spl0_193
| ~ spl0_86
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1730,f1706,f1301,f1779]) ).
fof(f1779,plain,
( spl0_193
<=> ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1706,plain,
( spl0_178
<=> ! [X4,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X4,X4,X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1730,plain,
( ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_RealDef_Oreal) = X0
| ~ spl0_86
| ~ spl0_178 ),
inference(resolution,[],[f1707,f1303]) ).
fof(f1707,plain,
( ! [X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X4,X4,X0) = X4 )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1706]) ).
fof(f1777,plain,
spl0_192,
inference(avatar_split_clause,[],[f329,f1775]) ).
fof(f329,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
fof(f1773,plain,
spl0_191,
inference(avatar_split_clause,[],[f309,f1771]) ).
fof(f1771,plain,
( spl0_191
<=> ! [X9,X0,X3] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f309,axiom,
! [X3,X0,X9] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X3,X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvdI_0) ).
fof(f1769,plain,
spl0_190,
inference(avatar_split_clause,[],[f308,f1767]) ).
fof(f1767,plain,
( spl0_190
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f308,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
fof(f1765,plain,
spl0_189,
inference(avatar_split_clause,[],[f307,f1763]) ).
fof(f1763,plain,
( spl0_189
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f307,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
fof(f1761,plain,
spl0_188,
inference(avatar_split_clause,[],[f304,f1759]) ).
fof(f1759,plain,
( spl0_188
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X4,X7,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f304,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X4,X7,X0),X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
fof(f1757,plain,
spl0_187,
inference(avatar_split_clause,[],[f303,f1755]) ).
fof(f1755,plain,
( spl0_187
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X4,X7,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f303,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X4,X7,X0),X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
fof(f1753,plain,
spl0_186,
inference(avatar_split_clause,[],[f290,f1751]) ).
fof(f290,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X7,c_Orderings_Oord__class_Omax(X4,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
fof(f1749,plain,
spl0_185,
inference(avatar_split_clause,[],[f289,f1747]) ).
fof(f1747,plain,
( spl0_185
<=> ! [X4,X0,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,c_Orderings_Oord__class_Omax(X4,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f289,axiom,
! [X0,X7,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,c_Orderings_Oord__class_Omax(X4,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
fof(f1739,plain,
( spl0_184
| ~ spl0_31
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1729,f1706,f1026,f1737]) ).
fof(f1729,plain,
( ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0
| ~ spl0_31
| ~ spl0_178 ),
inference(resolution,[],[f1707,f1028]) ).
fof(f1728,plain,
spl0_183,
inference(avatar_split_clause,[],[f660,f1726]) ).
fof(f1726,plain,
( spl0_183
<=> ! [X20,X8] :
( c_lessequals(X8,X20,tc_RealDef_Oreal)
| c_lessequals(X20,X8,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f660,axiom,
! [X8,X20] :
( c_lessequals(X8,X20,tc_RealDef_Oreal)
| c_lessequals(X20,X8,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
fof(f1724,plain,
spl0_182,
inference(avatar_split_clause,[],[f592,f1722]) ).
fof(f1722,plain,
( spl0_182
<=> ! [X4,X7] :
( X4 = X7
| c_Complex_Ocnj(X4) != c_Complex_Ocnj(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f592,axiom,
! [X7,X4] :
( X4 = X7
| c_Complex_Ocnj(X4) != c_Complex_Ocnj(X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
fof(f1720,plain,
spl0_181,
inference(avatar_split_clause,[],[f423,f1718]) ).
fof(f1718,plain,
( spl0_181
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f423,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
fof(f1716,plain,
spl0_180,
inference(avatar_split_clause,[],[f306,f1714]) ).
fof(f1714,plain,
( spl0_180
<=> ! [X8] : c_RealVector_Onorm__class_Onorm(c_Complex_Ocnj(X8),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(X8,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f306,axiom,
! [X8] : c_RealVector_Onorm__class_Onorm(c_Complex_Ocnj(X8),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(X8,tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__mod__cnj_0) ).
fof(f1712,plain,
spl0_179,
inference(avatar_split_clause,[],[f123,f1710]) ).
fof(f123,axiom,
! [X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X4,X4,X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
fof(f1708,plain,
spl0_178,
inference(avatar_split_clause,[],[f106,f1706]) ).
fof(f106,axiom,
! [X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X4,X4,X0) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
fof(f1704,plain,
~ spl0_177,
inference(avatar_split_clause,[],[f705,f1701]) ).
fof(f1701,plain,
( spl0_177
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f705,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pc0_0) ).
fof(f1699,plain,
spl0_176,
inference(avatar_split_clause,[],[f672,f1696]) ).
fof(f1696,plain,
( spl0_176
<=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_q____,tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_pa____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f672,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_q____,tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_pa____,tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_q_I1_J_0) ).
fof(f1694,plain,
spl0_175,
inference(avatar_split_clause,[],[f448,f1692]) ).
fof(f1692,plain,
( spl0_175
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f448,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
fof(f1689,plain,
spl0_174,
inference(avatar_split_clause,[],[f621,f1687]) ).
fof(f1687,plain,
( spl0_174
<=> ! [X4,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f621,axiom,
! [X0,X4] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1685,plain,
spl0_173,
inference(avatar_split_clause,[],[f620,f1683]) ).
fof(f1683,plain,
( spl0_173
<=> ! [X4,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f620,axiom,
! [X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1681,plain,
spl0_172,
inference(avatar_split_clause,[],[f570,f1679]) ).
fof(f1679,plain,
( spl0_172
<=> ! [X4,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f570,axiom,
! [X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1677,plain,
spl0_171,
inference(avatar_split_clause,[],[f569,f1675]) ).
fof(f1675,plain,
( spl0_171
<=> ! [X4,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f569,axiom,
! [X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1673,plain,
spl0_170,
inference(avatar_split_clause,[],[f568,f1671]) ).
fof(f568,axiom,
! [X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1669,plain,
spl0_169,
inference(avatar_split_clause,[],[f321,f1666]) ).
fof(f1666,plain,
( spl0_169
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f321,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Ozero_0) ).
fof(f1664,plain,
spl0_168,
inference(avatar_split_clause,[],[f104,f1662]) ).
fof(f1662,plain,
( spl0_168
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f104,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
fof(f1660,plain,
spl0_167,
inference(avatar_split_clause,[],[f873,f1658]) ).
fof(f1658,plain,
( spl0_167
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f873,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(f1656,plain,
spl0_166,
inference(avatar_split_clause,[],[f872,f1654]) ).
fof(f1654,plain,
( spl0_166
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f872,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Oorder) ).
fof(f1652,plain,
spl0_165,
inference(avatar_split_clause,[],[f871,f1650]) ).
fof(f1650,plain,
( spl0_165
<=> ! [X34] :
( ~ class_Ring__and__Field_Ofield(X34)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f871,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ofield(X34)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Oring__div) ).
fof(f1648,plain,
spl0_164,
inference(avatar_split_clause,[],[f870,f1646]) ).
fof(f1646,plain,
( spl0_164
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f870,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(f1644,plain,
spl0_163,
inference(avatar_split_clause,[],[f869,f1642]) ).
fof(f1642,plain,
( spl0_163
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f869,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(f1640,plain,
spl0_162,
inference(avatar_split_clause,[],[f868,f1638]) ).
fof(f1638,plain,
( spl0_162
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f868,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).
fof(f1636,plain,
spl0_161,
inference(avatar_split_clause,[],[f867,f1634]) ).
fof(f1634,plain,
( spl0_161
<=> ! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f867,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
fof(f1632,plain,
spl0_160,
inference(avatar_split_clause,[],[f866,f1630]) ).
fof(f1630,plain,
( spl0_160
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring(X34)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f866,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring(X34)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
fof(f1628,plain,
spl0_159,
inference(avatar_split_clause,[],[f865,f1626]) ).
fof(f1626,plain,
( spl0_159
<=> ! [X34] :
( ~ class_Ring__and__Field_Ofield(X34)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f865,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ofield(X34)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(f1624,plain,
spl0_158,
inference(avatar_split_clause,[],[f864,f1622]) ).
fof(f1622,plain,
( spl0_158
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f864,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if) ).
fof(f1620,plain,
spl0_157,
inference(avatar_split_clause,[],[f863,f1618]) ).
fof(f1618,plain,
( spl0_157
<=> ! [X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f863,axiom,
! [X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
fof(f1616,plain,
spl0_156,
inference(avatar_split_clause,[],[f862,f1614]) ).
fof(f1614,plain,
( spl0_156
<=> ! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f862,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
fof(f1612,plain,
spl0_155,
inference(avatar_split_clause,[],[f861,f1610]) ).
fof(f1610,plain,
( spl0_155
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f861,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
fof(f1608,plain,
spl0_154,
inference(avatar_split_clause,[],[f860,f1606]) ).
fof(f1606,plain,
( spl0_154
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring(X34)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f860,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring(X34)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
fof(f1604,plain,
spl0_153,
inference(avatar_split_clause,[],[f859,f1602]) ).
fof(f1602,plain,
( spl0_153
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f859,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).
fof(f1600,plain,
spl0_152,
inference(avatar_split_clause,[],[f858,f1598]) ).
fof(f1598,plain,
( spl0_152
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f858,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
fof(f1596,plain,
spl0_151,
inference(avatar_split_clause,[],[f857,f1594]) ).
fof(f1594,plain,
( spl0_151
<=> ! [X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f857,axiom,
! [X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
fof(f1592,plain,
spl0_150,
inference(avatar_split_clause,[],[f856,f1590]) ).
fof(f1590,plain,
( spl0_150
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f856,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).
fof(f1588,plain,
spl0_149,
inference(avatar_split_clause,[],[f855,f1586]) ).
fof(f1586,plain,
( spl0_149
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f855,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
fof(f1584,plain,
spl0_148,
inference(avatar_split_clause,[],[f854,f1582]) ).
fof(f1582,plain,
( spl0_148
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f854,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
fof(f1580,plain,
spl0_147,
inference(avatar_split_clause,[],[f853,f1578]) ).
fof(f1578,plain,
( spl0_147
<=> ! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f853,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
fof(f1576,plain,
spl0_146,
inference(avatar_split_clause,[],[f852,f1574]) ).
fof(f1574,plain,
( spl0_146
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f852,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
fof(f1572,plain,
spl0_145,
inference(avatar_split_clause,[],[f851,f1570]) ).
fof(f1570,plain,
( spl0_145
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f851,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).
fof(f1568,plain,
spl0_144,
inference(avatar_split_clause,[],[f850,f1566]) ).
fof(f1566,plain,
( spl0_144
<=> ! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f850,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
fof(f1564,plain,
spl0_143,
inference(avatar_split_clause,[],[f849,f1562]) ).
fof(f1562,plain,
( spl0_143
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f849,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
fof(f1560,plain,
spl0_142,
inference(avatar_split_clause,[],[f848,f1558]) ).
fof(f1558,plain,
( spl0_142
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f848,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1556,plain,
spl0_141,
inference(avatar_split_clause,[],[f847,f1554]) ).
fof(f1554,plain,
( spl0_141
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f847,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1552,plain,
spl0_140,
inference(avatar_split_clause,[],[f846,f1550]) ).
fof(f1550,plain,
( spl0_140
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f846,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).
fof(f1548,plain,
spl0_139,
inference(avatar_split_clause,[],[f845,f1546]) ).
fof(f1546,plain,
( spl0_139
<=> ! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f845,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
fof(f1544,plain,
spl0_138,
inference(avatar_split_clause,[],[f844,f1542]) ).
fof(f1542,plain,
( spl0_138
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f844,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).
fof(f1540,plain,
spl0_137,
inference(avatar_split_clause,[],[f843,f1538]) ).
fof(f1538,plain,
( spl0_137
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f843,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs) ).
fof(f1536,plain,
spl0_136,
inference(avatar_split_clause,[],[f842,f1534]) ).
fof(f1534,plain,
( spl0_136
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f842,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).
fof(f1532,plain,
spl0_135,
inference(avatar_split_clause,[],[f841,f1530]) ).
fof(f1530,plain,
( spl0_135
<=> ! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f841,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1528,plain,
spl0_134,
inference(avatar_split_clause,[],[f840,f1526]) ).
fof(f1526,plain,
( spl0_134
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f840,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
fof(f1524,plain,
spl0_133,
inference(avatar_split_clause,[],[f839,f1522]) ).
fof(f1522,plain,
( spl0_133
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f839,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
fof(f1520,plain,
spl0_132,
inference(avatar_split_clause,[],[f838,f1518]) ).
fof(f1518,plain,
( spl0_132
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f838,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
fof(f1516,plain,
spl0_131,
inference(avatar_split_clause,[],[f837,f1514]) ).
fof(f1514,plain,
( spl0_131
<=> ! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f837,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1512,plain,
spl0_130,
inference(avatar_split_clause,[],[f836,f1510]) ).
fof(f1510,plain,
( spl0_130
<=> ! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f836,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1508,plain,
spl0_129,
inference(avatar_split_clause,[],[f835,f1506]) ).
fof(f1506,plain,
( spl0_129
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f835,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1504,plain,
spl0_128,
inference(avatar_split_clause,[],[f834,f1502]) ).
fof(f1502,plain,
( spl0_128
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f834,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f1500,plain,
spl0_127,
inference(avatar_split_clause,[],[f833,f1498]) ).
fof(f1498,plain,
( spl0_127
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f833,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1496,plain,
spl0_126,
inference(avatar_split_clause,[],[f832,f1494]) ).
fof(f1494,plain,
( spl0_126
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f832,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1492,plain,
spl0_125,
inference(avatar_split_clause,[],[f831,f1490]) ).
fof(f1490,plain,
( spl0_125
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f831,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1488,plain,
spl0_124,
inference(avatar_split_clause,[],[f830,f1486]) ).
fof(f1486,plain,
( spl0_124
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f830,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1484,plain,
spl0_123,
inference(avatar_split_clause,[],[f829,f1482]) ).
fof(f1482,plain,
( spl0_123
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f829,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1480,plain,
spl0_122,
inference(avatar_split_clause,[],[f828,f1478]) ).
fof(f1478,plain,
( spl0_122
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f828,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1476,plain,
spl0_121,
inference(avatar_split_clause,[],[f710,f1474]) ).
fof(f1474,plain,
( spl0_121
<=> ! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f710,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f1472,plain,
spl0_120,
inference(avatar_split_clause,[],[f390,f1470]) ).
fof(f1470,plain,
( spl0_120
<=> ! [X8] : c_Complex_Ocnj(c_Complex_Ocnj(X8)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f390,axiom,
! [X8] : c_Complex_Ocnj(c_Complex_Ocnj(X8)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
fof(f1468,plain,
spl0_119,
inference(avatar_split_clause,[],[f623,f1466]) ).
fof(f1466,plain,
( spl0_119
<=> ! [X20] : c_lessequals(X20,X20,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f623,axiom,
! [X20] : c_lessequals(X20,X20,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
fof(f1464,plain,
~ spl0_118,
inference(avatar_split_clause,[],[f709,f1461]) ).
fof(f709,axiom,
c_Polynomial_Opoly(v_pa____,v_x____,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(v_x____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1459,plain,
spl0_117,
inference(avatar_split_clause,[],[f827,f1456]) ).
fof(f1456,plain,
( spl0_117
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f827,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f1454,plain,
spl0_116,
inference(avatar_split_clause,[],[f826,f1451]) ).
fof(f1451,plain,
( spl0_116
<=> class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f826,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
fof(f1449,plain,
spl0_115,
inference(avatar_split_clause,[],[f825,f1446]) ).
fof(f1446,plain,
( spl0_115
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f825,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f1444,plain,
spl0_114,
inference(avatar_split_clause,[],[f824,f1441]) ).
fof(f1441,plain,
( spl0_114
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f824,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(f1439,plain,
spl0_113,
inference(avatar_split_clause,[],[f823,f1436]) ).
fof(f1436,plain,
( spl0_113
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f823,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f1434,plain,
spl0_112,
inference(avatar_split_clause,[],[f822,f1431]) ).
fof(f1431,plain,
( spl0_112
<=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f822,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(f1429,plain,
spl0_111,
inference(avatar_split_clause,[],[f821,f1426]) ).
fof(f1426,plain,
( spl0_111
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f821,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(f1424,plain,
spl0_110,
inference(avatar_split_clause,[],[f820,f1421]) ).
fof(f1421,plain,
( spl0_110
<=> class_RealVector_Oreal__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f820,axiom,
class_RealVector_Oreal__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__vector) ).
fof(f1419,plain,
spl0_109,
inference(avatar_split_clause,[],[f819,f1416]) ).
fof(f819,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(f1414,plain,
spl0_108,
inference(avatar_split_clause,[],[f818,f1411]) ).
fof(f1411,plain,
( spl0_108
<=> class_RealVector_Oreal__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f818,axiom,
class_RealVector_Oreal__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra) ).
fof(f1409,plain,
spl0_107,
inference(avatar_split_clause,[],[f817,f1406]) ).
fof(f1406,plain,
( spl0_107
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f817,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(f1404,plain,
spl0_106,
inference(avatar_split_clause,[],[f816,f1401]) ).
fof(f1401,plain,
( spl0_106
<=> class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f816,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
fof(f1399,plain,
spl0_105,
inference(avatar_split_clause,[],[f815,f1396]) ).
fof(f1396,plain,
( spl0_105
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f815,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
fof(f1394,plain,
spl0_104,
inference(avatar_split_clause,[],[f814,f1391]) ).
fof(f1391,plain,
( spl0_104
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f814,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f1389,plain,
spl0_103,
inference(avatar_split_clause,[],[f813,f1386]) ).
fof(f1386,plain,
( spl0_103
<=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f813,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
fof(f1384,plain,
spl0_102,
inference(avatar_split_clause,[],[f812,f1381]) ).
fof(f1381,plain,
( spl0_102
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f812,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f1379,plain,
spl0_101,
inference(avatar_split_clause,[],[f811,f1376]) ).
fof(f1376,plain,
( spl0_101
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f811,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f1374,plain,
spl0_100,
inference(avatar_split_clause,[],[f810,f1371]) ).
fof(f1371,plain,
( spl0_100
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f810,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
fof(f1369,plain,
spl0_99,
inference(avatar_split_clause,[],[f809,f1366]) ).
fof(f1366,plain,
( spl0_99
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f809,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(f1364,plain,
spl0_98,
inference(avatar_split_clause,[],[f808,f1361]) ).
fof(f1361,plain,
( spl0_98
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f808,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1359,plain,
spl0_97,
inference(avatar_split_clause,[],[f807,f1356]) ).
fof(f1356,plain,
( spl0_97
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f807,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f1354,plain,
spl0_96,
inference(avatar_split_clause,[],[f806,f1351]) ).
fof(f1351,plain,
( spl0_96
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f806,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1349,plain,
spl0_95,
inference(avatar_split_clause,[],[f805,f1346]) ).
fof(f1346,plain,
( spl0_95
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f805,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1344,plain,
spl0_94,
inference(avatar_split_clause,[],[f804,f1341]) ).
fof(f1341,plain,
( spl0_94
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f804,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1339,plain,
spl0_93,
inference(avatar_split_clause,[],[f803,f1336]) ).
fof(f1336,plain,
( spl0_93
<=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f803,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
fof(f1334,plain,
spl0_92,
inference(avatar_split_clause,[],[f802,f1331]) ).
fof(f1331,plain,
( spl0_92
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f802,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
fof(f1329,plain,
spl0_91,
inference(avatar_split_clause,[],[f801,f1326]) ).
fof(f1326,plain,
( spl0_91
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f801,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1324,plain,
spl0_90,
inference(avatar_split_clause,[],[f800,f1321]) ).
fof(f1321,plain,
( spl0_90
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f800,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1319,plain,
spl0_89,
inference(avatar_split_clause,[],[f799,f1316]) ).
fof(f1316,plain,
( spl0_89
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f799,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1314,plain,
spl0_88,
inference(avatar_split_clause,[],[f798,f1311]) ).
fof(f1311,plain,
( spl0_88
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f798,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f1309,plain,
spl0_87,
inference(avatar_split_clause,[],[f797,f1306]) ).
fof(f1306,plain,
( spl0_87
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f797,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
fof(f1304,plain,
spl0_86,
inference(avatar_split_clause,[],[f796,f1301]) ).
fof(f796,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f1299,plain,
spl0_85,
inference(avatar_split_clause,[],[f795,f1296]) ).
fof(f1296,plain,
( spl0_85
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f795,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f1294,plain,
spl0_84,
inference(avatar_split_clause,[],[f794,f1291]) ).
fof(f1291,plain,
( spl0_84
<=> class_Ring__and__Field_Odvd(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f794,axiom,
class_Ring__and__Field_Odvd(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odvd) ).
fof(f1289,plain,
spl0_83,
inference(avatar_split_clause,[],[f793,f1286]) ).
fof(f1286,plain,
( spl0_83
<=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f793,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
fof(f1284,plain,
spl0_82,
inference(avatar_split_clause,[],[f792,f1281]) ).
fof(f1281,plain,
( spl0_82
<=> class_Ring__and__Field_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f792,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
fof(f1279,plain,
spl0_81,
inference(avatar_split_clause,[],[f791,f1276]) ).
fof(f1276,plain,
( spl0_81
<=> class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f791,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
fof(f1274,plain,
spl0_80,
inference(avatar_split_clause,[],[f790,f1271]) ).
fof(f1271,plain,
( spl0_80
<=> class_RealVector_Oreal__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f790,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__field) ).
fof(f1269,plain,
spl0_79,
inference(avatar_split_clause,[],[f789,f1266]) ).
fof(f1266,plain,
( spl0_79
<=> class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f789,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).
fof(f1264,plain,
spl0_78,
inference(avatar_split_clause,[],[f788,f1261]) ).
fof(f788,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f1259,plain,
spl0_77,
inference(avatar_split_clause,[],[f787,f1256]) ).
fof(f1256,plain,
( spl0_77
<=> class_RealVector_Oreal__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f787,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__vector) ).
fof(f1254,plain,
spl0_76,
inference(avatar_split_clause,[],[f786,f1251]) ).
fof(f786,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
fof(f1249,plain,
spl0_75,
inference(avatar_split_clause,[],[f785,f1246]) ).
fof(f1246,plain,
( spl0_75
<=> class_RealVector_Oreal__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f785,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra) ).
fof(f1244,plain,
spl0_74,
inference(avatar_split_clause,[],[f784,f1241]) ).
fof(f1241,plain,
( spl0_74
<=> class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f784,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
fof(f1239,plain,
spl0_73,
inference(avatar_split_clause,[],[f783,f1236]) ).
fof(f1236,plain,
( spl0_73
<=> class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f783,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring) ).
fof(f1234,plain,
spl0_72,
inference(avatar_split_clause,[],[f782,f1231]) ).
fof(f1231,plain,
( spl0_72
<=> class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f782,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) ).
fof(f1229,plain,
spl0_71,
inference(avatar_split_clause,[],[f781,f1226]) ).
fof(f1226,plain,
( spl0_71
<=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f781,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
fof(f1224,plain,
spl0_70,
inference(avatar_split_clause,[],[f780,f1221]) ).
fof(f1221,plain,
( spl0_70
<=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f780,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
fof(f1219,plain,
spl0_69,
inference(avatar_split_clause,[],[f779,f1216]) ).
fof(f1216,plain,
( spl0_69
<=> class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f779,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).
fof(f1214,plain,
spl0_68,
inference(avatar_split_clause,[],[f778,f1211]) ).
fof(f1211,plain,
( spl0_68
<=> class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f778,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) ).
fof(f1209,plain,
spl0_67,
inference(avatar_split_clause,[],[f777,f1206]) ).
fof(f1206,plain,
( spl0_67
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f777,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
fof(f1204,plain,
spl0_66,
inference(avatar_split_clause,[],[f776,f1201]) ).
fof(f1201,plain,
( spl0_66
<=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f776,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
fof(f1199,plain,
spl0_65,
inference(avatar_split_clause,[],[f775,f1196]) ).
fof(f1196,plain,
( spl0_65
<=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f775,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(f1194,plain,
spl0_64,
inference(avatar_split_clause,[],[f774,f1191]) ).
fof(f1191,plain,
( spl0_64
<=> class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f774,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
fof(f1189,plain,
spl0_63,
inference(avatar_split_clause,[],[f773,f1186]) ).
fof(f1186,plain,
( spl0_63
<=> class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f773,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) ).
fof(f1184,plain,
spl0_62,
inference(avatar_split_clause,[],[f772,f1181]) ).
fof(f1181,plain,
( spl0_62
<=> class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f772,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
fof(f1179,plain,
spl0_61,
inference(avatar_split_clause,[],[f771,f1176]) ).
fof(f1176,plain,
( spl0_61
<=> class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f771,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) ).
fof(f1174,plain,
spl0_60,
inference(avatar_split_clause,[],[f770,f1171]) ).
fof(f1171,plain,
( spl0_60
<=> class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f770,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
fof(f1169,plain,
spl0_59,
inference(avatar_split_clause,[],[f769,f1166]) ).
fof(f1166,plain,
( spl0_59
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f769,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f1164,plain,
spl0_58,
inference(avatar_split_clause,[],[f768,f1161]) ).
fof(f1161,plain,
( spl0_58
<=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f768,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
fof(f1159,plain,
spl0_57,
inference(avatar_split_clause,[],[f767,f1156]) ).
fof(f1156,plain,
( spl0_57
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f767,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f1154,plain,
spl0_56,
inference(avatar_split_clause,[],[f766,f1151]) ).
fof(f1151,plain,
( spl0_56
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f766,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1149,plain,
spl0_55,
inference(avatar_split_clause,[],[f765,f1146]) ).
fof(f1146,plain,
( spl0_55
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f765,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1144,plain,
spl0_54,
inference(avatar_split_clause,[],[f764,f1141]) ).
fof(f1141,plain,
( spl0_54
<=> class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f764,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
fof(f1139,plain,
spl0_53,
inference(avatar_split_clause,[],[f763,f1136]) ).
fof(f1136,plain,
( spl0_53
<=> class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f763,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
fof(f1134,plain,
spl0_52,
inference(avatar_split_clause,[],[f762,f1131]) ).
fof(f1131,plain,
( spl0_52
<=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f762,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).
fof(f1129,plain,
spl0_51,
inference(avatar_split_clause,[],[f761,f1126]) ).
fof(f1126,plain,
( spl0_51
<=> class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f761,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).
fof(f1124,plain,
spl0_50,
inference(avatar_split_clause,[],[f760,f1121]) ).
fof(f1121,plain,
( spl0_50
<=> class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f760,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) ).
fof(f1119,plain,
spl0_49,
inference(avatar_split_clause,[],[f759,f1116]) ).
fof(f1116,plain,
( spl0_49
<=> class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f759,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) ).
fof(f1114,plain,
spl0_48,
inference(avatar_split_clause,[],[f758,f1111]) ).
fof(f1111,plain,
( spl0_48
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f758,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1109,plain,
spl0_47,
inference(avatar_split_clause,[],[f757,f1106]) ).
fof(f1106,plain,
( spl0_47
<=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f757,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
fof(f1104,plain,
spl0_46,
inference(avatar_split_clause,[],[f756,f1101]) ).
fof(f1101,plain,
( spl0_46
<=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f756,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
fof(f1099,plain,
spl0_45,
inference(avatar_split_clause,[],[f755,f1096]) ).
fof(f1096,plain,
( spl0_45
<=> class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f755,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
fof(f1094,plain,
spl0_44,
inference(avatar_split_clause,[],[f754,f1091]) ).
fof(f1091,plain,
( spl0_44
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f754,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
fof(f1089,plain,
spl0_43,
inference(avatar_split_clause,[],[f753,f1086]) ).
fof(f1086,plain,
( spl0_43
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f753,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1084,plain,
spl0_42,
inference(avatar_split_clause,[],[f752,f1081]) ).
fof(f1081,plain,
( spl0_42
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f752,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1079,plain,
spl0_41,
inference(avatar_split_clause,[],[f751,f1076]) ).
fof(f1076,plain,
( spl0_41
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f751,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1074,plain,
spl0_40,
inference(avatar_split_clause,[],[f750,f1071]) ).
fof(f1071,plain,
( spl0_40
<=> class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f750,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).
fof(f1069,plain,
spl0_39,
inference(avatar_split_clause,[],[f749,f1066]) ).
fof(f749,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f1064,plain,
spl0_38,
inference(avatar_split_clause,[],[f748,f1061]) ).
fof(f1061,plain,
( spl0_38
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f748,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1059,plain,
spl0_37,
inference(avatar_split_clause,[],[f747,f1056]) ).
fof(f1056,plain,
( spl0_37
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f747,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1054,plain,
spl0_36,
inference(avatar_split_clause,[],[f746,f1051]) ).
fof(f1051,plain,
( spl0_36
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f746,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1049,plain,
spl0_35,
inference(avatar_split_clause,[],[f745,f1046]) ).
fof(f1046,plain,
( spl0_35
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f745,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1044,plain,
spl0_34,
inference(avatar_split_clause,[],[f744,f1041]) ).
fof(f1041,plain,
( spl0_34
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f744,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1039,plain,
spl0_33,
inference(avatar_split_clause,[],[f743,f1036]) ).
fof(f1036,plain,
( spl0_33
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f743,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1034,plain,
spl0_32,
inference(avatar_split_clause,[],[f742,f1031]) ).
fof(f1031,plain,
( spl0_32
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f742,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1029,plain,
spl0_31,
inference(avatar_split_clause,[],[f741,f1026]) ).
fof(f741,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1024,plain,
spl0_30,
inference(avatar_split_clause,[],[f740,f1021]) ).
fof(f1021,plain,
( spl0_30
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f740,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1019,plain,
spl0_29,
inference(avatar_split_clause,[],[f739,f1016]) ).
fof(f1016,plain,
( spl0_29
<=> class_Ring__and__Field_Odvd(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f739,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
fof(f1014,plain,
spl0_28,
inference(avatar_split_clause,[],[f738,f1011]) ).
fof(f738,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
fof(f1009,plain,
spl0_27,
inference(avatar_split_clause,[],[f737,f1006]) ).
fof(f737,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f1004,plain,
spl0_26,
inference(avatar_split_clause,[],[f736,f1001]) ).
fof(f1001,plain,
( spl0_26
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f736,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f999,plain,
spl0_25,
inference(avatar_split_clause,[],[f735,f996]) ).
fof(f996,plain,
( spl0_25
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f735,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f994,plain,
spl0_24,
inference(avatar_split_clause,[],[f734,f991]) ).
fof(f991,plain,
( spl0_24
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f734,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f989,plain,
spl0_23,
inference(avatar_split_clause,[],[f733,f986]) ).
fof(f986,plain,
( spl0_23
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f733,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f984,plain,
spl0_22,
inference(avatar_split_clause,[],[f732,f981]) ).
fof(f981,plain,
( spl0_22
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f732,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f979,plain,
spl0_21,
inference(avatar_split_clause,[],[f731,f976]) ).
fof(f976,plain,
( spl0_21
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f731,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f974,plain,
spl0_20,
inference(avatar_split_clause,[],[f730,f971]) ).
fof(f971,plain,
( spl0_20
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f730,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f969,plain,
spl0_19,
inference(avatar_split_clause,[],[f729,f966]) ).
fof(f966,plain,
( spl0_19
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f729,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f964,plain,
spl0_18,
inference(avatar_split_clause,[],[f728,f961]) ).
fof(f961,plain,
( spl0_18
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f728,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).
fof(f959,plain,
spl0_17,
inference(avatar_split_clause,[],[f727,f956]) ).
fof(f956,plain,
( spl0_17
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f727,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f954,plain,
spl0_16,
inference(avatar_split_clause,[],[f726,f951]) ).
fof(f951,plain,
( spl0_16
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f726,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f949,plain,
spl0_15,
inference(avatar_split_clause,[],[f725,f946]) ).
fof(f946,plain,
( spl0_15
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f725,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f944,plain,
spl0_14,
inference(avatar_split_clause,[],[f724,f941]) ).
fof(f941,plain,
( spl0_14
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f724,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f939,plain,
spl0_13,
inference(avatar_split_clause,[],[f723,f936]) ).
fof(f936,plain,
( spl0_13
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f723,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f934,plain,
spl0_12,
inference(avatar_split_clause,[],[f722,f931]) ).
fof(f931,plain,
( spl0_12
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f722,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f929,plain,
spl0_11,
inference(avatar_split_clause,[],[f721,f926]) ).
fof(f926,plain,
( spl0_11
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f721,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f924,plain,
spl0_10,
inference(avatar_split_clause,[],[f720,f921]) ).
fof(f921,plain,
( spl0_10
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f720,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f919,plain,
spl0_9,
inference(avatar_split_clause,[],[f719,f916]) ).
fof(f916,plain,
( spl0_9
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f719,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f914,plain,
spl0_8,
inference(avatar_split_clause,[],[f718,f911]) ).
fof(f911,plain,
( spl0_8
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f718,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f909,plain,
spl0_7,
inference(avatar_split_clause,[],[f717,f906]) ).
fof(f906,plain,
( spl0_7
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f717,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f904,plain,
spl0_6,
inference(avatar_split_clause,[],[f716,f901]) ).
fof(f901,plain,
( spl0_6
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f716,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f899,plain,
spl0_5,
inference(avatar_split_clause,[],[f715,f896]) ).
fof(f896,plain,
( spl0_5
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f715,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f894,plain,
spl0_4,
inference(avatar_split_clause,[],[f714,f891]) ).
fof(f891,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f714,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f889,plain,
spl0_3,
inference(avatar_split_clause,[],[f713,f886]) ).
fof(f886,plain,
( spl0_3
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f713,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f884,plain,
spl0_2,
inference(avatar_split_clause,[],[f712,f881]) ).
fof(f881,plain,
( spl0_2
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f712,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f879,plain,
spl0_1,
inference(avatar_split_clause,[],[f711,f876]) ).
fof(f876,plain,
( spl0_1
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f711,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG396-1 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.34 % Computer : n014.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Fri May 3 19:55:08 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (20414)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40 % (20438)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.40 % (20437)WARNING: value z3 for option sas not known
% 0.15/0.40 % (20436)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.40 % (20435)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.40 % (20439)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.40 % (20437)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)
% 0.15/0.40 % (20441)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.40 % (20440)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.45 TRYING [1]
% 0.21/0.46 % (20439)First to succeed.
% 0.21/0.46 TRYING [2]
% 0.21/0.47 % (20439)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20414"
% 0.21/0.47 % (20439)Refutation found. Thanks to Tanya!
% 0.21/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.48 % (20439)------------------------------
% 0.21/0.48 % (20439)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.48 % (20439)Termination reason: Refutation
% 0.21/0.48
% 0.21/0.48 % (20439)Memory used [KB]: 2444
% 0.21/0.48 % (20439)Time elapsed: 0.067 s
% 0.21/0.48 % (20439)Instructions burned: 108 (million)
% 0.21/0.48 % (20414)Success in time 0.124 s
%------------------------------------------------------------------------------